Efficient Integration of Planar Antennas Considering
Electromagnetic Interactions at Board Level
vorgelegt von
Diplom-Ingenieur
Florian Ohnimus
aus Lüneburg
von der Fakultät IV - Elektrotechnik und Informatik
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Promotionsausschuss
Vorsitzender: Prof. Dr. Bernd Tillack
1. Berichter: Prof. Dr. Dr. E.h. Herbert Reichl
2. Berichter: Prof. Dr. Ege Engin
Tag der wissenschaftlichen Aussprache: 1.4.2011
Berlin 2011
D 83
– II –
Danksagung
Die vorliegende Arbeit entstand während meiner Tätigkeit als wissenschaftlicher Mitarbeiter
in der Arbeitsgruppe RF & High-Speed System Design (RSD) der Abteilung System Design
and Integration (SDI) am Fraunhofer-Institut für Zuverlässigkeit und Mikrointegration (IZM)
und dem Forschungsschwerpunkt Technologien der Mikroperipherik der Technischen
Universität Berlin.
Ich möchte mich besonders bei meinem Doktorvater und Erstgutachter, Prof. Dr. Dr. E.h.
Herbert Reichl, für die Betreuung meiner Arbeit, das Feedback und die wertvollen Ratschläge
bedanken. Meinem Zweitgutachter, Prof. Dr. Ege Engin, möchte ich insbesondere für die
Aufnahme und Betreuung während meines zweimonatigen Aufenthalts an der San Diego
State University und die Fachdiskussionen danken. Für die Übernahme des Vorsitzes des
Promotionsausschusses danke ich außerdem Prof. Dr. Bernd Tillack.
Des Weiteren danke ich meinem Abteilungsleiter, Dr. Stephan Guttowski, für die
Unterstützung und Schaffung eines produktiven Arbeitsklimas. Ein ganz besonderer Dank gilt
meinem Mentor, Dr. Ivan Ndip, für den unermüdlichen Einsatz als Gruppenleiter, die
jahrelange Betreuung und die wertvollen Ratschläge, die maßgeblich zum Gelingen und zur
Qualität dieser Arbeit beigetragen haben.
Ein weiterer großer Dank gilt meinen Arbeitskollegen der Arbeitsgrupe RSD, insbesondere
Dr. Gerhard Fotheringham, Uwe Maaß, Christian Tschoban, Brian Curran, Robert Erxleben,
Kai Löbbicke und Micha Bierwirth für die zahlreichen Fachdiskussionen und die vielen
wertvollen Anregungen, sowie auch allen Kollegen der Abteilung SDI.
Nicht zuletzt möchte ich mich bei meinen Eltern, Dietlind und Hartwig Ohnimus, und Karl-
Werner Pagels bedanken, die den Grundstein meiner Ausbildung gelegt haben. Mein letzter
Dank gilt meiner langjährigen Freundin, Stefanie Zingelmann, denn du hast mir immer die
nötige Kraft gegeben.
– III –
Abstract
The (quasi) millimeter-wave range provides large spectral bandwidths for wireless short range
microelectronic communication systems. Efficient planar antennas, with dimensions on the
order of millimeters, are integrated at board level using printed circuit board technologies,
thus, facilitating the realization of compact and low cost wireless modules. However,
electromagnetic interactions occurring between planar antennas and board components
sharing the same substrate may detune the antenna characteristics and also cause a high
amount of undesired electromagnetic coupling at board level.
Therefore, in this work, an approach for defining a block out region around the planar
antenna, where no board components should be placed is developed, thereby ensuring that the
antenna characteristics remain within tolerable limits when the antenna is integrated at board
level. This region, bounded by what will be termed the electromagnetic antenna boundary, is
determined by evaluating the reactive electromagnetic power density excited on the substrate
and deducing a threshold value.
Furthermore, a method for efficient calculation of electromagnetic coupling between planar
antennas and transmission lines routed outside the electromagnetic antenna boundary is
developed. This method is based entirely on a post processing step to field simulations i.e.,
the coupling is calculated based on the previously computed field distribution excited by the
antenna on the ground plane. The coupling model uses the theory of field excited transmission
lines together with the Baum-Liu-Tesche integral equations for obtaining the terminal
voltages of the transmission line and, hence, the coupling terms.
Finally, planar shielding configurations including a mushroom-type electromagnetic bandgap
structure and a surface wave reduced patch antenna, suitable for integration on low cost
printed circuit boards, were implemented, characterized and compared.
Based on the proposed approaches, methods and results presented in this work, numerical
full-wave simulation efforts as well as trial-and-error iterations are considerably reduced
during the integration of planar antennas, thereby saving time and cost during the design
process of compact wireless modules.
– IV –
Zusammenfassung
Der Quasi-Millimeterwellenbereich bietet große spektrale Bandbreiten für drahtlose
mikroelektronische Kommunikationssysteme zum Datenaustausch über kurze Entfernungen.
Effiziente Planarantennen, mit Abmessungen von einigen Millimetern, werden mittels
Leiterplattentechnologien auf Board-Ebene integriert und ermöglichen somit die Realisierung von
kompakten und kostengünstigen drahtlosen Funkmodulen. Jedoch führen elektromagnetische
Interaktionen zwischen Planarantennen und Board-Komponenten auf demselben Substrat zu einer
möglichen Verstimmung der Antennencharakteristika und verursachen ein hohes Maß an
elektromagnetischer Kopplung auf Board-Ebene.
Aus diesem Grund wird in dieser Arbeit ein neuer Ansatz zur Definition einer Blockout-Region
um die Planarantenne entwickelt, innerhalb der keine Board-Komponenten platziert werden
sollten, um die Antennencharakteristika nach der Integration auf Board-Ebene innerhalb
tolerierbarer Grenzen zu halten. Der Rand dieser Region wird als elektromagnetische
Antennenumgrenzung (engl., electromagnetic antenna boundary) bezeichnet und wird durch die
Evaluierung der von der Antenne angeregten reaktiven elektromagnetischen Leistungsdichte auf
dem Substrat sowie der Festlegung eines Schwellwertes ermittelt.
Des Weiteren wird eine Methode zur effizienten Berechnung der elektromagnetischen Kopplung
zwischen Planarantennen und Transmissionsleitungen, die außerhalb der elektromagnetischen
Antennenumgrenzung geroutet werden, entwickelt. Diese Methode basiert ausschließlich auf
einem Post-Prozess-Schritt zu Feldsimulationen, d.h. die Kopplung wird basierend auf der zuvor
simulierten von der Antenne auf der Massefläche angeregten Feldverteilung berechnet. Das
Kopplungsmodel benutzt die Theorie der feldangeregten Transmissionsleitungen zusammen mit
den Baum-Liu-Tesche Integralgleichungen, um die Terminalspannungen der
Transmissionsleitung und somit die Kopplungsterme zu erhalten.
Zuletzt wurden Planar-Schirmungskonfigurationen einschließlich einer pilzartigen
elektromagnetischen Bandsperre und einer oberflächenwellenreduzierten Patch-Antenne, die zur
Integration in kostengünstigen Leiterplatten geeignet sind, implementiert, charakterisiert und
verglichen.
Basierend auf den in dieser Arbeit vorgeschlagenen Ansätzen, Methoden und Resultaten, werden
numerische Simulationsaufwände sowie Trial-und-Error-Iterationen während der Integration von
Planarantennen maßgeblich reduziert. Dadurch werden Zeit und Kosten in der Entwurfsphase von
kompakten drahtlosen Modulen eingespart.
– V –
Contents
Danksagung ................................................................................................................................ II
Abstract .................................................................................................................................... III
Zusammenfassung .................................................................................................................... IV
1 Introduction ...................................................................................................................... 1
1.1 Motivation .................................................................................................................. 1
1.2 State-of-the-Art in Planar Antenna Integration at Board Level ................................. 4
1.2.1 Antennas and Transmission Lines .......................................................................... 4
1.2.2 Techniques to Facilitate Integration ....................................................................... 7
1.3 Main Contributions of Work .................................................................................... 12
2 Determination of Electromagnetic Boundary of Planar Antennas ........................... 13
2.1 Overview of Proposed Approach ............................................................................. 14
2.2 Theoretical Analysis of Antenna Fields ................................................................... 15
2.2.1 Fundamentals of Antennas and Transmission Lines ............................................ 15
2.2.2 Complex Power Density of Excited Antenna ...................................................... 22
2.2.3 Modeling and Simulation of Antenna Fields ....................................................... 32
2.2.4 Determining the Electromagnetic Antenna Boundary ......................................... 40
2.3 Comparison of Planar Antennas and Application of Antenna Boundary ................ 44
2.3.1 Patch Antenna ...................................................................................................... 45
2.3.2 Slot Antenna ......................................................................................................... 46
2.3.3 Dipole Antenna .................................................................................................... 48
– VI –
2.3.4 Comparison of Antenna Characteristics ............................................................... 49
2.3.5 Deduction of Electromagnetic Antenna Boundary .............................................. 52
2.4 Summary .................................................................................................................. 59
3 Calculation of Coupling to Transmission Lines .......................................................... 60
3.1 Overview of Proposed Method ................................................................................ 60
3.2 Development of Coupling Model ............................................................................. 61
3.3 Quantification of Coupling Model ........................................................................... 69
3.3.1 Planar Antenna to Microstrip Line Coupling ....................................................... 69
3.3.2 Spectral Response of Complete Transmission Line Path ..................................... 73
3.3.3 Simulation Errors caused by Lumped Ports ......................................................... 75
3.3.4 Measurement Results ........................................................................................... 76
3.4 Summary .................................................................................................................. 78
4 Quantification of Planar Configurations to Reduce Coupling .................................. 79
4.1 Design and Implementation of Shielding Configurations ........................................ 80
4.1.1 Planar Electromagnetic Bandgap (EBG) Structure .............................................. 81
4.1.2 Planar Surface Wave Reduced (SWR) Antenna .................................................. 87
4.1.3 Comparison of Configurations and Measurement Results ................................... 91
4.2 Coupling between SWR Antenna and Transmission Lines ..................................... 94
4.3 Summary .................................................................................................................. 95
5 Design Recommendations, Conclusions and Outlook ................................................. 96
– VII –
Appendix 1 - Overview of Full-wave Electromagnetic Field Simulations ............................ 101
Appendix 2 - Examination of Numerical Solution Accuracy ................................................ 105
Appendix 3 - Microstrip Transmission Line Parameters ....................................................... 109
Appendix 4 - Prototyping and Measurement of Planar Structures ......................................... 110
References .............................................................................................................................. 113
List of Figures ........................................................................................................................ 122
List of Tables .......................................................................................................................... 127
Short Biography and List of Publications .............................................................................. 128
Chapter 1 - Introduction
– 1 –
1 Introduction
1.1 Motivation
Over the past decade, the wireless market has been one of the main driving forces for low cost
and high performance microelectronic equipment. The recent advances in system in package
(SIP) technologies as well as in analog radio frequency (RF) front-end components, such as
low noise amplifiers, power amplifiers, mixers, voltage controlled oscillators and frequency
dividers, are paving the way for low cost and broadband wireless communication applications
up into the millimeter-wave region [1-9]. The demand for even higher data-rates, lower power
consumption and more size reduction is increasing rapidly. This trend is expected to continue
in the future.
With the deployment of cellular networks for mobile terminals, there is an increasing interest
in facilitating high data-rates over short distances of several meters. Examples of applications
are wireless local/personal area networks (WLAN/WPAN), wireless sensor networks (WSN),
high definition (HD) video streaming and wireless high speed data synchronization. Wireless
systems operating in the (quasi) millimeter-wave range have distinct advantages over systems
operating at lower microwave frequencies below 10 GHz:
• There is a vast amount of spectral bandwidth available at (quasi) millimeter-wave
frequencies. The bandwidth can be exploited for very high data-rates.
• The required antenna size for efficient operation scales proportionally with the operating
wavelength. Integrated antennas become physically smaller with increasing frequency
potentially allowing for a high degree of system miniaturization.
• Planar antenna designs have been demonstrated with acceptable radiation performance at
millimeter-wave frequencies. These configurations can be manufactured using low cost
printed circuit board (PCB) technologies.
A desirable operation frequency is 24 GHz, where an unlicensed industrial, scientific and
medical (ISM) frequency band is available. It offers a bandwidth of 250 MHz for
communication and radar applications and is allocated by the International
Telecommunication Union (ITU). Consequently, there have been numerous research activities
Chapter 1 - Introduction
– 2 –
especially in the field of short range radar [10-22]. Strictly speaking, the millimeter-wave
range spans from 30 GHz to 300 GHz. However, millimeter-wave specific challenges, such as
surface wave propagation in substrates, also exist at 24 GHz considering typical PCB
dimensions and materials.
Miniaturization is one of the key enablers for reducing cost and increasing performance of RF
analog and high speed digital components. It is desirable to integrate analog and digital
functions including the antenna at board level in close proximity to save space and obtain a
high integration density. A conventional low cost integration concept of a wireless system is
schematically shown in Figure 1.
Figure 1: Illustration of a compact wireless module based on a low cost PCB configuration.
The RF front-end components are separated from the digital baseband components by the
ground plane, which also acts as a low impedance reference for the transmission lines and
supply voltages. The planar antenna is integrated together with the RF components on a low
loss dielectric substrate. In order to reduce the manufacturing cost, the RF substrate is
designed with only two metallization layers. The digital components, on the other hand, are
integrated on a low cost substrate, such as FR4, which is placed below the ground plane. Such
a configuration can be manufactured using standard PCB technologies.
The ideal integrated antenna is electromagnetically isolated from the board i.e., the signal fed
to the antenna is radiated into a space wave with an efficiency of 100 %. Also, the antenna
parameters, such as the input impedance and radiation patterns, are ideally independent of the
board environment. However, in the case of a real antenna, the electromagnetic interactions
between the antenna, the board as well as other system components, especially transmission
lines, cannot be neglected. Furthermore, as the integration density and operating frequencies
Chapter 1 - Introduction
– 3 –
increase, more electromagnetic coupling between the integrated antenna and transmission
lines occurs, degrading system performance.
In order to illustrate this, consider the coupling between two 50 Ω microstrip transmission line
segments compared to the coupling between a patch antenna and a microstrip transmission
line segment operating at 24 GHz. In Figure 2, the simulation results of the coupling
coefficients S21 in dependency of the edge-to-edge separation distance d are shown. The patch
antenna and microstrip line segments have a length l=3.125 mm and are placed on a 250 µm
thick grounded substrate with a relative permittivity of 3.75 and a dissipation factor of 0.006.
These are common RF substrate parameters. Ports are placed at both ends of the transmission
lines and at the end of the antenna feeding line.
Figure 2: Coupling between: (a) two transmission lines; and (b) a patch antenna and a transmission line at
24 GHz.
It is observed that the coupling between the patch antenna and the transmission line segment
is significantly higher (more than 10 dB) compared to the coupling between the two parallel
transmission line segments. This results from the resonance nature of the antenna i.e., the
excited electric and magnetic fields of the antenna are orders of magnitude higher than those
on the transmission line. Therefore, the coupling between planar antennas and neighboring
transmission lines must be considered as a major contributor to electromagnetic reliability
(EMR) issues at board level. Controlling EMR issues is essential for the realization of
compact wireless modules operating in the (quasi) millimeter-wave frequency bands and
beyond.
Chapter 1 - Introduction
– 4 –
1.2 State-of-the-Art in Planar Antenna Integration at Board Level
One of the challenges in integrating planar antennas in proximity to other board components
on the same substrate is controlling undesired electromagnetic coupling. This undesired
coupling can originate in the near- and far-field regions of the antenna. Unlike at lower
frequencies, the far-field condition is met at board level in wireless modules operating at
(quasi) millimeter-wave frequencies. This section gives an overview of the state-of-the-art in
planar antenna design, planar transmission line analysis as well as techniques to facilitate
antenna integration by reducing undesired coupling. The focus is on configurations, which
can be manufactured using only two metallization layers on one dielectric substrate in low
cost PCB technology.
1.2.1 Antennas and Transmission Lines
In recent years, research has focused on the design of planar passive components including
antennas and transmission lines to facilitate (quasi) millimeter-wave modules using low cost
PCB technologies. Up to date, a myriad of different planar antenna configurations have been
proposed and demonstrated. The proposed planar antennas basically comprise three
fundamental configurations. These include patch [23, 24], slot [25-27], and dipole [28-30]
antenna types. Figure 3 shows an illustration of these three fundamental configurations with
excitation voltage U.
Figure 3: Cross sections of the three fundamental antenna types: (a) patch antenna on grounded
substrate; (b) slot antenna in ground plane; and (c) dipole antenna on ungrounded substrate.
Chapter 1 - Introduction
– 5 –
The patch antenna is excited with a voltage between the patch and the ground plane. The slot
antenna, comprising a slot in the ground plane, is excited with a voltage across the slot in the
ground plane. The dipole antenna, comprising two planar strips, is ideally operated without
the presence of a ground plane to reduce the effects on undesired image currents.
Slot and patch antennas are unbalanced configurations and are generally fed through single
ended transmission lines. Dipoles are balanced antennas, which are fed through differential
transmission lines. A balun is required when the dipole is fed through a single ended
transmission line.
These fundamental antenna configurations can be tailored to achieve characteristics such as:
(1) high gain; (2) high efficiency/bandwidth; and (3) electronic reconfigurability, or a
combination of these.
1) High gain has been achieved by grouping single antenna elements in an array
configuration and designing the feeding network in such a way that the radiated fields
produced by the current distribution on the individual elements are superimposed in phase
for the desired angle of high gain (constructive interference). Examples of such
configurations are single layer patch antenna arrays [31, 32], multilayer configurations
including aperture coupled patches [33] as well as configurations comprising alternatively
arranged electromagnetically coupled patches [34, 35].
Other designs have exploited dielectric lenses to achieve high gain in direction normal to
the substrate by focusing the radiation [36].
For high gain operation in lateral direction (end-fire radiation), planar Yagi-Uda arrays
[20] have also been proposed.
2) Dielectric losses in the substrate, which increase with frequency, cause a reduction of the
antenna efficiency. Elevated patch antennas supported by metal stubs [37, 38] have been
proposed, significantly improving both bandwidth and efficiency. The bandwidth is
simultaneously increased by this because the effective permittivity underneath the patch is
also reduced.
To overcome the bandwidth limitation imposed by substrates with a high dielectric
constant yet low losses (e.g., ceramics), stacked patch configurations have been
demonstrated [17].
Chapter 1 - Introduction
– 6 –
3) The gain of an antenna is a passive quantity. Therefore, a high gain results in reduced
space coverage and poses orientation restrictions for wireless modules. As a result,
electronic beam reconfigurability is desirable in many applications to compensate the
reduced space coverage by scanning the environment. Also, for many radar applications,
beam steering is of fundamental importance to obtain an angular resolution. Multibeam
radiation patterns and directivity diversity have been demonstrated [39]. Electronically
reconfigurable radiation patterns have also been demonstrated [40, 41].
In conclusion, there has been much research in the field of tailoring and improving the
characteristics of planar antennas suitable for low cost PCB applications.
However, up to date, electromagnetic interactions occurring between the excited antenna
fields and board components, potentially resulting in a degradation of the antenna parameters,
have not received much attention. Reports of a study on a 2.4 GHz patch antenna and a
microstrip transmission line in close proximity [42] have shown that the antenna and
transmission line parameters are degraded if the transmission line is routed too close to the
antenna. Hence, the antenna cannot be treated as an isolated component as defined by its
geometrical configuration.
The concept of defining electrical boundaries was introduced in [43, 44]. In these works, a
methodology was developed for defining the electrical boundaries of geometrical
discontinuities (such as transmission line bends, vias, wire bonds, bumps etc.) along a
complete signal path at chip, package and board level. The main idea is that the electrical
length of a component extends until the reactive power excited by the component (through
higher order modes) diminishes. Defining these electrical boundaries enables the components
to be analyzed independently without considering the impact of other components in the
immediate vicinity. This leads to a better understanding of their electromagnetic behavior and
also facilitates the development of design rules for integration. However, integrated planar
antennas were not considered.
Planar transmission lines routed at board level are essential components of wireless modules
required for signal distribution purposes as well as for antenna feeding lines. Transmission
lines are placed directly on the substrate as conducting strips, representing signal lines, and
are referenced to the ground plane. In the case of a microstrip line, the ground plane is
situated underneath the substrate below the signal line. The ground plane of the coplanar
waveguide, on the other hand, is situated in the same plane as the signal line and separated by
Chapter 1 - Introduction
– 7 –
a gap, thus, requiring only one metallization layer. These two configurations are the most
commonly used impedance controlled transmission lines in low cost PCB applications.
However, their open field nature makes these transmission lines vulnerable towards undesired
coupling through neighboring board components, such as the antenna. To date, single and
coupled transmission lines have been thoroughly modeled and analyzed [45]. Based on the
telegrapher's equations, analytical and simulation techniques have been employed to extract
the propagation constant and impedance as well as the characteristic per-unit-length
parameters of single and coupled transmission lines.
Coupling from external fields to transmission lines has also been analyzed. Formulations for
the equivalent sources of the inhomogeneous telegrapher's equations of transmission lines
have been developed [46-55]. Together with the Baum-Liu-Tesche (BLT) integral equations,
coupling from external plane waves has been efficiently calculated [56]. In [57], an approach
for assessing coupling between integrated mobile phone antennas and PCB transmission lines
together with a fitting algorithm is proposed.
However, although techniques for the calculation of coupling between transmission lines
(crosstalk) and from external fields to transmission lines have been proposed, no techniques
are available for calculating coupling between planar antennas and transmission lines sharing
the same substrate apart from complete time and resource consuming full-wave field
simulations. As was shown previously, this coupling can be significantly higher than crosstalk
between neighboring transmission lines. These aspects are essential for the integration of
planar antennas in compact wireless modules at board level.
1.2.2 Techniques to Facilitate Integration
Planar antennas are printed directly on dielectric substrates. Grounded and ungrounded
substrates are capable of guiding electromagnetic energy in the form of surface waves [58].
These surface waves have been thoroughly analyzed in the context of antenna arrays i.e.,
multiple antenna elements grouped together on the same substrate. Surface waves are
undesirable for array applications because they result in a reduction of the array gain. A
percentage of the power is coupled into a surface wave mode and not launched into the space
wave mode. Furthermore, based on analyses of the coupling between rectangular patch
antennas [58], ring shaped patch antennas [59] and slot antenna arrays [60], it was concluded
that the primary reason for an increased mutual coupling between these antenna elements is
surface wave excitation and propagation in the substrate. Reflections and stray radiation of the
Chapter 1 - Introduction
– 8 –
surface waves at the substrate edges also distort the radiation pattern. Moreover, antenna array
configurations suffer from impedance mismatch at the antenna feeding points caused by
mutually coupled surface waves. Altogether, surface waves are considered as one of the
primary coupling mechanisms at board level.
Figure 4: Classification of techniques for the reduction of undesired electromagnetic coupling caused by
surface waves.
Therefore, in order to facilitate the integration of planar antennas, research has focused on
techniques for the reduction of undesired coupling between antenna elements caused by
surface waves. The primary motivation for this research has been in the field of improving
antenna array performance. Figure 4 shows an overview and classification of the state-of-the-
art techniques that have been proposed and studied so far.
Basically, the techniques can be grouped into two categories. These include techniques for
surface wave suppression in the substrate and techniques by which the antenna elements are
modified for reduced surface wave excitation.
1.2.2.1 Surface Wave Suppression
One approach to reduce undesired electromagnetic coupling is to suppress the surface wave in
the substrate once it has been excited by the antenna.
Figure 5 shows an illustration of the different techniques for surface wave suppression in
substrates. The three main techniques that have been studied in literature include: (1)
integration of electromagnetic bandgap structures (EBG); (2) integration of defected ground
plane structures (DGS); and (3) modification of the substrate material itself.
Chapter 1 - Introduction
– 9 –
1) EBG structures have been exploited to reduce undesired mutual coupling [61, 62] between
planar antennas. Within a band of frequencies, the EBG structure behaves like a
distributed LC filter for the surface wave. EBG structures are designed periodically in two
dimensions on the substrate. Apart from the cell dimensions and cell spacing, the number
of cells determine the suppression properties [63, 64]. A commonly used geometry is the
mushroom type EBG structure [65] comprising metal patches on the substrate which are
shorted to the ground plane by vias. Multilayer substrate configurations have also been
proposed to allow a separate optimization of patch antenna and EBG cells [66, 67].
Although the majority of studies regarding the integration of EBG structures have been
conducted on patch antennas, the use of EBG structures for suppressing mutual coupling
has also been studied with slot [68] and dipole [69] antennas. Since vias introduce a high
cost factor for the manufacturing of the EBG structure, planar EBG structures have been
proposed [70, 71]. Furthermore, the radial propagation of surface waves have led to the
development of EBG structures with circular symmetry [72, 73].
Other techniques to suppress surface wave propagation in substrates include metal via
fences embedded periodically in the substrate [74]. It must be noted that these via fences
are not resonant cells and, thus, strictly speaking cannot be considered as EBG structures.
However, because of the required periodicity, they are categorized in this group.
2) Another technique to reduce undesired electromagnetic coupling caused by surface waves
is to implement a structure that allows controlled scattering of the surface wave. For this
purpose, DGS have been proposed [75-77]. The basic idea is to realize a defect in the
ground plane that disturbs the current distribution of the surface wave mode. A drawback,
however, is that the scattering of surface waves distort the far-field radiation pattern.
3) Techniques that artificially modify the substrate e.g., with periodic rectangular holes [78],
have also been studied for surface wave suppression. The basic idea here is that the
effective dielectric constant of the substrate is decreased, which lowers the surface wave
power propagated by the surface wave mode. Of course, complete substrate removal [79]
would reduce the surface wave power effectively. From a practical point of view this
approach is less feasible because the substrate also acts as a carrier in wireless modules.
Research has also focused on meta-materials [80]. These materials behave as a double
negative medium displaying a negative permeability and a negative permittivity.
Chapter 1 - Introduction
– 10 –
However, these materials are also dispersive and their surface wave suppression effect is
frequency band limited.
4)
Figure 5: Cross sections of configurations for surface wave suppression: (a) conventional substrate
with ground plane; (b) integration of EBG structure; (c) integration of DGS; and (d) modification of
substrate material.
So far, the proposed techniques have mainly aimed at reducing mutual coupling in antenna
arrays i.e., between the antenna elements of the array. The main drawback to this set of
techniques originates from the required large lateral dimensions of these configurations. This
arises from the resonance properties as well as the required periodicity needed to ensure the
surface wave suppression effect. In the case of low cost board applications with only two
metallization layers, these structures need to be integrated adjacent to the antenna where the
surface wave propagates, typically requiring more board space than the antenna element itself.
1.2.2.2 Planar Antennas with Reduced Surface Wave Excitation
Some of the limitations of the surface wave suppression techniques discussed in the previous
section have lead to research focusing on the modification of the antenna element itself in
Chapter 1 - Introduction
– 11 –
such a way that the surface wave mode excitation is reduced. By this, surface wave
suppressing structures placed beside the antenna can be avoided and board space is potentially
saved.
The antenna elements have been modified in many ways to achieve a reduction of surface
wave excitation such as: (1) antenna mode synthesis; (2) substrate removal; and (3)
integration of additional elements.
1) A commonly employed technique is to synthesize the field distribution of the antenna
mode by ensuring phase cancellation of the surface wave fields produced by the radiating
apertures of the antenna [81]. For this purpose, the antenna must have a critical size [82],
which is generally larger than the required physical dimensions needed to obtain the
resonance condition. Therefore, the antennas need to be modified in order to obtain the
resonance condition simultaneously with the surface wave field cancellation condition.
Shorting posts [83] and elliptical patch geometries [84] have been proposed. Another
approach to overcome the problem of simultaneously meeting the two conditions is
proposed in [85] by introducing a slot antenna with two arcs.
Higher order mode patch antennas have been studied in [86] and were found to reduce
surface wave excitation.
2) Techniques by which substrate material underneath as well as in the vicinity [87] of the
antennas is selectively removed have been demonstrated to achieve a reduction of surface
wave excitation. Since the surface wave uses the dielectric (grounded or ungrounded) as a
waveguide, the surface wave excitation is reduced. Although the performance can be
substantially improved, expensive processing technologies are required for the
manufacturing.
3) Additional elements have also been integrated in the near-field region of patch antennas.
These additional elements are considered as being part of the antenna since the input
impedance and radiation pattern are strongly dependent on them. Examples of such
configurations include resonant embedded strips in the substrate [88] or parasitic strips on
top of the substrate [89] beside the antenna as well as an annular ring [90] or an octagonal
metallic bar [91] around the antenna. Other designs have implemented a cavity comprising
a metal ring shorted to the ground plane with via fences acting as shielding walls [92].
Chapter 1 - Introduction
– 12 –
In conclusion, techniques to reduce surface wave excitation of planar antenna elements have
been demonstrated. However, in general, the modifications of the antenna elements to ensure
reduced surface wave mode excitation result in physically larger antenna elements compared
to conventional antenna elements, thus, requiring more board space. Since the antennas are
optimized for minimum surface wave excitation, co-optimization of a different antenna
parameter (e.g. impedance bandwidth, gain or polarization) is generally challenging.
Furthermore, the feasibility of implementing these techniques for reducing coupling to
transmission lines and, hence, facilitating compact wireless modules has not be shown.
1.3 Main Contributions of Work
In order to support and optimize the design process of compact wireless modules with
integrated planar antennas, the main contributions of this work are as follows:
• Development of an approach for defining the block out region around planar
antennas, where no board components should be placed thereby ensuring that the
antenna characteristics remain within tolerable limits when the antenna is integrated
at board level. This block out region is bounded by what will be termed the
electromagnetic antenna boundary.
• Development of a method for efficient calculation of coupling from the planar
antenna fields to transmission lines routed on the same substrate outside the
electromagnetic antenna boundary. This method is based entirely on a post
processing step to full-wave field simulations i.e., the coupling is readily determined
based on the previously computed field distribution excited by the antenna on the
ground plane.
• Quantification of planar configurations to reduce coupling suitable for
implementation on low cost PCBs and evaluation of these with regards to shielding
effectiveness and required board space.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 13 –
2 Determination of Electromagnetic Boundary of Planar Antennas
An antenna transforms the power of a guided mode on a transmission line into the power of a
spherical transverse electromagnetic (TEM) space wave mode. If the antenna is a linear
system and all materials are isotropic, this mode conversion process is reciprocal. The power
propagated by these fundamental modes is illustrated in Figure 6 by considering a patch
antenna on a grounded dielectric substrate for low cost PCB applications.
Figure 6: Illustration of the complex power density transfer to and from a planar antenna configuration
integrated on a PCB. The coordinate system is centered, and the plane z=0 is on the ground plane.
Pin1 and Pout1 are the input and output powers of the quasi TEM mode on the microstrip
transmission line, and Pin2 and Pout2 are the input and output powers of the TEM space wave
mode in the far-field of the antenna. The mode conversion is achieved in the antenna structure
where a resonance mode is excited.
However, the antenna also radiates a portion of the power in the lateral plane on the substrate
where other board components are placed. This is indicated by the real power density
Re{ }S
.
Furthermore, as a result of an enforced resonance condition on the planar antenna (resonator),
the stored energy in the near-field region is high. This is indicated by the reactive power
density
Im{ }S
. The antenna parameters depend primarily on this near-field distribution.
Intuitively, the near-field region is larger than the geometrical dimensions of the antenna,
loosely indicated by V. Board components placed on the substrate close to the antenna interact
with the near-fields potentially altering the antenna parameters. Hence, in order to integrate
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 14 –
planar antennas, it is desirable to deduce a 2D block out region in the plane of the substrate
around the physical antenna structure where no components should be placed such that the
antenna parameters remain within acceptable limits. This region is bounded by what will be
termed the electromagnetic antenna boundary.
2.1 Overview of Proposed Approach
An overview of the proposed approach for determining the electromagnetic antenna boundary
is shown in Figure 7.
Figure 7: Overview of approach to determine electromagnetic antenna boundary.
In the first step, the excited fields of the planar antenna are computed on the plane of the
substrate. These comprise primarily the tangential magnetic field components, Hx and Hy, and
the normal electric field component Ez on a grounded substrate configuration. With these field
components, the complex power density
S
is calculated. The reactive power density, given
by the imaginary part
Im{ }S
, is then evaluated in order to deduce the electromagnetic
antenna boundary. A threshold value of
Im{ }S
is calculated next, and the distance from the
antenna at which this threshold value is reached is determined, marking the electromagnetic
antenna boundary. Board components placed beyond this distance outside the block out
region will not alter the antenna characteristics significantly, and weak coupling can be
assumed i.e., the secondary fields excited on the board component (victim) by the primary
antenna fields (aggressor) do not alter the near-field distribution of the antenna beyond
tolerable limits. Based on this approach, the antenna can be safely integrated.
In the next section, a theoretical analysis of the excited antenna fields and a characterization
of the complex Poynting vector are presented.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 15 –
2.2 Theoretical Analysis of Antenna Fields
In order to describe the behavior of electric and magnetic fields in the vicinity of an antenna,
Maxwell’s equations, comprising Ampere’s law, Faraday’s law of induction and Gauss’s laws
provide the foundation for further analysis [93]:
HJjE
ωε
∇× = +
(1)
E jH
ωµ
∇× =−
(2)
0H
µ
∇=
(3)
Eq
ε
∇=
(4)
Under the assumption of simple linear media, as is the case for the planar antennas considered
in this work, the source quantities,
J
(current density) and
q
(charge density), as well as the
field quantities
E
(electric field) and
H
(magnetic field) are expressed in the frequency
domain. Charge density and current density are related through the continuity equation.
J jq
ω
∇=−
(5)
2.2.1 Fundamentals of Antennas and Transmission Lines
The next step in solving for the field quantities is to find general solutions to Maxwell’s
equations. For this purpose, wave equations are derived for free space propagation and guided
modes on transmission lines.
2.2.1.1 Wave Equations for General Radiation Problems
In the general analysis of radiation problems, the sources are known and must be brought into
connection with the fields [94]. A common procedure is to define potential functions for the
fields. The magnetic flux density has no divergence. Therefore, the magnetic field in a
homogeneous space can be written as the curl of a vector potential.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 16 –
HA=∇×
(6)
Inserting (6) into (2) results in the following expression:
( )
0Ej A
ωµ
∇× + =
(7)
Because the curl of the expression within the parenthesis is zero, the expression can also be
written as a scalar potential:
EjAE jA
ϕ ωµ ϕ ωµ
∇ = − − ↔ = −∇ −
(8)
In order to derive the wave equation with these potential functions, equation (8) can be
inserted into (1).
2
A AJ j
ω εµ ωε ϕ
∇×∇× = + − ∇
(9)
Finally, together with the vector identity (10) and the Lorentz convention (11) the
inhomogeneous wave equation (12) is found.
( )
2
A AA∇×∇× =∇ ∇ −∇
(10)
1
Aj A
j
ωεϕ ϕ ωε
∇=− ↔ =− ∇
(11)
22
A AJ
ω εµ
∇+ =−
(12)
The Lorentz convention is chosen based on the fact that no physical information about the
divergence of the vector potential is given. Thus, it can be defined to simplify the equation.
In an analogue manner, the wave equation can also be expressed in terms of the scalar
potential:
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 17 –
22 q
ϕ ω εµϕ ε
∇+ =−
(13)
The next step is to find solutions to the above wave equations. Possible solutions for both
scalar and vector auxiliary functions are retarded potentials [93].
( )
1
4
jr
s
V
e
A J r dV
r
β
π
−
=∫∫∫
(14)
( )
1
4
jr
s
V
e
q r dV
r
β
ϕπε
−
=∫∫∫
(15)
fS
rr r= −
(16)
β ω εµ
=
(17)
The vectors
s
r
and
f
r
point to the source volume and to the point of observation, respectively.
The expressions indicate that the effects need a finite time of propagation. The phase constant
β has a negative leading sign indicating that the radiated energy moves away from its sources.
Finally, the sources can be brought into connection with the fields by using (6) and (8).
( )
1
4
jr
s
V
e
H J r dV
r
β
π
−
=− ×∇
∫∫∫
(18)
( ) ( )
1
44
jr jr
ss
VV
je e
E J r dV q r dV
rr
ββ
ωµ
π πε
−−
=− −∇
∫∫∫ ∫∫∫
(19)
Auxiliary Concept of Magnetic Charge: In some radiation problems, a vector potential is
introduced for the electric field by assuming there exists a magnetic current density
m
J
and,
hence, a magnetic charge density
m
q
. Consequently, (2) and (3) are modified accordingly.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 18 –
m
E j HJ
ωµ
∇× =− +
(20)
m
µH q∇=
(21)
In analogy to the above approach for defining a vector potential for the magnetic field vector,
it will be further assumed that both the electric current density and charge density are zero.
Then, the electric displacement field has no divergence:
0E
ε
∇=
(22)
A vector potential for the electric field can now be defined in analogy to (6).
EF= −∇×
(23)
With the same procedure as above for deriving (12), the wave equation for the vector
potential
F
is found.
22
m
F FJ
ω εµ
∇+ =−
(24)
The introduction of vector and scalar potential functions for the field quantities simplifies the
analysis of boundary value problems significantly. This is essential for the analytical
calculation of propagating modes and simple radiating structures.
The wave equations in terms of fields and auxiliary functions can be simplified when
considering guided wave structures such as transmission lines. Transmission lines are used as
examples of typical board components in this work because they are prone to high coupling
with antenna fields as a result of their open field structure. Therefore, the classical
transmission line model for describing wave propagation is presented next.
2.2.1.2 Wave Equation for Transmission Lines
Transmission lines are guided wave structures, which are described with a 1D wave equation.
Furthermore, since the fields are bound to the transmission line, voltages and currents are
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 19 –
introduced for the electric and magnetic fields, respectively. The voltages and currents on the
transmission line are not only time and frequency dependent but also have a spatial
dependency when the transmission line length is on the order of or larger than the wavelength.
Therefore, it is necessary to describe transmission lines with distributed elements.
Figure 8 shows the equivalent circuit of an infinitesimally short transmission line of length dx
and the distributed per-unit-length parameters [45]. The inductance L´ and capacitance C´ per-
unit-length result from the current flow and charge storage on the transmission line.
Figure 8: Equivalent circuit model of an infinitesimal transmission line piece with the distributed per-
unit-length parameters.
The resistance R´ and conductance G´ per-unit-length account for the conductor and dielectric
losses, respectively. The voltages, U(x) and U(x+dx), as well as the currents, I(x) and I(x+dx),
characterize the terminals of the transmission line section. Based on the equivalent circuit,
U(x) and I(x) are expressed in the form of differential equations with the limit that dx0
(telegrapher’s equations).
( ) ( ) ( )
Ux R jLIx
x
ω
∂′′
=−+
∂
(25)
( ) ( ) ( )
Ix G jCUx
x
ω
∂′′
=−+
∂
(26)
Inserting (25) into (26) yields the wave equation for the voltage on the transmission line.
( ) ( )
2
2
2
Ux Ux
x
γ
∂=
∂
(27)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 20 –
The propagation constant
γ
depends on the per-unit-length transmission line parameters.
( )( )
R jL G jC
γ ωω
′ ′′ ′
=++
(28)
The characteristic impedance Z0 of the transmission line is given as follows:
0
R jL
ZG jC
ω
ω
′′
+
=′′
+
(29)
In the case of a transmission line with low losses i.e., ωL'>>R' and ωC'>>G', the impedance
becomes real and the propagation constant is imaginary with only the phase constant β.
0
L
ZC
′
=′
(30)
LC
βω
′′
=
(31)
Based on these transmission line parameters, wave propagation on transmission lines is fully
described. Finally, in order to round off this section, two fundamental theorems applicable to
the results in this work are presented next.
2.2.1.3 Important Theorems applicable to Antennas and Transmission Lines
Reciprocity of antennas and transmission lines is an important characteristic. Consider two
antennas or, more generally, two electromagnetically coupled structures termed 1 and 2. The
Lorentz reciprocity theorem states that in a volume V surrounded by the surface
A
the
following relationship is valid for electric and magnetic fields and their current sources [93]:
( ) ( )
12 21 1 2 2 1
VA
J E J E dV E H E H dA− = × −×
∫∫∫ ∫∫
(32)
1
J
and
2
J
are the current sources, and
1
E
,
2
E
,
1
H
and
2
H
are the corresponding electric and
magnetic fields of the sources, respectively. The volume integral can be evaluated as [93]:
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 21 –
( )
12 21 1 2 2 1
V AS A S
J E J E dV J dA E ds J dA E ds−= −
∫∫∫ ∫∫ ∫ ∫∫ ∫
(33)
12 21
IU IU= −
(34)
I1, I2, U1 and U2 are the currents and the voltages at the terminals of 1 and 2, respectively. The
above relationship assumes that the medium inside the volume is linear and isotropic. For a
very large volume V∞, it can be further shown that [93]:
12 21
IU IU=
(35)
Thus, it can be concluded that two passive transmitting and receiving antennas behave like a
reciprocal two port network. The same applies to the radiation pattern of an antenna, which is
the same in transmitting mode and in receiving mode.
Another important theory is the duality theorem. It is possible to express the fields of one
antenna as the fields of the complementary antenna by interchanging the field quantifies and
material parameters [95]. Consider the magnetic current density
m
J
introduced above. The
first two of Maxwell’s equations are then written as follows:
HjE
ωε
∇× =
(36)
m
E j HJ
µω
∇× =− +
(37)
Maxwell’s equations are now fully symmetric. The fields produced by the electric current
source
J
can be interchanged to yield those produced by the magnetic current source
m
J
.
EH
′
→
(38)
HE
′
→−
(39)
m
JJ
′
→
(40)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 22 –
εµ
′
→
(41)
In the next subsection, an in-depth analysis of the complex power density produced by the
antenna fields is given.
2.2.2 Complex Power Density of Excited Antenna
The antenna fields can be expressed in terms of power and energy. Consider the schematic
representation of the patch antenna configuration with the microstrip feeding line in Figure 6.
The Poynting theorem is the energy conservation law in electrodynamics [93]. It is expressed
in the frequency domain in integral form as follows:
( )
*
12
2EM
AV V
SdA E J dV j w w dV
ω
=− +−
∫∫ ∫∫∫ ∫∫∫
(42)
*
1
2
S EH= ×
(43)
The power density
S
(Poynting vector) exiting or entering the volume V through the surface
element dA
is equal to the power delivered by the sources
J
plus the rate of change
(described by jω in the frequency domain) of the stored energy densities wE and wM inside V.
2
1
4
E
wE
ε
=
(44)
2
1
4
M
wH
µ
=
(45)
If losses are present, μ and ε can be expressed as complex quantities. In this case, the
imaginary parts account for the electric and magnetic losses, respectively. However, to
simplify the following discussion, a lossless environment is considered and the spatial power
decay of evanescent near-fields as well as propagating space and surface waves are analyzed.
An understanding of the spatial behavior of the propagating and reactive power density is
essential for defining the electromagnetic antenna boundary.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 23 –
2.2.2.1 Power Decay of Evanescent Near-fields and Propagating Space Waves
The complex spatial power decay is analyzed next using a basic radiating structure, which can
be treated analytically. The Hertzian dipole comprises an infinitesimal current source
z
I
pointing in z direction with the length dl. This is considered an ideal antenna for which a
closed form analytical expression of its fields can be derived. The vector potential (14)
reduces to [94]:
1
4
jr
z
z
I dl
Ae
r
β
π
−
= ⋅
(46)
Equation (46) can be transformed into a spherical coordinate system.
( ) ( ) ( ) ( )
( )
1
cos sin cos sin
4
jr
z
z rz r
I dl
A A e A e e ee
r
β
θθ
θ θ θθ
π
−
=−= −
(47)
The rotation operator (6) can also be expressed in spherical coordinates [93].
( )
( ) ( )
( )
1sin
sin
r
A
Ae A
r
θ
ϕ
θ
θθ ϕ
∂
∂
∇× = −
∂∂
(48)
( )
( )
1
r
A
A e rA
rr
ϕθ
θ
∂
∂
∇× = −
∂∂
(49)
( )
( )
( )
11
sin
r
A
A e rA
rr
θϕ
θϕ
∂∂
∇× = −
∂∂
(50)
Applying (47) to (48)-(50) yields the magnetic field component of the current source after
some minor calculation steps [96].
( ) ( )
2
2
11
sin
4
jr
z
I dl
Hj e
rr
β
ϕ
βθ
πβ
β
−
= +
(51)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 24 –
Finally, the electric field components can be found by inserting (51) into (1) yielding:
( ) ( ) ( )
2
023
11
2 cos
4
jr
z
r
I dl
EZ j e
rr
β
βθ
πββ
−
= −
(52)
( ) ( ) ( )
2
023
11 1
sin
4
jr
z
I dl
EZ j j e
rrr
β
θβθ
πβ
ββ
−
= +−
(53)
Z0 is the free space wave impedance. With these field components, the complex Poynting
vector (43) is found.
( )
**
1
2
rr
S EHe EHe
ϕθ θ ϕ
=−−
(54)
( ) ( )
22
4
02sin
16
z
rr
I dl
S Z Xe Xe
θθ
βθ
π
= +
(55)
( ) ( ) ( )
25
11
sin
r
Xj
rr
θ
ββ
= −
(56)
( ) ( ) ( )
35
11
cosXj
rr
θθ
ββ
= +
(57)
It can be observed in (56) and (57) that the reactive power density
Im{ }S
spatially decays
with 1/r5 (15 dB/octave) and 1/r3 (9 dB/octave) and, thus, dominates for small values of r,
hence, close to the antenna.
{ }
1
Im ~ , n=3,5
n
Sr
(58)
On the other hand, the real power density
Re{ }S
decays with 1/r2 (6 dB/octave) in r direction
(56). This term, pointing away from the source, describes the propagation of power away
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 25 –
from the antenna. The power density of the radiated space wave can be described as the
distribution of power on a spherical surface 4πr2 in the far-field of the antenna.
{ }
2
1
Re ~Sr
(59)
The real power density dominates for large values of r further away from the antenna. Thus
far, the influence of the dielectric substrate has not been considered. Therefore, an analysis of
surface wave modes and their spatial decay behavior is given in the next subsection.
2.2.2.2 Power Decay of Propagating Surface Waves
A grounded dielectric substrate is capable of guiding surface waves. An in depth study of
surface waves on grounded and ungrounded substrates was done by Collin [97] and
Harrington [98]. In this section, a typical PCB substrate configuration used for (quasi)
millimeter-wave applications is considered, and the influence of the substrate height and
dielectric constant on the surface wave fields is analyzed. As a starting point, consider the
grounded substrate configuration in Figure 9. The substrate has a height h and relative
permittivity εr.
The configuration is assumed to extend infinitely in y direction. Therefore, there is no spatial
field dependency on y. The wave propagation is considered in x direction with the wave
number kx (propagation constant). At this stage, only the transverse magnetic (TM) modes are
considered.
Figure 9: Grounded substrate used for the calculation of surface wave fields.
Solutions are constructed with the vector potential and the scalar solution function
TM
ψ
assuming the following condition:
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 26 –
TM x
Ae
ψ
= ⋅
(60)
Note that the electric and magnetic fields are easily found using (6), (8) and (11). A set of
solutions for region 1 (
0zh<<
) and region 2 (
hz< <∞
) is given in [98]:
( )
,1
sin
x
jk x
TM
A uz e
Ψ
−
=
(61)
,2
x
jk x
vz
TM Be e
Ψ
−
−
=
(62)
A and B are amplitude factors. The separation equations for the wave numbers in each region
are readily found [98].
2
22
2
0
xr
uk c
ωε
+=
(63)
2
22
2
0
x
vk c
ω
−+ =
(64)
The notation of the wave numbers u and v is chosen such that both are real in the case of wave
propagation. Next, the wave number kx is eliminated by inserting (63) into (64).
( )
2
22
2
0
1
r
uv c
ωε
+= −
(65)
Boundary conditions are evaluated next. The tangential electric and magnetic field
components in the plane of the substrate/air interface at z=h must be equal. The following
expression results [98]:
( )
tan r
uh uh vh
ε
=
(66)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 27 –
Next, the characteristic transcendental equations can be set up and brought into a convenient
form for a graphical solution.
( ) ( ) ( )
( )
1/2
2
2
0
tan
r
uh uh
f uh r uh
ε
= = −
(67)
( )
2
2
0
0
1
r
h
rc
ωε
= −
(68)
The equation of circles with radius r0 is observed on the RHS of (67). On the LHS, there are
tangent functions. A direct analytical solution of the transcendental equation does not exist.
However, it can be solved graphically. The solutions are the intersection points of the two
functions. The graphical solution technique for transcendental equations has an advantage
over numerical solution techniques because it allows for physical insight into the behavior of
the parameters. Figure 10 shows solutions to (67) corresponding to the intersection points of
the tangent and circle functions. The parameter h is normalized to the wavelength λ for
generality of the results.
Figure 10: Solutions of the transcendental equations for different values of εr and h.
Solutions are plotted for three εr and three h values of the substrate. It is observed that for the
chosen values of εr and h (relative to λ) there only exists one solution in the first quadrant.
Therefore, only the lowest order TM0 mode exists on these substrate configurations for the
analyzed wavelength. Once the graphs are plotted, the intersections points can be determined,
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 28 –
and the values of u are calculated. The values of v are determined by inserting u into the
separation equations. Once both values are found for a parameter set (εr and h), the problem is
solved, and the fields can be evaluated. The field variation in the direction normal to the
substrate i.e., the variation with respect to z, is of interest.
Figure 11 and Figure 12 show the plots of the longitudinal and transverse electric field
components for three variations of εr and three variations of h with λ=16.67 mm (f=18 GHz).
Figure 11: Longitudinal electric field of TM0 surface wave with λ=16.67 mm (f=18 GHz).
Figure 12: Transverse electric field of TM0 surface wave with λ=16.67 mm (f=18 GHz).
It is observed that the magnitude of the longitudinal component Ex is about 10 times smaller
than the transverse component Ez. The influence of the dielectric constant of the substrate is
more significant on the magnitude of the electric field than the height of the substrate. The
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 29 –
field strength at the substrate/air interface increases with increasing substrate height and
increasing dielectric constant. It is also observed that Ez is insensitive to the substrate height.
The radial propagation of the surface waves away from the region of excitation has not been
considered so far. The surface wave was assumed to propagate in x direction. To estimate the
spatial decay rate, cylindrical coordinates are introduced. These offer the advantage of a
realistic radial spatial dependency of the propagating surface wave power density.
The TM and TE surface wave modes propagate in radial direction. It is assumed that the
surface wave is excited at the origin of the coordinate system. For propagation in r direction,
the vector potentials (6) and (23) in cylindrical coordinates assume the following simple
forms:
TM r
Ae
Ψ
= ⋅
(69)
TE r
Fe
Ψ
= ⋅
(70)
Note that r=(x2+y2)0.5 is the radius in cylindrical coordinates (also referred to as ρ). The radial
variation of the nth mode of the potentials is described with a Hankel function of second kind
[98].
( )
(2)
/
~
TM TE n r
H kr
Ψ
(71)
A set of solutions for region 1 (
0zh<<
) and region 2 (
hz< <∞
) can be found [98]:
( ) ( ) ( )
(2)
,1
sin cos
TM TM n r
A uz n H k r
Ψϕ
=
(72)
( ) ( ) ( )
(2)
,1
cos cos
TE TE n r
A uz n H k r
Ψϕ
=
(73)
( ) ( )
(2)
,2
cos
vz
TM TM n r
B e n H kr
Ψϕ
−
=
(74)
( ) ( )
(2)
,2
cos
vz
TE TE n r
B e n H kr
Ψϕ
−
=
(75)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 30 –
The separation equations for the two regions are given by the following:
2
22
2
0
rr
uk c
ωε
+=
(76)
2
22
2
0
r
vk c
ω
−+ =
(77)
After some calculations, the equation for determining the cut-off frequencies of the modes is
obtained [98].
( )
0
41
c
r
c
fn
h
ε
=−
(78)
Only odd TM modes with even orders n=0, 2, 4 ,… and even TE modes with odd orders n=1,
3, 5, … exist on a grounded substrate. The lowest order n=0 TM surface wave mode
propagates down to DC. The cut-off frequency for the first higher order surface wave mode,
the TE1 mode, considering a typical PCB substrate configuration with h=250 µm and εr=4, is
272 GHz. Therefore, for the frequencies and PCB technology considered in this work, only
propagation of the fundamental TM0 mode needs to be considered. Finally, from (72)-(75),
the power density distribution of the TM0 surface wave mode is obtained.
{ }
( )
2
(2)
0
1
Re ~ ~
rr
S H kr r
→∞
(79)
The power density decay is proportional to 1/r (3 dB/octave). The power is guided by the
dielectric material along the substrate and distributed on a cylindrical surface. The spatial
decay rate of surface waves is, thus, slower than the spatial decay rate of space waves (59).
2.2.2.3 Comments on Power Coupling to Board Components
Based on the previous results, Figure 13 shows an overview of the possible coupling
mechanisms that are evoked by planar antennas. The planar antenna radiates a surface wave
on the substrate in addition to the primary desired space wave. These far-field modes were
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 31 –
differentiated by their characteristic spatial decay behavior (59) and (79). However, close to
the antenna, reactive power stands in the near-field and decays rapidly with increasing
distance (58). Coupling mechanisms are also evoked in the near-field.
Figure 13: Overview of coupling mechanisms between planar antennas and board components.
To illustrate this, Figure 14 shows the current and charge distributions,
J
and
q
, on the patch
antenna. The charge distribution on the patch antenna has a maximum at the edge of the
radiating apertures of the patch. At the center of the patch, the charge distribution exhibits a
node. Therefore, capacitive coupling is highest at the radiating apertures. On the other hand,
the current distribution has a maximum at the center of the patch. Therefore, inductive
coupling is at its maximum at the center of the patch. These capacitive and inductive coupling
mechanisms are illustrated with the capacitance C12 and the mutual inductance M12.
Figure 14: Illustration of distributed nature of capacitive and inductive coupling from a resonant patch
antenna.
These electromagnetic interactions at the antenna near-fields directly affect the charge and
current distribution on the antenna, inevitably also altering the antenna parameters. This is one
of the main reasons to define the electromagnetic antenna boundary at which the reactive
power density of the near-fields has decayed far enough so that the weak coupling assumption
can be made.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 32 –
2.2.3 Modeling and Simulation of Antenna Fields
The electromagnetic fields excited by antennas have been analyzed from a theoretical point of
view in the previous section. A specific example of an ideal planar antenna is studied in this
section in order to quantify the spatial decay of the propagating and reactive power density as
well as the influence of the substrate and antenna feed on the excited fields. In literature,
models for describing and approximating the fields and parameters of planar antennas and
linking these to the physical dimensions of the antenna have been proposed. These are
necessary for first order designs, which are used to create 3D models containing the
geometrical and material parameters of the antenna and to compute the antenna with a
numerical full-wave electromagnetic field solver. The most commonly employed planar
antenna is the patch antenna. Therefore, it is used as an example in this section.
2.2.3.1 Analytical Planar Antenna Models
Figure 15 shows the geometry of a typical patch antenna on a grounded substrate, which is
used in the analysis throughout this section. The patch resonator comprises a rectangular
patch of width w and length l. The height of the substrate is h, and it has a relative dielectric
constant εr. The feeding point is located at a distance s in negative x direction from the center
of the patch resonator. The coordinate system is located at the center of the patch resonator on
the ground plane.
Figure 15: Model of patch antenna on a grounded dielectric substrate.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 33 –
Three common methods for the design and analysis of patch antennas have been studied and
applied in literature [94, 99]: (1) the cavity model; (2) the transmission line model; and (3) the
full-wave simulation model.
With the cavity model, the field distribution of the excited patch antenna is approximated
analytically by finding the field distribution between patch and ground plane with simplified
boundary conditions. For this purpose, the patch is modeled as a parallel plate waveguide with
magnetic walls. The resonance frequencies of the cavity are determined for all cavity
resonance modes (m, n and p are the mode orders and c0 is the speed of light).
22 2
2
2
0
r
mnp
c l wh
ω πππ
ε
= ++
(80)
Based on the cavity model, the electric and magnetic field distributions underneath the patch
antenna can be approximated for the fundamental TM100 resonance mode. The electric field of
this mode is z directed and sinusoidal along the non radiating apertures and constant along the
radiating apertures.
0sin
z
E jE x
l
π
=
(81)
At the antenna resonance frequency, a standing wave is excited on the patch i.e., the magnetic
field underneath the patch antenna is 90° out of phase with the electric field. E0 and H0 are the
field amplitudes at the resonance frequency.
0cos
y
HH x
l
π
=
(82)
The transmission line model, on the other hand, treats the patch antenna like a microstrip
transmission line. Consider again the lowest order TM100 mode on the patch antenna. Figure
16 shows a circuit model of the patch antenna. The radiating apertures of the antenna are
modeled with a parallel RC circuit (R1, R2, C1 and C2) to capture the effects of the stray fields
and radiation. The patch itself is modeled with a wide and low impedance microstrip
transmission line with characteristic impedance Z0 and phase constant β. The antenna feeding
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 34 –
point, where the source voltage Uin with source impedance Zin is connected, is located at a
distance s from the center of the patch, as also illustrated in Figure 15.
Figure 16: Parameterized transmission line model of a conventional rectangular patch antenna for
excitation with the TM100 mode.
Analytical approximations for the design of patch antennas are available in open literature
[100]. These approximations are useful for determining the physical patch antenna parameters
prior to simulations. The patch width w is typically chosen first. The practical patch width
should be chosen in order to ensure that no additional resonance mode is excited across the
patch width. Next, the effective relative dielectric constant εreff for this patch width is
calculated in the static case [94]:
11
22 1 12
rr
reff h
w
εε
ε
+−
= +
+
(83)
To consider the effects of the fringing fields of the patch antenna at the radiating apertures,
the effective patch length extension Δl is used.
( )
( )
0.3 0.264
0.412
0.258 0.8
reff
reff
w
h
lh w
h
ε
ε
++
∆=
−+
(84)
Finally, the required patch length l for obtaining resonance at the frequency fR is determined
using the following expression.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 35 –
012
2Rreff
c
ll
f
∆
ε
= −
(85)
A good impedance match for the excitation of the TM100 mode is obtained by placing the
feeding point s between the center and the edge of the patch, roughly according to the
following approximation for the input resistance Rin at resonance [94]:
2
sin 2
in edge
RR x
ll
π
∆
≈
+
(86)
Redge is the effective resistance of both radiating apertures as seen at the feeding point. The
input reactance is ideally zero at the resonance frequency of the patch.
Although the cavity and transmission line models provide physical insight into the operation
of patch antennas and are useful for first qualitative approximations, the parasitic effects
cannot be captured accurately. Therefore, numerical full-wave simulations need to be
performed to obtain a realistic and accurate distribution of the complex power density as well
as of its spatial decay behavior as its transitions from the near- to the far-field. Appendix 1
gives an overview of the numerical full-wave solution techniques and the solver used in this
work.
2.2.3.2 Simulation of Antenna Field under Idealized Conditions
The analytical approximations allow a first estimation of the antenna dimensions. Numerical
full-wave simulations are required to compute the fields excited by the antenna on the
substrate in the vicinity of the antenna. The dimensions of the patch in the preceding example
were approximated first with (83)-(85) and fine tuned for operation with the TM100 and a
resonance frequency f=c0/λ0. Since all materials are linear, this model is frequency scalable
and all the physical dimensions are normalized to the wavelength λ0. The substrate height was
set to h=0.02 λ0 with a relative dielectric constant εr =3.75. First, a practical width for the
patch was chosen w=0.25 λ0. Next, εreff =3.34 was determined with (83). Finally, the patch
length l=0.24 λ0 was calculated using (84) and (85). Based on these values, a simulation
model was constructed. The antenna is excited with an idealized horizontal current at the
center of the patch i.e., an x directed current across the entire patch width in order to remove
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 36 –
the influence of the antenna feed (at first) on the excited fields. Figure 17 shows a plot of the
current density of the TM100 mode.
Figure 17: Distribution of current density on the patch resonator with the "idealized" current excitation.
Two regions in the direction of the arrows were defined for studying the magnitude and
spatial decay of the electric and magnetic fields (see Figure 15). The regions are oriented in
the two principle planes of the patch antenna on the ground plane: region 1 in the E-plane
(x<0, y=0, z=0); and region 2 in the H-plane (x=0, y>0, z=0). Since the antenna is symmetrical
in both principle planes, it is sufficient to define these regions from the center of the patch
because the spatial field decays on the other side are identical.
The simulated electric and magnetic field distributions, which were computed directly by the
field solver in the volume, are evaluated in the vicinity of the patch antenna on the ground
plane. The complex power density is calculated with the tangential magnetic field
components, Hx and Hy, and the normal electric field Ez, according to (43).
( )
**
1
2
z yx z xy
S EH e EH e=−−
(87)
Of course, the complex power density can also be computed on top of the substrate. Since the
substrate height is electrically short, however, the variation with respect to the z coordinate of
the fields within the substrate can be assumed constant.
Figure 18 shows the logarithmic plot of the simulated propagating power density excited by
the patch antenna on the ground plane. The power in the lateral plane is primarily launched in
region 1 in the form of a surface wave mode. It is observed that the power decays slowly with
increasing distance in region 1. The propagating power density in region 2, on the other hand,
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 37 –
decays faster with increasing distance. The current anti node on the patch resonator is also
indicated with an arrow. The antenna is excited with a current source on the patch.
Figure 18: Simulation of the propagating power density excited by the patch antenna on the ground plane.
Figure 19: Simulation of the spatial complex power density excited by the patch antenna on the ground
plane in region 1.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 38 –
The complex power density in region 1, where the surface wave power of the patch antenna is
primarily radiated, is studied in more depth. Figure 19 shows the simulated complex power
density in region 1 in dependency of distance from the center of the patch resonator.
The magnitudes of the real and imaginary parts, describing the propagating power and
reactive power density, are plotted in decibels. The curves are normalized to the maximum
reactive power density underneath the patch resonator.
The reactive power density dominates underneath the patch resonator with a 12 dB higher
magnitude. However, it is observed that the reactive power density decays faster than the
propagating power density with increasing distance from the physical boundary of the patch
cavity. The point of intersection, where the reactive power equals the propagating power, is
located at a distance of approximately 0.17 λ0 from the center of the patch. Beyond this
distance, the reactive power density quickly decays below -50 dB.
Next, the influence of the antenna feed and the substrate height h on the excited fields of the
antenna is quantified. A probe feed was introduced into the simulation model comprising a
signal via connected to the patch. Figure 20 shows an illustration of the probe feed
configuration. The probe feed is a common technique to excite a patch antenna. The signal via
is isolated from the ground plane and fed from underneath the ground plane through a coaxial
connection. The probe feed offset s=0.09 λ0 was determined by simulations based on the
relationship in (86). The probe feed causes the resonance frequency of the antenna to drop by
1.5 % as a result of the additional feed inductance.
Figure 20: Configuration of the coaxial probe feed and the inset distance s from the patch edge.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 39 –
Figure 21 and Figure 22 show the simulated magnetic fields on the ground plane with
increasing distance from the antenna in regions 1 and 2 where only the y component of the
magnetic field exists.
Figure 21: Simulation of the normalized magnetic field excited by the patch antenna on the ground plane
in region 1.
Figure 22: Simulation of the normalized magnetic field excited by the patch antenna on the ground plane
in region 2.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 40 –
The results of the nominal configuration (with ideal current feed and substrate height h) are
compared to the results of the antenna with probe feed and with a thicker substrate i.e., double
of the height 2h, respectively. The physical boundary of the patch resonator is also indicated
in the figures.
It is observed that the magnitudes of the magnetic fields increase by 3 dB and 10 dB for the
cases with the probe feed and increased substrate height, respectively. Thus, more power is
launched into the substrate. The spatial decay rates of the fields are approximately
4 dB/octave beyond a distance of roughly 0.25 λ0 from the patch center for the three cases in
region 1. This indicates not only the presence of the surface wave mode but also the settling
of the reactive near-fields. Considering the magnetic field in region 2, on the other hand, only
the configuration with increased substrate height causes higher field strengths to occur.
Furthermore, since the spatial decay of the fields is greater than 12 dB/octave, propagating
surface and space wave modes are not dominant in this region.
The results in this subsection are based on numerical simulations. The accuracy of numerical
simulations needs to be verified. Therefore, a quantification of the solver accuracy as well as
measurement results are presented in Appendix 2.
In summary, it is concluded that the antenna feed and substrate configuration have a
significant effect on the excited fields of planar antennas. It was also shown that the reactive
power density decays fast with increasing distance from the antenna while the propagating
power density decays slower yielding high field strengths in the substrate and on the ground
plane.
2.2.4 Determining the Electromagnetic Antenna Boundary
So far in this chapter, the excited antenna fields were characterized from a theoretical point of
view. It was shown that planar antennas give rise to propagating surface and space waves.
Figure 23 shows an illustration of these far-field modes at board level.
The power of the space wave mode is distributed on a spherical surface (~1/r2), and the power
of the surface wave mode is distributed on a cylindrical surface (~1/r) and depends primarily
on the substrate parameters h and εr. Furthermore, reactive power density stands in the near-
field of planar antennas, which decays with at least ~1/r3 with increasing distance from the
antenna. Table 1 shows a summary of the different near- and far-field spatial decay rates that
were examined.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 41 –
Figure 23: Illustration of far-field waves radiated by a planar antenna configuration including: (a) the
space wave mode; and (b) the surface wave mode.
Type Spatial field decay
Far-field propagation Surface wave 1/r 3 dB/octave
Space wave
1/r2
6 dB/octave
Reactive near-fields Evanescent 1/rn, n>3 >9 dB/octave
Table 1: Summary of the spatial field decay rates near excited planar antennas.
In literature, the space around an excited antenna has been divided into three general regions
[94]: (1) the reactive near-field; (2) the radiating near-field and; (3) the far-field region. These
regions are defined through the maximum physical dimension d of the antenna in relationship
to the operating wavelength λ. The boundaries r1 and r2 of the three general field regions are
in the range 0<r1<r2<
∞
.
3
1
0.62 /rd
λ
=
(88)
2
2
2/rd
λ
=
(89)
The radiating near-field, as defined above, only exists if d is large compared to λ. For small
antennas with similar properties to short dipoles, the boundary between reactive near-field and
far-field is defined by r0 as:
0
1/ /2r
βλπ
= =
(90)
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 42 –
Unfortunately, the ideal infinitesimal dipole is practically the only antenna type, where this
region can be given precisely. For this ideal structure, the averaged radial components of the
reactive and propagating power densities (55) at the radian distance are equal. Furthermore,
these field regions are very general and do not include the actual geometrical and material
properties of planar antennas. Besides, defining a radius does not seem to be appropriate for
planar antennas. In compact wireless modules, determining a realistic boundary for the
reactive near-fields is necessary for efficient component placement and electromagnetic
antenna size estimation.
Therefore, the proposed electromagnetic antenna boundary in this work is not based on
specifying a distance directly, but is determined by evaluating the reactive power density
Im{ }S
of the excited planar antenna and deducing a threshold value
max
Im{ }S
. The block
out region is then defined as the set of all points in the plane for which the reactive power
density is above the threshold value. Accordingly, the electromagnetic antenna boundary is
defined as follows:
max
max
inside EM antenna boundary
outside EM antenna boundary
Im{ } ,
Im{ } Im{ } ,
S
S
S
>
<
(91)
A 2D block out region is desired in the context of planar antennas. Therefore, the
considerations will be restricted to the ground plane (or substrate) of the antenna. Since the
substrate is electrically thin, the values of the fields do not change in the direction of the z axis
within the substrate i.e., they are practically the same on the top and bottom plane of the
substrate.
Different approaches for defining the threshold value were considered. Since the reactive
power density has a faster spatial decay rate in comparison to the propagating power density,
a maximum ratio could be defined as
Im{}/Re{}SS
, or a maximum tolerable limit of
Im{ }S
could be given directly. However, these limits do not consider the antenna parameters
including the operating frequency, antenna efficiency, input reflection coefficient and input
power, which all take direct influence on the reactive near-field distribution and, hence, the
reactive power density. Consequently, one possibility to define the threshold value is relating
it to the power exiting the antenna structure Pout2 (refer to Figure 6).
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 43 –
{ }
2
2
max
Im
out
P
S
π
λ
=
(92)
This definition is motivated by the infinitesimal dipole, where the averaged radial components
of the reactive and propagating power densities (55) at the radian distance are equal and
assume this value.
Figure 24: Graphical illustration of the reactive power density, the threshold value for determining the
electromagnetic antenna boundary as well as the antenna parameters.
This threshold value can then also be expressed in terms of the input power of the antenna
Pin1, the antenna efficiency η (including dielectric and conductor losses of the antenna) and
the input reflection coefficient S11.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 44 –
( )
{ }
( )
2
1
1 11 11
2
max
Im , , 1
in
in
P
SP S S
π
ηη
λ
= −
(93)
The actual power delivered to the antenna is contained in the term 1-|S11|2 considering
impedance mismatch with the feeding line. The power contained in the near-fields including
the power loss (conductor and dielectric losses) is given by η. Therefore, the expression is
also valid for different antenna efficiencies.
Figure 24 shows a graphical illustration of the reactive power density and the electromagnetic
antenna boundary defined in the 2D plane. The feasibility of defining the electromagnetic
antenna boundary is shown in the next section by considering three planar antenna
configurations. It is shown that additional space near the antenna needs to be considered as
being part of the antenna and that board components should not be placed there. This ensures
that the antenna parameters are preserved when the antenna is integrated.
2.3 Comparison of Planar Antennas and Application of Antenna Boundary
In this section, different planar antenna configurations are studied and compared with regards
to their excited field distributions, and their electromagnetic antenna boundaries are deduced.
Three planar antennas comprising a patch antenna, slot antenna and dipole antenna are
considered. These antennas are differentiated by their geometry and radiation characteristics.
The patch antenna primarily radiates perpendicular to the ground plane in one direction. The
slot antenna also primarily radiates perpendicular away from the ground plane, but in both
directions above and below. The dipole antenna primarily radiates in lateral direction i.e., in
the plane of the substrate. Another differentiation between the antenna configurations is the
antenna feed. The patch and slot antennas are single ended configurations i.e., they are fed
through a single microstrip line referenced to the ground plane. The dipole antenna, on the
other hand, is fed through a differential line comprising two microstrip lines operated with
180° phase shift between them. As a result, the dipole is not driven against the ground plane.
All three antennas were designed to operate at 24 GHz on the same substrate configuration.
Appendix 1 gives an overview of the numerical full-wave solution techniques and the solver
that was used to design and optimize of the antennas. A typical high frequency PCB substrate
with two copper metallization layers was used. The substrate has a relative dielectric constant
εr=3.75, dielectric loss tangent tan(δ)=0.006, height h=250 µm and copper metallization
thickness t=17.5µm. The copper metallization has a conductivity of 58 MS/m. In Appendix 4,
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 45 –
an overview of the manufacturing process, used for the fabrication of all planar
configurations, is given. The antennas, fed through impedance controlled microstrip lines (see
Appendix 3), are optimized for impedance matching with less than -10 dB reflection
coefficient and high radiation efficiency within the bandwidth of operation. The antennas
were driven with 1 mW (0 dBm) source power in the simulations.
2.3.1 Patch Antenna
The patch antenna depicted in Figure 25 comprises a metallic patch above the ground plane.
The patch is excited with its fundamental λ/2 resonance mode (lowest order TM mode). The
patch length lp and width wp, which primarily determine the resonance frequency and
impedance of the patch resonator, respectively, were optimized for resonance at 24 GHz on
the substrate configuration. The dimensions lp=3.175 mm and wp=4.25 mm were determined
after the optimization.
The concept of this antenna is similar to the ideal patch antenna already analyzed in
Section 2.2.3.2 apart from the feeding technique. The inset feed is used so that the microstrip
line can be placed on the same layer as the patch. The length s of the inset and the width g of
the gaps were optimized to ensure impedance matching to the 50 Ω microstrip line at 24 GHz.
Figure 25: Simulation model and dimensions of the 24 GHz inset fed patch antenna.
In order to characterize the input reflection coefficient and impedance bandwidth, a test
structure of the antenna was manufactured and measured. Figure 26 shows the measured
reflection coefficient S11 and a comparison with the full-wave simulation results.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 46 –
Figure 26: Measurement of the reflection coefficient S11 of the patch antenna and comparison to full-wave
simulation. The top view of the manufactured antenna with the feeding line and contact pads is also
shown.
The impedance bandwidth of the antenna is evaluated at the -10 dB points around the
resonance frequency. A slight discrepancy of the resonance frequency between the simulation
and measurement results is observed. The slightly higher measured bandwidth of 600 MHz,
compared to 500 MHz in simulation, is primarily caused by technological tolerances as well
as by additional losses such as the surface roughness of the copper. It must also be considered
that the influence of the GSG (ground, signal, ground) probe adapter was not included in the
simulation model.
2.3.2 Slot Antenna
The slot antenna configuration in Figure 27 comprises a λ/2 slot resonator. The antenna is fed
through a 50 Ω microstrip line at the edge of the slot. A shorting via is used to connect the end
of the microstrip line to the ground plane. This allows good impedance matching to 50 Ω. The
position of the shorting via can be adjusted to match the slot antenna to a variety of feeding
line impedances. A slot length ls=4.5 mm and width ws=150 µm were determined after
optimization to ensure resonance near 24 GHz.
Note that the slot resonator radiates above and below the ground plane. Its radiation pattern
and field distribution are similar to those of a magnetic λ/2 dipole antenna, where the
equivalent magnetic current density is assumed to flow in the slot. The radiation patterns are
analyzed further on in Section 2.3.4.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 47 –
Figure 27: Simulation model and dimensions of the 24 GHz edge fed slot antenna.
The measurement of the slot antenna poses challenges with respect to the placement on a
metallic wafer chuck. Therefore, the slot antenna was placed on a 3 cm thick Styrofoam™
block at the edge of the chuck before it was probed. This is necessary to reduce the influence
of the parasitic proximity effects introduced by the metallic wafer chuck. The ground plane of
the slot antenna is not continuous, and the radiation below the ground plane causes image
currents to be excited and reflections to occur inevitably altering the antenna parameters.
Styrofoam™ is chosen for its low dielectric constant and loss tangent ensuring negligible
capacitive loading of the antenna. Figure 28 shows the measurement and simulation results of
the slot antenna.
Figure 28: Measurement of the reflection coefficient S11 of the slot antenna and comparison to full-wave
simulation. The top view of the manufactured antenna with the feeding line and contact pads is also
shown.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 48 –
Similarly to the results of the patch antenna, it is observed that the measured bandwidth of
1.2 GHz is slightly higher than the simulated bandwidth of 1 GHz. This higher value is
attributed to additional losses such as the surface roughness of the copper metallization. The
GSG probe adapter was also not included in the simulation model.
2.3.3 Dipole Antenna
The dipole antenna in Figure 29 is fed through a differential microstrip line with an
impedance of 100 Ω. The differential line comprises two 50 Ω microstrip lines connected to
the two printed dipole arms.
Figure 29: Simulation model and dimensions of the 24 GHz center fed dipole antenna.
The ground plane underneath the dipole is truncated to eliminate image currents, which would
inevitably cancel the antenna mode. The dipole is designed to operate in approximately 3/4 λ
mode and is located at a distance sd=1.35 mm from the edge of the ground plane. This is
necessary to ensure that the ground plane acts as a reflector. The dipole length ld=5.95 mm
and the dipole width wd=0.75 mm were fine tuned with full-wave simulations.
The reflection coefficient of the dipole antenna was measured by implementing a two port S-
parameter measurement. By converting the single ended S-parameters to differential S-
parameters, the differential response of the antenna was obtained. Figure 30 shows the results.
Note that the dipole antenna was also measured on a 3 cm thick Styrofoam™ block to
minimize the influence of the chuck. The experimental characterization is in satisfactory
agreement with the simulation results.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 49 –
Figure 30: Measurement of the reflection coefficient S11 of the dipole antenna and comparison to full-wave
simulation. The top view of the manufactured antenna with the feeding line and contact pads is also
shown.
2.3.4 Comparison of Antenna Characteristics
In comparison to other board components, planar antennas excite particularly strong electric
and magnetic fields in the lateral plane of the substrate. Figure 31 and Figure 32 show the
simulated magnitudes of the electric and magnetic fields of the patch, slot and dipole antennas
on the ground plane, respectively. The slight ripples, observed in both figures, are a result of
reflections at the substrate and ground plane edges, reflections at the antenna feeding point,
due to impedance mismatch, and minor stray reflections at the PML boundary conditions (see
Appendix 1). All these effects cause standing waves to occur. The sizes of the substrate areas
are 25 mm X 25 mm.
Figure 31: Comparison of the simulated electric field distributions on the ground planes in the vicinity of
the: (a) patch antenna; (b) slot antenna; and (c) dipole antenna.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 50 –
Since a standing wave is excited on the antenna structures at resonance, a voltage maximum
exists at the radiating apertures of the patch antenna, in the center of the slot antenna and at
the ends of the dipole antenna. These are the regions of high electric field strength. The
electric field is orientated normal on the ground plane comprising primarily the z component.
On the other hand, there are current maxima in the center of the patch antenna, at the ends of
the slot antenna and in the center of the dipole antenna. In this region, the magnetic field of
the standing wave is at its maximum. The magnetic field is orientated tangential to the ground
plane comprising only the x and y components.
Figure 32: Comparison of the simulated magnetic field distributions on the ground planes in the vicinity
of the: (a) patch antenna; (b) slot antenna; and (c) dipole antenna.
The field distributions of the patch and slot antennas are qualitatively similar. On the other
hand, the electric and magnetic fields, excited by the dipole on the ground plane near the
differential feeding line, are significantly lower compared to the patch and slot antenna. The
reason for this is that the antenna is balanced and not driven against the ground plane.
Therefore, the amount of coupling to be expected to components referenced to the same
ground plane as the unbalanced patch or slot antenna is significantly higher than in the case of
the balanced dipole antenna. However, in the case of the dipole antenna the ground plane is
truncated below the dipole itself. Therefore, valuable board space on the substrate around the
dipole cannot be used for components that need a ground reference.
The radiation patterns of the three antennas are also compared. Figure 33 shows a comparison
of the computed radiation patterns of the gain in the two principle elevation planes i.e., the xz
and yz planes.
The radiation of the patch antenna is directed primarily in positive z direction i.e., in the
direction normal to the substrate and ground plane, with a maximum gain of 6.5 dBi. The slot
antenna radiates in both positive and negative z directions with a maximum gain of 4.5 dBi.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 51 –
On the other hand, the dipole radiates in lateral x direction with a maximum gain 5 dBi. All
three antennas are linear polarized.
Figure 33: Comparison of the simulated radiation patterns (gain) of the patch, slot and dipole antenna in
two principle elevation planes.
Table 2 shows a summary and comparison of the simulated antenna parameters. These
include the impedance bandwidth, radiation efficiency η and gain as well as the physical
dimensions at 24 GHz.
Type
Antenna Parameters
-10 dB BW [GHz]
η [%] / Gain [dBi]
Phys. dimensions [mm2]
Patch 0.5 80 / 6.5 3.175x4.25
Slot
1
90 / 4.5
4.5x0.15
Dipole
9.5
94 / 5
5.95x0.75 (2.1)
Table 2: Comparison of the simulated parameters of the planar antennas at 24 GHz.
The simulated radiation efficiencies of the antennas (including dielectric and conductor
losses) show that the patch antenna has the lowest efficiency of 80 %. The slot antenna
achieves an efficiency of 90 % and the dipole antenna has the highest efficiency of 94 %. The
dipole antenna also displays the highest bandwidth of 9.5 GHz, attributed not only to its larger
physical dimensions compared to the other antennas, but also to its spatial separation from the
ground plane. Typical wireless modules employ large ground planes to ensure low impedance
references for the transmission lines, active components and power distribution network.
Since the dipole needs to be separated from the ground plane, which acts as a reflector,
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 52 –
valuable board space is potentially inefficiently utilized. Also, since single ended transmission
lines are often used, an additional balun is required to feed the dipole. These are the main
disadvantages of the planar dipole antenna because both factors, truncated ground plane and
additional balun, require additional board space.
In conclusion, the characterized antennas exhibit satisfactory radiation performance for
24 GHz communication applications.
2.3.5 Deduction of Electromagnetic Antenna Boundary
The electromagnetic antenna boundary, as introduced in Section 2.2.4, is defined for the three
planar antenna configurations. For this purpose, (93) is evaluated. All antennas are fed with
Pin1=1 mW (0 dBm) input power. The antenna efficiencies η are taken from Table 2. Since all
the antennas exhibit small reflection coefficients, <-10 dB at 24 GHz, S11 is neglected. Table 3
shows the calculated reactive power density threshold values for the antenna boundaries.
Type
S
max
Im{ }
[µW/mm2]
Patch antenna
16
Slot antenna
18
Dipole antenna
19
Table 3: Comparison of the calculated threshold values.
The patch antenna exhibits the lowest threshold because it has the lowest efficiency. The
dipole antenna, on the other hand, exhibits the highest efficiency and also has the highest
threshold value.
Figure 34: Simulated reactive power density on the ground plane of the planar antennas.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 53 –
The electric and magnetic fields of the three planar antennas have been simulated (Figure 31
and Figure 32 show the results). With these fields, the Poynting vector was computed
according to (43), and the magnitude of the imaginary part was determined and evaluated on
the ground planes of the planar antennas. In Figure 34, the isolines of the reactive power
density, as given in Table 3, are shown.
Two rectangles are constructed around the structures of each antenna. The geometrical
parameters Δl, Δl´ and Δw, Δw´ are introduced to describe the electrical size increase
compared to the physical antenna lengths l and antenna widths w, respectively. Please note
that the block out area so defined is not rectangular. For practical design guidelines, it is
advantageous to work with the circumscribed rectangle. The inner rectangles define the
proposed electromagnetic antenna boundary. The outer rectangles define the conventional
textbook reactive near-field boundary (90) located at the distance λ/2π from the antenna
surfaces/edges. This corresponds to a minimum distance of approximately 2 mm on each side
of the antenna. Notice that the conventional reactive near-field boundary is considerably
larger than the proposed electromagnetic antenna boundary. The electrical size of the antenna
is “overestimated” using the standard textbook approach. This potentially leads to inefficient
usage of available board space during antenna integration.
Table 4 shows a summary of the deduced antenna boundaries of the three planar antenna
types. From here on, l+Δl is referred to as the electrical antenna length. Likewise, w+Δw is
referred to as the electrical antenna width.
Antenna
Dimensions
Physical size
Electrical size
l [mm]
w [mm]
Area [mm2]
l+Δl [mm]
w+Δw [mm]
Area [mm2]
Patch
3.175
4.25
13.5
4.6
6.5
29.9
Slot
4.5
0.15
0.7
5.5
2.7
14.9
Dipole
5.95
0.75 (2.1)
12.4
9
3.75
33.8
Table 4: Deduced dimensions of the electromagnetic antenna boundary of the antennas.
Figure 35 shows a graphical representation of the physical antenna dimensions in comparison
to the electrical antenna dimensions as defined by the electromagnetic antenna boundaries.
The patch antenna has the smallest physical and electrical length. Note that the length is the
resonance determining dimension because it supports the standing wave. The physical and
electrical length of the dipole is largest. Unlike the patch and slot antenna, which are operated
in λ/2 resonance mode, the dipole is operated in 3λ/4 resonance mode. On the other hand, the
patch antenna has the largest physical and electrical width. The fields of the resonance mode
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 54 –
of the patch antenna are almost completely confined in the substrate. Primarily, the widths of
the antennas determine the bandwidth and impedance properties. The slot has the smallest
physical width. Since the currents flow along the perimeter of the slot, the electrical width is
increased significantly in comparison to its physical width.
Figure 35: Comparison between the physical and additional electrical sizes of the planar antennas.
In order to illustrate the feasibility of using the electromagnetic antenna boundary for the
integration of planar antennas, it is necessary to quantify the effects of components, such as
transmission lines placed inside this boundary, on the antenna parameters.
2.3.5.1 Influence of Transmission Lines Routed within the Antenna Boundary
The magnitude of the electromagnetic interactions, occurring when board components are
placed inside the electromagnetic antenna boundary, depends on the size, orientation, distance
and material properties of the component. A typical board component is a planar transmission
line, which, similar to the antenna, has an open field structure. It is desirable to route
transmission lines close to planar antennas in order to efficiently exploit available board
space. The assumption of weak coupling is valid when the secondary fields excited on the
victim have negligible effects on the characteristics and fields of the aggressor. In this section,
it is shown that transmission lines routed outside the electromagnetic antenna boundary only
have a negligible effect on the antenna parameters.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 55 –
Figure 36: Illustration of the planar antennas with microstrip transmission lines routed inside
electromagnetic antenna boundary of the (a) patch and (b) slot antennas.
Figure 36 shows an illustration of the patch and slot antennas with additional microstrip lines.
The microstrip lines are routed past the antennas with a separation distance d as illustrated.
Complete full-wave simulations were conducted so that the electromagnetic interactions
between the planar antennas and transmission lines are captured. The inputs and outputs of the
transmission lines are marked with IO. At these ends, the transmission lines are matched
terminated such that only minimal reflections <-10 dB occur. The power coupled to the
transmission line mode is, thus, directed away from the antenna. Notice that the dipole
antenna is not considered in this study because the dipole antenna is not directly placed on the
ground plane. Hence, grounded microstrip lines cannot be routed inside its electromagnetic
antenna boundary.
The microstrip lines are designed for a characteristic impedance of 50 Ω (see Appendix 3).
This corresponds to a width of 500 µm based on the substrate configuration. The transmission
lines are routed orthogonal and parallel to the antennas, denoted as case 1 and case 2,
respectively. Figure 37 shows the simulation results of the relative change of the resonance
frequency Δf of the antennas in dependency of the separation distance d. The corresponding
electrical sizes, as specified by the electromagnetic antenna boundaries, are also depicted for
both antennas. It is observed that the resonance frequencies settle below 0.1 % from their
nominal values with increasing values of d (the nominal values refer to the case where no
additional transmission lines are on the substrate). Close to the antennas, when the
transmission line is routed inside the electromagnetic antenna boundaries, the resonance
frequencies are detuned by over 1 % for the patch antenna and over 0.6 % for the slot antenna.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 56 –
Figure 37: Effects on the resonance frequencies of the antennas for different transmission line separation
distances d.
The detuning in case 1 is attributed to parallel inductive loading increasing the resonance
frequency, whereas in case 2, shunt capacitive loading causes the frequency to decrease.
Figure 38: Effects on the insertion loss of the microstrip transmission line routed inside the antenna
boundaries.
The strong electromagnetic interactions occurring when the transmission line is routed inside
the electromagnetic antenna boundary also have effects on the transmission line parameters.
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 57 –
Consider the simulated transmission coefficient S21 between the IOs of the microstrip line as
depicted in Figure 38. The transmission line has a total length of 6.25 mm in each case.
The transmission coefficient of the microstrip line was simulated in the case that the line is
routed outside the electromagnetic antenna boundary. This is used as a reference. It is
observed that the electromagnetic interactions with the antenna are negligible in this case, and
the insertion loss remains unperturbed. The transmission coefficients of the different
transmission line routing paths in the vicinity of the patch and slot antenna undergo
degradation concerning their attenuation. As can be observed, the fields on the transmission
line strongly couple to the resonance modes of the antennas. The highest transmission loss is
observed at the antenna resonance frequencies.
The results in this subsection have shown that the electromagnetic antenna boundary can be
used to determine the critical region around the antenna where the weak coupling assumption
is not fulfilled. Degradation of the antenna parameters must be considered if transmission
lines are routed within the electromagnetic antenna boundary. Keeping transmission lines
outside the electromagnetic antenna boundary ensures that the antenna parameters are not
altered significantly.
2.3.5.2 Influence of Ground Plane Size
The ground plane of the planar antenna plays a significant role for the distribution of reactive
power density and, hence, the resulting antenna parameters. Therefore, the influence of the
ground plane size on the antenna gain is studied on all three planar antenna configurations.
Figure 39: Illustration of the planar antennas with reduced ground plane sizes.
Consider Figure 39, where the antenna configurations with their respective ground planes are
shown. For illustrative purposes, the substrate is not visible. The parameter d is introduced to
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 58 –
define the ground plane size respective to the physical antenna size. In the case of the patch
and slot antennas, the ground plane sizes are directly related to the patch and slot sizes,
respectively. In the case of the dipole antenna, the distance between the dipole and ground
plane is preserved, since it acts as a reflector and is, thus, part of the antenna. It should also be
noted that the ground plane width and length are varied together as described by d for all three
antennas. The electromagnetic antenna boundaries are evaluated at the distance where the
rectangular size of the ground plane is at least the size as defined by the antenna boundaries
i.e., at d=max{Δl/2, Δw/2}.
The influence of the ground plane size on the antenna gains is studied. Figure 40 shows the
plot of the simulated antenna gains in dependency of the ground plane sizes as described by d.
Figure 40: Simulation results of the effects of reduced ground plane sizes on the antenna gains.
The gain is evaluated in fixed directions. The patch antenna gain is given in positive z
direction. The slot antenna gain is given in negative z direction. The dipole antenna gain is
given in positive x direction. In the case of the patch antenna, the gain gradually increases
with increasing values of d until it stabilizes at approximately 6.5 dBi. This is the value of the
gain that was computed previously for large ground plane dimensions of 25 mm X 25 mm.
The gain of the slot antenna is below 4 dBi for d<1 mm. This can be explained by the reduced
lateral space that the slot current, flowing around the perimeter of the slot, has on the ground
plane. The intermediate ground plane size, before the gain reaches 4.5 dBi for d>4 mm, is
Chapter 2 - Determination of Electromagnetic Boundary of Planar Antennas
– 59 –
explained by an overcompensation of the stray fields. Notice that in the case of the dipole
antenna, the gain is below 0 dBi for d=0.1 mm. Similarly to a Yagi-Uda antenna, the small
ground plane acts like a director (shorted parasitic resonant dipole element) and not as a
reflector and, hence, distorts the desired radiation pattern. For all antenna gain values,
however, it is observed that their maximum changes, for ground plane sizes larger than the
electromagnetic antenna boundaries, are below 1 dB. The gain values settle on larger ground
planes.
Considering these results, it is concluded that the size of the ground is a crucial performance
determining component of planar antennas. The size of the ground plane should be kept at
least larger than the area specified the electromagnetic antenna boundary.
2.4 Summary
In this chapter, an approach for defining the electromagnetic antenna boundary was
introduced. The approach is based on evaluating the distribution of reactive power density
excited by the planar antenna on the ground plane and determining a threshold value.
As a starting point, a theoretical analysis of excited antenna fields was conducted at the
beginning of this chapter in Section 2.2. The complex Poynting vector was used to
characterize the propagating space and surface wave fields as well as the reactive near-fields,
which are excited by planar antennas at board level. Modeling and simulation results for
quantifying the influence of the dielectric substrate and antenna feed on the excited fields
were presented. It was shown that the substrate height and antenna feed have significant
influence on the magnitude of the excited fields of the antenna.
In Section 2.3, simulation and measurement results of three planar antennas, comprising a
patch, slot and dipole configuration for operation at 24 GHz, were presented. The
electromagnetic antenna boundaries were deduced. The influences of microstrip transmission
lines, routed inside the electromagnetic antenna boundaries as well as the effects of finite
ground plane sizes on the antenna gain were quantified.
The results in this chapter have shown that the electromagnetic antenna boundary can be used
to: (1) define the block out region around the antenna where no board components should be
placed; and (2) define the actual electromagnetic antenna size. This is beneficial for the
integration of planar antennas since the antenna can now be treated as an “isolated” board
component with respect to its electrical characteristics.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 60 –
3 Calculation of Coupling to Transmission Lines
In the design phase of a wireless module, it is desirable to determine favorable positions and
orientations of the transmissions lines routed in the vicinity of the planar antenna without
performing extensive full-wave simulations for each possible case. Due to their open field
structure, planar transmission lines are inherently sensitive to coupling from antenna fields.
Thus, they may serve as prototypes of victims. In the previous chapter, an approach for
defining the electromagnetic antenna boundary was developed. Transmission lines, placed
within the electromagnetic antenna boundary, interact strongly with the near-field of the
antenna such that the antenna parameters are potentially degraded. However, antenna fields
also couple to transmission lines placed outside the electromagnetic antenna boundary on the
same substrate. In this case, the weak coupling assumption is fulfilled. Based on this, an
efficient method to calculate coupling is developed.
A typical example of the minimum isolation for an integrated antenna from the system is
given in [101]. Here a maximum tolerable coupling value of -30 dB is required to obtain the
desired bit-error-rate (BER) of 10-6 at the receiver emphasizing the importance of rigorously
examining the influence of undesired coupling during system design.
3.1 Overview of Proposed Method
The proposed method is based entirely on a post processing step to a full-wave field
simulation. This implies that the coupling is calculated based on the previously computed
fields of the antenna. Although the weak coupling assumption is made i.e., the secondary
fields excited on the transmission line have negligible influence on the primary antenna fields,
the coupling is nevertheless reciprocal (see Section 2.2.1.3). All materials considered are
isotropic and linear. Figure 41 shows an overview of the proposed method.
First, the magnetic field components, tangential to and on the ground plane, Hx and Hy, are
computed for the designed antenna configuration. Next, the transmission line parameters of
the transmission line, which is to be routed on the antenna substrate, are computed, using a
2D quasi-static or full-wave solver. The per-unit-length transmission line parameters,
specifically the inductance L´ and capacitance C´ per-unit-length, are extracted. Based on the
routing path p of the transmission line, the distributed current I's and voltage U's sources along
the transmission line are determined. These distributed sources satisfy the inhomogeneous
telegrapher’s equations as will be shown in the next section.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 61 –
Figure 41: Overview of method to calculate coupling from antenna fields to transmission lines.
Figure 42 shows an illustration of a possible transmission line routing path p with all the
relevant parameters. The letter p will be used as the natural parameterization (
0pl≤≤
) for
the transmission line routing path. The terminal voltages U(0) and U(l) are calculated using
the BLT (Baum, Liu, Tesche) integral formulations. Finally, together with the antenna input
voltage Uin, coupling terms between the antenna and transmission line are estimated.
Figure 42: Illustration of method to calculate coupling from antenna fields to transmission lines.
3.2 Development of Coupling Model
In order to derive a model for the coupling of the antenna fields to transmission lines,
distributed sources along the transmission line need to be derived. These distributed sources
Chapter 3 - Calculation of Coupling to Transmission Lines
– 62 –
are integrated over the transmission line path p to obtain terminal voltages at the ends. As a
starting point, the telegrapher’s equations are modified for the inhomogeneous case.
The telegrapher's equations (25) and (26) for the voltage and current on a transmission line
are modified to include the coupling from an external field to the transmission line [56]. To
illustrate this, Figure 43 shows the configuration of a terminated microstrip line on top of a
grounded dielectric substrate. For simplicity, it is assumed that the transmission line is routed
only in x direction i.e., p=x. The derived equations are easily extended to include also a y
directed routing path.
Figure 43: Configuration of a microstrip transmission line on a grounded substrate.
In order to derive the induced voltage on a transmission line from an external magnetic field
excited by the antenna [56], the starting point is intuitively Faraday’s law of induction (2),
written in integral form by employing Stokes’ theorem:
0
AA
Eds j HdA
ωµ
∂
= −
∫ ∫∫
(94)
The contour integral of the electric field is calculated along the perimeter of the signal and
reference conductors. The surface element
dA
is y directed. Considering only one
infinitesimally short transmission line section Δx yields the following expression:
( ) ( )
( ) ( )
( )
00
0
0
,,
,0 ,
,
hh
zz
xx xx
xx
xx
hx x
y
x
E x x z dz E x z dz
E x dx E x h dx
j H x z dxdz
∆∆
∆
∆
ωµ
++
+
+−
+−
=
∫∫
∫∫
∫∫
(95)
Enforcing the condition that the transmission line is lossless simplifies the above equation
significantly since the tangential electric fields Ex on the transmission line are zero.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 63 –
Furthermore, if the height of the transmission line h is small compared to the signal
wavelength, a line voltage can be defined:
( ) ( )
0
,
h
z
U x E x z dz=∫
(96)
The transverse fields on the transmission lines, hence, are assumed to behave as static fields.
The total voltage per-unit-length on the transmission line is given by:
( ) ( )
0
0
,
h
y
dU x j H x z dz
dx
ωµ
= − ∫
(97)
Furthermore, in the case that the substrate height h is assumed electrically short, the integral
can be approximated by a multiplication i.e., the magnetic field is independent of z and the
substrate height h.
( ) ( )
0y
dU x j hH x
dx
ωµ
= −
(98)
Although this is an approximation and only valid for very thin substrate heights, h0, it
shows that the induced voltage per-unit-length is roughly proportional to the magnetic field
orthogonal to the transmission line.
It must be noted at this stage that the magnetic field describes the total magnetic field
comprising the incident field i.e., the excitation field of the antenna Hy,antenna, and the field
from the transmission line mode Hy,tml.
( ) ( ) ( )
( )
0, ,y tml y antenna
dU x j hH x H x
dx
ωµ
=−+
(99)
It is observed that the first term in brackets resembles the per-unit-length inductance L´ of the
transmission line. Therefore, the first telegrapher’s equation with a distributed voltage source
term U´s(x) is deduced directly.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 64 –
( ) ( ) ( )
s
dU x j LI x U x
dx
ω
′
′
+=
(100)
The first telegrapher’s equation is now inhomogeneous because it contains a source term U's.
( ) ( )
0,s y antenna
U x j hH x
ωµ
′= −
(101)
For reasons of simplicity, the magnetic field excited by the antenna will be referred to as Hy
and not Hy, antenna from here on.
( ) ( )
0sy
U x j hH x
ωµ
′= −
(102)
In a similar manner, Ampere’s law (1) can be used to derive the second inhomogeneous
telegrapher’s equation [56]. Here the theorem is applied to a closed surface Ac so that the
integral over the curl of the magnetic field vanishes.
( ) ( )
0
cc
cc
AA
H dA j E J dA
ωε
∇× = = +
∫∫ ∫∫
(103)
Note that Ac is interpreted as a closed cylinder surface of length Δx surrounding the signal
conductor. Considering the directions of both electric field and current density, the following
expression can be set up:
( ) ( )
0
c
c
A
Ix x Ix j EdA
∆ ωε
+− + =
∫∫
(104)
I is the current flowing on the transmission line. Ac denotes the “side wall” of the cylinder.
This is the field theory equivalent formulation of Kirchhoff’s well known circuit law.
The total charge on the transmission line is given by the charge induced by the antenna fields
antenna
q
and the charge of the transmission line mode tml
q
. The charge can also be expressed in
terms of capacitance and voltage.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 65 –
( ) ( )
( )
( ) ( )
( )
c
c antenna tml z
A
j EdA j q x q x j C U x E x h dx
ωε ω ω
′
= += +
∫∫
(105)
Considering the RHS of (105), it is observed that the voltage on the transmission line is split
up into the term U(x) of the transmission line mode and the term Ez(x)h induced by the
antenna fields on the transmission line. Finally, the second inhomogeneous telegrapher's
equation with the distributed current source term I´s(x) is deduced.
( ) ( ) ( )
s
dI x j CU x I x
dx
ω
′
′
+=
(106)
( ) ( )
sz
I x j C hE x
ω
′′
= −
(107)
The electric field can also be expressed in terms of the magnetic field, using Maxwell's first
equation (1).
( ) ( ) ( )
1
z yx
Ex Hx Hx
jx y
ωε
∂∂
= −
∂∂
(108)
At this point, the distributed sources of the transmission line with external excitation by the
antenna fields have been derived. The fields must be integrated along the transmission line,
considering the propagation constant and impedance characteristics of the transmission line in
order to obtain the terminal responses. For this purpose, the BLT (Baum, Liu and Tesche)
equations [56] are used. The transmission line parameters L´, C´ and β must be known.
( ) ( ) ( )
( )
( )
0
0
1
0 exp
2
l
ss
U x U x Z I x j l j x dx
ββ
′′
==−− −
∫
(109)
( ) ( ) ( )
( )
( )
0
0
1exp
2
l
ss
Uxl Ux ZIx jxdx
β
′′
= = +
∫
(110)
Note that the transmission line is assumed impedance controlled and matched at the terminals
such that the reflection coefficients at the loads are small and can be neglected. The
Chapter 3 - Calculation of Coupling to Transmission Lines
– 66 –
transmission line losses are also considered negligible. E.g., the losses of the microstrip
transmission line from Table 10 in Appendix 3 are small (ωL'>>R' and ωC'>>G') and can be
neglected for this analysis. Therefore, the characteristic transmission line impedance Z0 is
real. Expanding these equations yields the following terms.
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
0
0
0
0
0 exp exp
2
exp exp
2
l
y
l
yx
jh
U x j l H x j x dx
ChZ j l H x H x j x dx
xy
ωµ ββ
ββ
ε
= = −
′
∂∂
− −−
∂∂
∫
∫
(111)
( ) ( ) ( )
( ) ( ) ( )
0
0
0
0
exp
2
exp
2
l
y
l
yx
jh
U x l H x j x dx
ChZ H x H x j x dx
xy
ωµ β
β
ε
= = −
′
∂∂
−−
∂∂
∫
∫
(112)
At this stage, the transmission line terminal voltages U(0) and U(l) have been formulated in
dependency of the exciting antenna fields. To estimate the coupling, the antenna terminal
voltage is required. The antenna driving voltage Uin can be estimated based on the input
power Pin and feeding line impedance Z0. Note that the phase of Uin is suppressed. The
antenna should also be matched with a low input reflection coefficient <-10 dB for accurate
results.
0
2
in in
U PZ=
(113)
Now the coupling coefficients are formulated. Only the power transmission is of interest for
the coupling model. Therefore, only the S-parameter magnitudes S12 [dB] and S13 [dB] are
considered respective to the ports (terminals) of the transmission line.
( )
12
0
[ ] 20log
in
Ux
S dB dB
U
=
=
(114)
Chapter 3 - Calculation of Coupling to Transmission Lines
– 67 –
( )
13 [ ] 20log
in
Ux l
S dB dB
U
=
=
(115)
Generalization for an arbitrary routing path p: So far, the coupling model has only been
derived for an x directed transmission line. Transmission lines can be routed arbitrarily in x
and y directions (2D). Therefore, the coupling model needs to be generalized to account for
this. The first step is to modify the distributed voltage and current sources (102) and (107)
along the transmission line to include x and y dependencies, which are included in p.
( ) ( )
0s
U p j hH p
ωµ
⊥
′= −
(116)
( ) ( ) ( )
s yx
Ch
Ip H p Hp
xy
ε
′
∂∂
′=−−
∂∂
(117)
Note the field component
( )
Hp
⊥
is introduced describing the orthogonal magnetic field
component along the transmission line. Secondly, the integration paths of (109)-(112) are
modified for integration along the transmission line path p, which is routed in x and y
direction. With these modifications, the coupling model is generalized for arbitrary 2D
transmission line paths on the ground plane.
As a result, it has been shown that the induced voltage U´s and current I´s per-unit-length on a
transmission line are proportional to the external magnetic field orthogonal to the
transmission line (116) and its spatial derivative (117). Therefore, transmission lines can be
systematically placed, based on the magnetic field distribution excited by the planar antenna
on the ground plane. For this purpose, the magnetic field excited by the antenna is
decomposed into the two tangential components Hx and Hy on the ground plane.
Figure 44 shows a plot of the tangential magnetic field components excited by the 24 GHz
patch antenna on the ground plane. Favorable transmission line positions and orientations can
be deduced qualitatively based on the magnetic field distribution. The marked positions
indicate low, moderate and high potential coupling, respectively. E.g., a critical position for a
transmission line orientated in the same direction as the antenna mode current is at the non
radiating apertures of the patch antenna where the x component of magnetic field is high.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 68 –
Figure 44: Simulation of the magnetic field distribution of the patch antenna split up into the two
tangential components on the ground plane.
Finally, in the following a summary of the simplifications and assumptions of the coupling is
given:
• Weak coupling is assumed i.e., the secondary fields excited on the transmission lines have
no influence on the primary antenna fields. In other words, the transmission line must be
placed outside the electromagnetic antenna boundary.
• Quasi TEM mode wave propagation is assumed on the transmission line so that it can be
modeled with characteristic per-unit-length parameters.
• The effects of transmission line discontinuities are assumed to have negligible influence
on the propagation of the QTEM mode in comparison to a straight transmission line.
• Only the tangential magnetic field components on the ground plane are evaluated to
determine the coupling. The normal magnetic field is assumed zero. This is only valid for
high ground plane conductivity values.
• The spatial dependency of the magnetic field on the height in the substrate is assumed
constant for 0<z<h. This is only valid for electrically small substrate heights h<<λ.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 69 –
• The transmission line is assumed matched at both terminals. Therefore, standing waves
and resulting transmission line resonances are assumed negligible.
Consequently, the accuracy of the coupling model needs to be quantified. This is done in the
next section.
3.3 Quantification of Coupling Model
In order to illustrate the feasibility of using the magnetic field components on the ground
plane to calculate the coupling to neighboring transmission lines, case studies were
conducted, and the results are compared to complete full-wave simulations. The three planar
antenna configurations that were designed and characterized in Section 2.3 are used to
quantify the accuracy of the proposed coupling model. Impedance controlled and matched
terminated microstrip transmission lines were routed in the vicinity of these antennas.
3.3.1 Planar Antenna to Microstrip Line Coupling
Figure 45 shows four possible transmission line orientations in the vicinity of the patch, slot
and dipole antennas denoted cases 1-4. The microstrip line is impedance controlled with a
characteristic impedance of 50 Ω (see Appendix 3 for details on the transmission line
parameters). The line is terminated with 50 Ω lumped ports (p2 and p3) at each end. The
antenna is driven through port p1 at the end of the feeding line.
Figure 45: Overview of the different cases used to study the coupling between the three planar antennas
and the microstrip transmission lines.
In case 1, the microstrip line is parallel to the feeding lines and at the side of the antennas. In
case 2, the microstrip line is orientated orthogonally to the feeding lines and is in front of the
Chapter 3 - Calculation of Coupling to Transmission Lines
– 70 –
antennas. Case 3 has the same transmission line orientation as case 2 but in this case, the
microstrip line is placed beside the antennas. Likewise, case 4 has the same line orientation as
case 1 but the line is placed in front of the antennas. Notice that the ground plane underneath
the dipole antenna is truncated. Thus, grounded transmission lines cannot be placed in front of
and directly beside the dipole element. Therefore, only slightly modified cases 1 and 3 are
considered for the dipole antenna. The separation distance d and transmission line length l
define the location and length of the transmission line on the substrate. Figure 46 shows a
comparison between complete full-wave simulations and the coupling model (field
integration).
Figure 46: Comparison of full-wave simulation with field integration (coupling model) results for the
patch, slot and dipole antenna with l= λ/4 and d=λ/4.
Both parameters d=3.125 mm and l=3.125 mm, corresponding to a quarter wavelength λ at
24 GHz, are selected for this first comparison. The transmission line was routed outside the
electromagnetic antenna boundaries. The results of the coupling model (field integration) are
obtained by evaluating (114) and (115) based on the previously computed magnetic field
distribution of the antenna with no transmission lines on the substrate. To obtain the full-wave
simulation results, the entire transmission line is simulated together with the antenna.
It is observed that a good correlation between full-wave simulation and field integration is
obtained. A discrepancy of less than 1 dB is obtained for all transmission line routing cases
and antenna types. The highest coupling values are obtained for cases 1 and 4 when the
transmission line is parallel to the current anti nodes on the antennas. The coupling to the
dipole antenna for cases 1 and 3 is smaller compared to the coupling in the other cases. This
Chapter 3 - Calculation of Coupling to Transmission Lines
– 71 –
can be attributed to the differential nature of the dipole i.e., the magnetic field strengths
excited by the dipole on the ground plane are smaller than those excited by the patch and slot
antennas (see Figure 32).
Next, the influence of different transmission line lengths l and separation distances d are
studied. For this purpose, the patch antenna configuration is considered. Three values of l,
including 1.563 mm (λ/8), 3.125 mm (λ/4) and 12.5 mm (λ), as well as three values of d,
including 1.563 mm (λ/8), 3.125 mm (λ/4) and 6.25 mm (λ/2), are considered. Notice that in
all cases, the transmission line is again routed outside the electromagnetic antenna boundary.
Figure 47 to Figure 50 show the obtained results for cases 1, 2, 3 and 4. A comparison
between complete full-wave simulation and field integration is conducted.
Figure 47: Comparison of full-wave simulation with field integration (coupling model) results for case 1.
In Figure 47, it is observed that the predicted coupling values obtained by field integration
and full-wave simulation are within 2 dB accuracy in comparison to each other.
Similarly to case 1, the coupling values obtained by field integration and full-wave simulation
for case 2 in Figure 48 correlate well. The biggest discrepancy of 2 dB is observed for the
coupling values of the long transmission line with l=λ.
The separation distance d has more influence on the magnitude of the coupling than the line
length l. The phase and amplitude of the magnetic field are not uniformly distributed along
the transmission line paths. Furthermore, the individual contributions of the distributed
sources along the transmission line are integrated with the appropriate phase of the
transmission line mode yielding constructive and destructive forms of superposition at the
transmission line terminals.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 72 –
Figure 48: Comparison of full-wave simulation with field integration (coupling model) results for case 2.
For case 3, all the coupling values in Figure 49 are well below -40 dB. This results from the
direction of the magnetic flux density being primarily parallel to the transmission line. This is
also observed in Figure 44.
Figure 49: Comparison of full-wave simulation with field integration (coupling model) results for case 3.
The long transmission line with l=12.5 mm is not considered for cases 3 and 4 because a large
portion of the board would be required for routing. Finally, the results of the coupling for
case 4 are depicted in Figure 50. The coupling to p3 is smaller than to p2 since p2 is closer to
the antenna.
As a result, it is concluded that the predicted coupling values using the developed coupling
model yield results with an accuracy of at least 2 dB compared to complete full-wave
Chapter 3 - Calculation of Coupling to Transmission Lines
– 73 –
simulations for a variety of antenna types, transmission line lengths, orientations and
positions.
Figure 50: Comparison of full-wave simulation with field integration (coupling model) results for case 4.
3.3.2 Spectral Response of Complete Transmission Line Path
So far, the transmission line was uniform with no bends. However, in a realistic scenario, a
routed transmission line can have multiple bends. Furthermore, it is of interest to evaluate not
only one frequency point but an entire frequency band around the resonance frequency of the
antenna. Therefore, the coupling model is also quantified for these cases.
Figure 51: Overview of the patch antenna with the two transmission line routing cases with multiple
bends. The x-y coordinates specify the segments of the transmission line.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 74 –
Figure 51 shows the two cases that are used in this study. The microstrip transmission line is
routed past the antenna with two bends. It is matched terminated at the ends (p2 and p3). The
patch antenna is fed through the feeding line at port p1. The coupling is evaluated using the
proposed coupling model (field integration) with the equations (114) and (115). The spectral
response is obtained by evaluating the equations at discrete frequency points from 22 GHz to
26 GHz in 0.5 GHz steps. The magnetic fields of the excited antenna were computed at these
frequency points prior to applying the coupling model.
Figure 52: Comparison of full-wave simulation with field integration (coupling model) results with
spectral response for case 1.
The results are compared to complete full-wave simulations of the antenna and the
transmission line. The frequency response was obtained by extrapolating the solution
frequency at 24 GHz with a sweep. Figure 52 shows the results for case 1.
The coupling is largest at the resonance frequency of the antenna where the excited fields
have maximum magnitude. It is observed that the coupling to p3 is larger than the coupling to
p2. The predicted coupling values by field integration are accurate within 1 dB compared to
the complete full-wave simulation across the entire spectrum of interest.
Figure 53 shows the coupling results for case 2. Again, a satisfactory correlation between the
field integration and full-wave simulation results is obtained across the entire frequency span.
A maximum deviation of 2 dB is observed. The coupling to p2 is slightly higher than to p3.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 75 –
As a result, it is concluded that the proposed coupling model is suitable for efficiently
calculating the spectral response of coupling from planar antennas to neighboring
transmission lines with multiple bends.
Figure 53: Comparison of full-wave simulation with field integration (coupling model) results with
spectral response for case 2.
3.3.3 Simulation Errors caused by Lumped Ports
In the full-wave simulations, the lumped ports are not infinitesimally small such that a
fraction of power couples directly to the ports. The ports are not included in the coupling
model. Therefore, the influence of the ports on the coupling values needs to be quantified.
Figure 54 shows the patch antenna with two different transmission line orientations with and
without the transmission line. With this configuration, the magnitude of the coupling to the
ports was examined.
The coupling to the ports reduces by 23 dB and 19 dB, respectively, for configuration (a)
when the transmission line is removed. For configuration (b), the coupling is reduced by 9 dB
for both ports when the transmission line is removed. These cases are considered a worst case
scenario since the transmission lines and ports are placed directly at the electromagnetic
antenna boundary. It is concluded that the coupling directly to the ports has negligible
influence on the coupling results.
Chapter 3 - Calculation of Coupling to Transmission Lines
– 76 –
Figure 54: 3D simulation models used to study the coupling to the ports for two transmission lines, (a) and
(b), with and without the microstrip transmission line, respectively.
3.3.4 Measurement Results
The full-wave simulation results, which are used to quantify the accuracy of the coupling
model, need to be verified experimentally with measurements. Therefore, test structures of the
patch antennas coupled to the microstrip transmission lines were designed and manufactured.
The antenna is a one port network, and the transmission line is a two port network. Therefore,
a full three port S-parameter measurement is required. With the three port measurement, all
six coupling terms are characterized by magnitude and phase. Since the configurations are
reciprocal, the problem reduces to three coupling terms. One of the three coupling terms is the
transmission coefficient of the transmission line, which is not of interest here. Measurement
results of the transmission line characteristics are presented separately in Appendix 4.
Figure 55 shows photos of two test structures (a) and (b) that were designed and
manufactured. The antenna and transmission lines are contacted with GSG (ground, signal,
ground) probes. At the ports p1, p2 and p3, probe adapters were designed. These comprise
three pads, two of which are shorted to the ground plane with vias. The manufacturing process
and measurement environment is described in Appendix 4.
Since the transmission lines are placed close to the antenna for two test structures, it is
necessary to ensure that the probe adapters are not too close to the patch antenna. This is
necessary to ensure that stray antenna fields do not couple strongly to the GSG probes and,
hence, falsify the measurement results. Furthermore, the probe positioners of the network
analyzer are orientated orthogonally to one another. Therefore, the probe adapters also need to
be orientated orthogonally to one another. For these two reasons, the bends were introduced at
Chapter 3 - Calculation of Coupling to Transmission Lines
– 77 –
the ends of the microstrip lines to facilitate the contacting with GSG probes. These additional
bends are depicted in the simulation models and photos of Figure 55.
Figure 55: Test structures and 3D simulation models used for experimental verification of the simulated
coupling between the patch antenna and the microstrip transmission lines.
Table 5 shows a summary of the measured coupling values of the test structures and a
comparison to the results of the coupling model and complete full-wave simulations. Note
that the effects of the GSG probe adapters are not included in the coupling model, in which an
ideal termination is assumed.
Test structure
Coupling model
Full-wave simulation
Measurement
S12 [dB]
S13 [dB]
S12 [dB]
S13 [dB]
S12 [dB]
S13 [dB]
a
-28
-29
-31
-29
-31
-28
b
-32
-32
-30
-30
-29
-29
Table 5: Comparison of the calculated, simulated and measured coupling values between the patch
antenna and microstrip transmission lines at 24 GHz.
A discrepancy of up to 3 dB is observed between the calculated values based on the coupling
model and the simulation and measurement results. This is traced back to the parasitics of the
GSG probe adapters and GSG probed themselves, which also couple to the fields. However,
the measured coupling values match well with the results from the complete full-wave
simulations. A discrepancy of 1 dB is observed here. The slight differences in measured and
simulated data are also due to numerous effects. Influence factors include calibration
inaccuracies, influences of the GSG probes and technological fluctuations. It must be
Chapter 3 - Calculation of Coupling to Transmission Lines
– 78 –
considered that the excited antenna fields do not only couple to the transmission lines but also
directly to the GSG probes.
As a result, the full-wave simulations have been verified with measurements. Since the full-
wave simulations have been used to quantify the accuracy of the coupling model, the results
of the coupling model have also been verified.
3.4 Summary
In this chapter, a method for efficiently calculating electromagnetic coupling from planar
antennas to neighboring transmission lines has been developed. The main advantage of the
coupling model is that it is based on field integration of the previously computed magnetic
fields on the ground plane of the excited antenna. Therefore, the coupling is calculated
entirely in the post processing phase of full-wave simulations, and the coupling to different
transmission line routing paths can be calculated without performing additional full-wave
simulations for each routing path. By reciprocity, this also includes coupling from
transmission lines, in this case the aggressor, to the antenna. It must, however, be ensured that
the weak coupling assumption is fulfilled i.e., the transmission line must be routed outside the
electromagnetic antenna boundary. Furthermore, it is assumed that the transmission lines are
impedance controlled and matched at the ends.
The accuracy of the coupling model was quantified with a case study. It was shown that the
method is suitable for efficiently obtaining coupling values to neighboring transmission lines
of arbitrary length, with multiple bends as well as the spectral response.
Therefore, the coupling method efficiently supports the integration process of planar antennas
in compact wireless modules by reducing simulation efforts.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 79 –
4 Quantification of Planar Configurations to Reduce Coupling
This chapter focuses on the quantification of techniques to reduce undesired electromagnetic
coupling as well as a comparison of these techniques with regards to shielding effectiveness
and integration density. The focus is on shielding configurations, which can be implemented
on a dielectric substrate with only two metallization layers and vias in order to facilitate low
cost PCB applications.
As a starting point, the E- and H-plane coupling between two patch antennas was simulated
and used as a basis for the comparison i.e., the patch antennas are used as the reference for the
evaluation of the shielding effectiveness. The coupling between two resonant antennas is a
worst-case-scenario. Therefore, the configurations should not be viewed from the point of an
antenna array. The second antenna should rather be interpreted as a surface and space wave
probe. Figure 56 shows two configurations comprising the E- and H-plane coupling cases.
Figure 56: 3D simulation models of the coupled patch antennas including: (1) E-plane case; and (2) H-
plane case.
The patch antennas are based on the same configuration and substrate build up that was used
for the other antennas presented in Section 2.3. The coupling coefficient S21 between the ends
of the feeding lines of the antennas was simulated for different separation distances d at the
resonance frequency of the patch antennas (24 GHz).
Figure 57 shows the simulation results of the coupling. As is observed, the E-plane coupling
is smaller for distances d<2.5 mm. Below this distance, the E-plane coupling between the
antennas is primarily capacitive in nature resulting from the opposing charge densities at the
radiating apertures of the antennas. However, the E-plane coupling "overtakes" the H-plane
coupling for larger distances and does not decay as rapidly. Close to the antenna, where the
H-plane coupling dominates, the primary coupling mechanism is inductive coupling. This
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 80 –
results from the parallel flowing currents on the antennas. It is evident that the inductive
coupling is stronger than the capacitive coupling in the near-field.
Figure 57: Simulation results of the coupling coefficient S21 between the patch antennas at 24 GHz.
The fast decreasing H-plane coupling beyond 2.5 mm is primarily attributed to the space wave
coupling, which decays faster with distance compared to surface wave coupling. To illustrate
this, the coupling is evaluated at a separation distance d of 6 mm and 12 mm, and the
difference is calculated. The difference corresponds to a spatial decay rate of 7 dB/octave.
The theoretical value for the decay rate of the space wave mode is 6 dB/octave. Thus, the
primary coupling mechanism is the space wave. For the E-plane coupling case, on the other
hand, the surface wave is the primary contributor. A decay rate of 3 dB/octave is observed.
This corresponds to the theoretical decay rate for the surface wave mode. As a result, surface
waves can cause significant coupling at board level, especially in the E-plane of patch
antennas.
4.1 Design and Implementation of Shielding Configurations
In the state-of-the-art presented in Section 1.2.2, two main sets of techniques for the reduction
of coupling caused by surface waves were classified. The first approach is to attenuate the
surface wave once it has been launched. The second approach is to design the planar antenna
element in such a way that it does not excite surface waves. Therefore, in Section 4.1.1 and
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 81 –
Section 4.1.2, the results of the design and implementation of two of these configurations are
presented and discussed.
4.1.1 Planar Electromagnetic Bandgap (EBG) Structure
The impedance properties of surface waveguides on grounded substrates can be altered by
integrating special periodic structures with resonance properties. Such structures are known as
electromagnetic bandgap (EBG) structures and prohibit the propagation of surface waves
within a bandgap region. A popular geometry is the mushroom-type EBG structure proposed
by Sievenpiper [65]. This structure has been thoroughly studied in literature and comprises
square metallic patches, which are shorted to the ground plane by vias. Thus, it can also be
manufactured using the same low cost PCB technologies as the planar antenna. The bandgap
region is determined by the resonance frequency of the EBG cell elements. The operation of
the EBG is explained by considering its cross section depicted in Figure 58.
Figure 58: Physical and electrical concept of the mushroom-type EBG structure
The strong magnetic field of the surface wave mode, propagating in the plane of the substrate,
excites a current which flows on the patches, through the shorting vias and over the ground
plane. This forms a current loop between two patches. The current loop is closed by the
displacement current through the gap of the patches. Based on this, an equivalent circuit
model can be extracted. The lumped elements are roughly approximated using the closed
form expressions given in [102]. The inductance L depends on the area enclosed by the
current loop. The height of the substrate is h. This results in a sheet inductance of:
0
Lh
µ
=
(118)
The capacitance C depends on the EBG cell gap spacing g and the EBG patch width w:
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 82 –
( )
1
0
2
1 cosh
r
w wg
Cg
εε
π
−
+
= +
(119)
The relative dielectric constant of the substrate is given by εr. The resonance frequency f of
the EBG cells can be roughly estimated by neglecting edge effects and fringing fields.
11
2
fLC
π
=
(120)
Roughly around the resonance frequency of the EBG cells, the secondary fields, which are
excited on the EBG, counter the fields of the surface wave mode propagating on the grounded
substrate ideally causing a cancellation of the total fields. Thus, the propagation of the surface
wave is ideally completely prohibited. From a circuit model point of view, the EBG cells
behave like a distributed parallel LC filter.
The characteristics of an EBG cell are characterized with a dispersion diagram for the surface
wave mode. In [103], a detailed overview of creating dispersion diagrams for EBG structures
is given. Based on this approach, a dispersion diagram for the above mushroom-type EBG
was created using full-wave simulations.
Figure 59 shows the Brillouin zone of a 2D periodic structure with two planes of symmetry.
In the case that the unit cell is symmetrical with regards to both xz and yz planes, only
combinations of orthogonal wave numbers kx and ky need to be considered. In this case, it is
sufficient to only consider one characteristic triangle in the Brillouin zone [104]
corresponding to one eighth of the entire zone.
Figure 59: Illustration of the Brillouin zone (left) for an EBG unit cell (right).
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 83 –
The corresponding wave numbers of the three paths are defined in the following. For
simplicity, the unit cell side lengths are normalized in this representation.
• Γ to X: kx=0 deg/m to 180 deg/m, ky= 0 deg/m.
• X to M: kx=180 deg/m, ky=0 deg/m to 180 deg/m.
• M to Γ: kx=180 deg/m to 0 deg/m, ky= 180 deg/m to 0 deg/m.
The EBG unit cell was simulated using the eigenmode solver of Ansys HFSS™ (see
Appendix 1). Conductor and dielectric loss are considered by assigning a finite conductivity
to the copper and a dielectric loss tangent to the substrate. Radiation losses (leaky waves) are
also considered. For this purpose, a PML boundary is allocated above the EBG. Master and
slave boundaries are set on the outer faces of the air box in the xz and yz planes. The phases of
the modes are varied according to the defined regions of the triangle. These are simulated for
the lowest order TM0 surface wave mode.
Figure 60: Full dispersion diagram for the space and surface wave modes of the EBG cell.
Figure 60 shows the results of the complete dispersion diagram. In addition to the surface
wave mode, the space wave mode is also shown. It is evaluated by considering the wave
numbers in vacuum.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 84 –
0
2
xy
f
kk c
π
= =
(121)
At low frequencies, the dispersion of the EBG is similar to that of the space wave mode. At
approximately 20 GHz, the resonance properties of the EBG become apparent. It is also
observed that the EBG exhibits a negative dispersion for the TM0 mode propagation. The
lower frequency of the TM0 mode bandgap can readily be determined. Above approximately
23 GHz, the dispersion diagram shows no solution for the TM0 mode. Determining the upper
frequency bandgap involves determining the dispersion diagram of the next higher order TE1
mode. The point of intersection of the TE1 mode with the space wave mode in the dispersion
diagram represents the upper bandgap frequency. However, determining this point of
intersection with sufficient accuracy involves obtaining accurate eigenvalue solutions for the
TE1 mode.
Although the dispersion diagram allows an in-depth analysis of the EBG structure with
respect to surface wave suppression properties, a major drawback results from the fact that the
EBG is assumed to extend to infinity in the lateral plane. Thus, the edge effects of a finite size
EBG are not considered.
In a next step, the analyzed EBG was integrated between the patch antennas (reference
structure). Altogether 15 EBG cells were chosen comprising three rows with five elements
each. Since the EBG has finite lateral dimensions, the edge effects at the ends of the EBG
structure and their influence on the suppression and tuning of the EBG need to be considered.
Therefore, a complete full-wave simulation model was set up, as depicted in Figure 61.
Figure 61: Model of E-plane patch antennas with integrated EBG for the suppression of coupling.
To determine the values of the EBG for suppression of surface waves at 24 GHz, the
analytical expressions (118)-(120) were used as a first approximation and fine tuned with full-
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 85 –
wave simulations. In order to obtain high capacitance between the cells and, hence, ensure
minimum EBG cell dimensions at 24 GHz, a small value of the cell gap g was chosen such
that manufacturing with PCB technologies is still possible. The parameters w=1.85 mm and
d=300 µm were designed with the given εr=3.75, t=17.5 µm and h=250 µm values of the
substrate technology.
In order to achieve high integration densities, it is desirable to place the antenna close to the
EBG. Therefore, the influence of the edge-to-edge distance a is studied on the suppression
properties of the EBG for the E-plane coupling case where the surface wave is excited and
propagates. Figure 62 shows the simulation results.
Figure 62: Simulation results of the coupling coefficient S21 between the E-plane coupled patch antennas
in dependency of the separation distance a.
The edge-to-edge separation distance between the antenna elements and the EBG is a=2 mm
(0.16 λ). At this distance, the electromagnetic interactions between the antenna’s reactive
near-field and the EBG is negligible i.e., the antennas are not significantly detuned by the
presence of the EBG. The EBG is placed outside of the electromagnetic antenna boundary.
The coupling between the patch antennas with the EBG is -37 dB with a separation distance
a=2 mm. As is observed, the EBG improves the suppression between the patch antennas by
12 dB compared to the case without the EBG. However, the plots also show that below a
critical separation distance, in this case a=0.8 mm (0.06 λ), the EBG causes a degradation of
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 86 –
the coupling suppression between the patch antennas. The electromagnetic interactions at the
antenna near-field cause a shift in impedance parameters of the EBG.
However, in order to allow a high integration density, the EBG may need to be placed closer
than the critical distance to the antenna i.e., inside the electromagnetic antenna boundary. It is
shown next that the EBG can be tuned to operate with high suppression when it is placed
closer to the antenna.
To compensate the additional capacitive loading of the patch antenna, the EBG patch size is
increased slightly. By this means, the inductance L in (118) remains constant and the
capacitance C in (119) is increased slightly. With the aid of numerical simulations, the EBG
patch dimensions were optimized for suppression at a distance of a=400 µm. The square EBG
patch size is altered from w=1.85 mm to w=2.05 mm. The gap g between the patches remains
at 150 µm. Figure 63 shows the simulation results of the coupling coefficients as well as a
comparison with the conventional EBG structure. As is observed, the suppression of the
optimized EBG is substantially improved compared to the conventional EBG for separation
distances a<1 mm. The suppression of the optimized EBG has a maximum at a=400 µm
where the suppression is 27 dB higher compared to the conventional EBG. However, for
larger distances, the conventional EBG performs better. The optimized EBG only operates
well close to the antenna, where it is capacitively coupled to the reactive near-field.
Figure 63: Simulation results of the coupling coefficient S21 between the E-plane coupled patch antennas
in dependency of the separation distance a.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 87 –
Ideally, the EBG structure has no influence on the antenna parameters. However, since the
optimized EBG is placed at a=400 µm within the electromagnetic antenna boundary, changes
in the antenna parameters also need to be considered. This is shown further on in
Section 4.1.3.
4.1.2 Planar Surface Wave Reduced (SWR) Antenna
In order to reduce the high E-plane coupling between the patch antennas, it is also possible to
design the antenna in such a way that it does not excite surface waves or only reduced surface
wave power. Such antenna configurations are referred to as surface wave reduced (SWR)
antennas. In this section, the results of the implementation of a SWR patch antenna are
presented, and the shielding effectiveness as well as the required board space are
characterized.
A commonly used planar geometry for SWR antennas is a circular patch. The general
approach of analysis is to introduce an equivalent magnetic current density (37) along the
outer contour of the patch resonator. The magnetic current density is then regarded as the
source, and the fields are calculated. Finally, the critical radius of the circular patch is
determined such that the TM0 surface wave mode is not excited. The smallest patch radius rp
with respect to the surface wave phase constant βTM0 to obtain this condition was derived by
Jackson et al. [82].
0
1.84
TM p
r
β
≈
(122)
Based on this analysis and on the theory presented by Jackson et al., a circular patch antenna
with critical radius was designed for operation at 24 GHz.
Figure 64: Configuration and dimensions of the designed SWR patch antenna.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 88 –
The circular patch antenna design is based on the design of an annular ring antenna [105]. An
inset feed is employed to excite the antenna. Figure 64 shows the dimensions of the SWR
patch antenna, which was designed on the same substrate configuration as the other antenna
designs in this work (see Section 2.3).
The radius of the SWR patch resonator rp=3.75 mm. The inset feed for impedance matching is
positioned at the distance s=0.9 mm from the outer edge of the patch. The gap g=0.25 mm,
and the impedance controlled microstrip line has the width w=0.5 mm. The circular via fence
is placed at the distance lv=1.5 mm from the outer perimeter of the patch and is used to tune
the resonance frequency. The standing wave is formed between the outer open circuit of the
patch and the inner shorted circular via fence enforcing a λeff/4 resonance. Therefore, lv is a
sensitive and technologically critical parameter for the resonance frequency of the antenna.
Figure 65 (b) shows the SWR antenna and its excited current distribution at 24 GHz. The
current distribution on the conventional rectangular patch antenna is shown in Figure 65 (a).
In comparison, the conventional patch excited with the lowest order TM mode only has one
current anti node at the center.
Figure 65: Surface current distribution: on the excited (a) conventional patch antenna; and on the (b)
SWR antenna. The arrows indicate the direction of the current anti nodes.
The current on the SWR antenna flows primarily on the via fence. At the center of the patch,
only small leakage currents are observed. The outer ring between the via fence and the
radiating apertures can be described as a shorted parallel plate waveguide excited with its first
higher order mode (enforced by the shorting wall). The current anti nodes caused by the
resonance on the circular ring are both x directed. However, since the separation distance of
the two current anti nodes is approximately one half wavelength at 24 GHz, the surface waves
launched in positive and negative x direction are eliminated by destructive interference.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 89 –
Figure 66 shows a comparison of the simulated and measured reflection coefficient of the
SWR antenna. The fabrication process is highlighted in Appendix 4.
Figure 66: Measurement results of the reflection coefficient S11 of the SWR patch antenna and comparison
to full-wave simulation.
It is observed that the antenna resonates at about 23 GHz with an impedance bandwidth of
700 MHz. The measured resonance frequency is slightly lower than the envisaged resonance
of 24 GHz during the design of the antenna. This shift is due to technological fluctuations of
the PCB prototype. The resonance frequency of the SWR antenna is particularly sensitive to
the positions of the shorting vias. Therefore, the simulations were adapted slightly after
fabrication and measurement. The simulated bandwidth is also slightly lower with 500 MHz.
The additional losses are a result of the via fence, which is fabricated using a conductive
polymer paste yielding lower conductivity values compared to conventional copper vias. The
additional losses reduce the antenna Q factor resulting in an increased impedance bandwidth.
Next, the electromagnetic antenna boundary of the SWR antenna is also evaluated. Figure 67
shows the simulated reactive power density on the ground plane of the SWR antenna. The
same approach as already implemented in Section 2.3.5 is used to deduce the electromagnetic
antenna boundary.
The width w=2rp and length l=2rp are introduced for better comparison with the conventional
patch, slot and dipole antennas. The threshold value of the SWR antenna was calculated using
(93). The SWR antenna parameters including the radiation efficiency η=67 % were computed
resulting in a threshold value of 13.5 mW/mm2.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 90 –
Figure 67: Simulation of the reactive power density on the ground plane of the SWR patch antenna.
The same procedure for estimating the electromagnetic size of the antenna, given by l+Δl and
w+Δw, is applied. Table 6 shows the results in comparison to the conventional patch antenna.
Antenna
Dimensions
Physical size
Electrical size
l [mm]
w [mm]
Area [mm2]
l+Δl [mm]
w+Δw [mm]
Area [mm2]
Conventional patch
3.175
4.25
13.5
4.6
6.5
29.9
SWR patch
7.5
7.5
56.3
8.8
9
79.2
Table 6: Deduced electromagnetic antenna boundary values of the SWR patch antenna and comparison
to the conventional patch antenna.
The physical and electromagnetic dimensions of the SWR antenna are significantly larger
than the patch antenna. The SWR antenna requires more board space.
The shielding effectiveness of the SWR antenna is characterized next by considering the
E-plane coupling and comparing the results to the results of the conventional patch antennas
in Figure 56.
Figure 68: 3D simulation models of the coupled antennas: (1) conventional patch antennas; and (2) SWR
patch antennas.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 91 –
Figure 68 shows the 3D simulation models that were used for the shielding effectiveness
characterization. Figure 69 shows the simulation results of the E-plane coupling for different
separation distances d.
Figure 69: Simulation results of the coupling coefficient S21 between two conventional patch antennas and
two SWR patch antennas.
In the near-field of both the conventional and SWR antenna, capacitive coupling at the
radiating apertures dominates, and the coupling decay with distance is similar up to a distance
of 1 mm. This shows that the SWR antenna is not effective in reducing capacitive near-field
coupling. This is also approximately the distance where the electromagnetic antenna boundary
exists, indicating that the antennas couple power through the reactive near-field. Beyond this
distance, the surface wave coupling dominates for the conventional patch antenna. In the case
of the SWR antenna, neither the space wave nor the surface wave coupling dominates. It is
observed that the coupling decays with 11 dB/octave distance, which is faster than the space
and surface wave decay rates with distance. Thus, the SWR patch antenna effectively reduces
the E-plane coupling by suppressing surface wave and lateral space wave excitation in the E-
plane.
4.1.3 Comparison of Configurations and Measurement Results
The shielding effectiveness of the EBG structure and the SWR antenna were verified with
measurements. For this purpose, test structures for measuring the coupling were
manufactured. Figure 70 shows photos of the test structures. The geometrical and material
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 92 –
properties of the structures correspond to those of the simulation models in the previous
sections.
Figure 70: Photos of the test structures used to measure the coupling: (1) conventional patch antennas; (2)
patch antennas with EBG structure; and (3) SWR patch antennas.
It is noted that the separation distance d between the patch antennas of 7.25 mm is slightly
larger than between the SWR antennas of 6 mm. This was necessary to integrate the EBG
structure between the patch antennas. The reflection coefficients of the antennas S11 and
transmission coefficients between the antennas S21 were measured for all test structures. Since
the structures are symmetrical, the coefficients S22=S11 and S12=S21. Figure 71 shows the
measurement results.
Figure 71: Comparison of coupling measurement results: (a) conventional patch antennas; (b) patch
antennas with EBG structure; and (c) SWR patch antennas.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 93 –
The coupling is evaluated within regions marked (a), (b) and (c) in the plot. These represent
the frequency ranges around the resonance frequencies of the antennas. Note that the
resonance frequency of the SWR antenna is approximately 23 GHz, slightly lower than the
envisaged 24 GHz. Table 7 summarized the results.
Patch antennas
(Region a)
Patch antennas with EBG
(Region b)
SWR antennas
(Region c)
Coupling [dB]
-25
-40
-37
Table 7: Evaluated coupling values of the three configurations.
The coupling between the patch antennas is -25 dB. This matches well with the simulation
results in Figure 57 and Figure 62. At the resonance frequency of the patch antenna, the EBG
provides coupling of -40 dB. Therefore, the shielding is improved by 15 dB. In comparison,
the simulation results (see Figure 63) predicted a coupling of -43 dB, which is only slightly
lower than the measured coupling.
The resonance frequency of the patch antennas is slightly influenced by the presence of the
EBG. The impedance bandwidth is decreased slightly. Furthermore, at antenna resonance, S11
of the patch antenna is reduced to -20 dB. This results from the presence of the EBG inside
the electromagnetic antenna boundary. The EBG was, however, optimized to reside at the
near-field of the patch antenna for direct coupling through the reactive near-field. Concerning
the SWR antennas, it is observed that the coupling is lower than -37 dB. The measurement
results match well with the simulation results in Figure 69 at a distance of 6 mm.
Configuration
EBG integration
SWR antenna
Suppression
15 dB
16 dB
Occupied board area
13.5 mm2 + 70 mm2
13.5 mm2
42 mm2
Percentage area increase
520 %
147 %
Table 8: Comparison of shielding effectiveness and required board space between EBG structure and
SWR patch antenna.
Finally, a comparison of the shielding effectiveness of both shielding configurations is
conducted. For this purpose, the coupling between the antennas is evaluated at a fixed
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 94 –
distance. The separation distance d between the patch antennas with integrated and optimized
mushroom-type EBG structure of 7.25 mm is selected. In the case of the SWR antenna, the
reduction of the coupling between the SWR antennas at a distance of d=7.25 mm is evaluated.
The results are summarized in Table 8.
The additional space, required by the EBG structure, is calculated by evaluating the total area
of the EBG. Approximately 70 mm2 of additional board space is required. The SWR antenna
occupies more than three times the area compared to the conventional patch antenna. In total,
however, the SWR antenna occupies less board space and at the same time provides higher
shielding effectiveness than the EBG structure.
4.2 Coupling between SWR Antenna and Transmission Lines
The SWR antenna has improved performance compared to the EBG structure with regards to
shielding effectiveness and required board space. In order to illustrate its feasibility for system
integration with transmission lines, the coupling to the same transmission line routing path as
already evaluated in Section 3.3.2 was simulated with the SWR patch antenna. Figure 72
shows the configuration with the two transmission line routing paths.
Figure 72: Overview of the SWR patch antenna with the two microstrip transmission line routing cases
with multiple bends. The x-y coordinates specify the absolute routing path of the transmission line.
Note that the transmission lines are routed outside the electromagnetic antenna boundary of
the SWR antenna (see Figure 67). Also note that the transmission lines are closer to the SWR
antenna in comparison to the patch antenna and the transmission lines in Figure 51. The SWR
antenna occupies 147 % more board space than the conventional patch antenna.
Chapter 4 - Quantification of Planar Configurations to Reduce Coupling
– 95 –
Since the transmission lines are routed outside the electromagnetic antenna boundary, the
weak coupling assumption is valid. The microstrip transmission line has a characteristic
impedance of 50 Ω and is matched terminated at the ports p2 and p3. The coupling is also
reciprocal (see Section 2.2.1.3). The coupling terms S21 and S31 are computed using full-wave
simulations. Table 9 shows the results and a comparison with the conventional patch antenna.
Case
Conventional patch antenna
SWR patch antenna
Improvement [dB]
S12 [dB]
S13 [dB]
S12 [dB]
S13 [dB]
ΔS12 [dB]
ΔS13 [dB]
1
-32
-26
-43
-31
11
5
2
-30
-32
-30
-30
0
-2
Table 9: Comparison of simulated coupling to the transmission lines for cases 1 and 2.
The coupling in case 1 is reduced by 11 dB to p2 and 5 dB to p3 compared to the conventional
patch antenna, respectively. For case 2, the coupling to p2 remains the same and is increased
slightly to p3, respectively. This is mainly attributed to the closer transmission line spacing.
Also note that the current anti nodes on the SWR antenna are not located at the origin of the
coordinate system but shifted slightly in positive and negative x direction (see Figure 65).
Therefore, the current anti nodes are even closer to the transmission line for case 2.
Nevertheless, the SWR patch antenna does effectively reduce coupling in case 1. Therefore,
its feasibility for integration with transmission lines at board level is concluded.
4.3 Summary
Two planar shielding configurations, suitable for low cost PCB applications, were designed,
implemented and characterized with regards to shielding effectiveness and required board
space. Only two metallization layers are required to manufacture the structures. The SWR
antenna obtains a higher shielding effectiveness while simultaneously occupying less board
space than the EBG structure. It was also shown that the SWR antenna is suitable for
integration with transmission lines, lowering the coupling to neighboring traces. As a result,
the SWR antenna design is considered an appropriate technique for reducing undesired
coupling and efficiently utilizing available board space.
Chapter 5 - Design Recommendations, Conclusions and Outlook
– 96 –
5 Design Recommendations, Conclusions and Outlook
This work focused on three essential aspects for facilitating efficient board level planar
antenna integration at (quasi) millimeter-wave frequencies:
• An approach for determining the electromagnetic antenna boundary for planar antennas
was developed, defining the block out region around the antenna where no board
components should be placed when the antenna is integrated at board level.
• A method for calculating coupling to transmission lines routed outside the
electromagnetic antenna boundary on the same substrate was developed, allowing
efficient evaluation of coupling in the post process to 3D full-wave electromagnetic field
simulations.
• Two planar shielding configurations, comprising an EBG structure and a SWR antenna
suitable for integration on low cost PCBs, were quantified. It was shown that the SWR
antenna reduces coupling while efficiently utilizing available board space.
Figure 73: Overview of an optimized design process for planar antenna integration including the
approaches, methods and results proposed in this work.
Chapter 5 - Design Recommendations, Conclusions and Outlook
– 97 –
The proposed approaches, methods and results significantly reduce the required full-wave
simulation efforts as well as trial-and-error iterations during the design process of compact
and low cost wireless modules.
Figure 73 shows an overview of an optimized design process for planar antenna integration,
considering electromagnetic interactions at board level with the aim of minimizing these.
1) The maximum tolerable coupling values between the planar antenna and neighboring
board components are estimated prior to integration. Note that this coupling is primarily
governed by the coupling between the antenna and transmission lines routed on the same
substrate. Parameters such as the transmit power, receiver sensitivity, link budget and
required signal-to-noise ratio also need to be considered for this estimation.
2) The planar antenna configuration is selected and implemented on the substrate
configuration. The choice of antenna type is mainly influenced by the desired radiation
characteristics (above/below of or in lateral direction to the ground plane), the required
impedance bandwidth as well as on the available ground plane size and topology. Full-
wave simulations are required in the design and optimization phase of the planar antenna.
The considered 24 GHz planar antennas in this work have the following characteristics:
a. The patch antenna has 6.5 dBi gain in the direction normal to the ground plane, an
impedance bandwidth of 500 MHz (2 %) and a radiation efficiency of 80 %. The
physical dimensions are 4.25 mm x 3.175 mm (0.34 λ x 0.25 λ).
b. The slot antenna has 4.5 dBi gain in normal direction above and below the ground
plane, an impedance bandwidth of 1 GHz (4.2 %) and a radiation efficiency of
90 %. The physical dimensions are 4.5 mm x 0.15 mm (0.36 λ x 0.01 λ).
c. The dipole antenna has 5 dBi gain in lateral direction to the ground plane, an
impedance bandwidth of 9.5 GHz (39.6 %) and a radiation efficiency of 94 %. The
physical dimensions are 5.95 mm x 0.75 mm (0.47 λ x 0.06 λ). Note that a
separation distance between the dipole and the ground plane is required. Therefore,
the total dipole width from the ground plane is 2.1 mm (0.17 λ).
Chapter 5 - Design Recommendations, Conclusions and Outlook
– 98 –
3) In the next step, the electric and magnetic fields on the substrate are computed once for
the optimized antenna design. These are used for the determination of the electromagnetic
antenna boundary and for calculating the coupling to neighboring transmission lines.
4) Based on this field distribution, the electromagnetic antenna boundary is deduced by
evaluating the reactive power density and its threshold value. The threshold value is
calculated using the resonance frequency, input power (with which the antenna fields were
computed), efficiency and return loss of the antenna. Regions around the antenna with
lower reactive power densities as specified by the threshold value are considered to be
outside the electromagnetic antenna boundary. Board components placed there have
negligible influence on the antenna parameters.
The considered planar antennas in this work have the following electromagnetic sizes as
defined by their electromagnetic antenna boundaries:
a. Patch antenna: 6.5 mm x 4.6 mm (0.52 λ x 0.37 λ)
b. Slot antenna: 5.5 mm x 2.7 mm (0.44 λ x 0.22 λ)
c. Dipole antenna (including the required separation distance from the ground plane):
9 mm x 3.75 mm (0.72 λ x 0.3 λ)
The ground plane sizes of the antennas should always be kept larger than the
electromagnetic antenna boundary when the antenna is integrated. The ground plane
should also remain unperturbed inside the electromagnetic boundary.
5) Next, the coupling between the planar antenna and different transmission line routing
paths outside the electromagnetic antenna boundary can be evaluated to assist in board
component placement and signal interconnection. The coupling model allows fast and
efficient evaluation of coupling. Some design guidelines are summarized in the following:
a. Coupling from planar antennas to impedance controlled transmission lines and
vice versa is typically maximal around the resonance frequencies of the antenna.
Chapter 5 - Design Recommendations, Conclusions and Outlook
– 99 –
b. Routing transmission lines outside the electromagnetic antenna boundary ensures
that the antenna characteristics remain unperturbed.
c. Coupling values above -30 dB need to be considered, if transmission line segments
are routed close to the antenna at distances smaller than λ/4.
d. Individual transmission line segments should be routed orthogonally to the antenna
mode currents when placed close to the antenna for distances between up to λ/2. In
general, the transmission line segments should also not be routed orthogonally to
the computed magnetic field on the ground plane in order to reduce the magnitude
of the excited equivalent sources along the transmission line.
e. The transmission line length has a less significant influence on the magnitude of
the coupling than the separation distance of the transmission line from the antenna.
To minimize coupling, a long transmission should rather be routed far away from
the antenna.
f. The dipole antenna, being a differential configuration, inherently has the lowest
coupling values to transmission lines <-45 dB for the cases considered in this
work.
6) If the coupling values exceed the tolerable levels as governed by the application, a planar
shielding configuration may need to be implemented. The additional required board space
of the two shielding configurations considered in this work are summarized as follows:
a. The mushroom-type EBG structure comprising 15 elements needs to be integrated
on the substrate beside the antenna where the surface waves are launched into the
substrate. It occupies an area of 10.85 mm x 6.45 mm (0.87 λ x 0.52 λ). Note that
the EBG was optimized to operate in the near-field of the patch antenna.
b. The SWR patch antenna has 7.5 dBi gain in the direction normal to the ground
plane, an impedance bandwidth of 500 MHz (2 %) and a radiation efficiency of
67 %. The circular patch has a diameter of 7.5 mm (0.6 λ). In comparison to the
Chapter 5 - Design Recommendations, Conclusions and Outlook
– 100 –
conventional patch antenna, it occupies 147 % more board space. The
electromagnetic antenna boundary is located at 8.8 mm x 9 mm (0.7 λ x 0.72 λ).
7) If the coupling values are within tolerable limits for the desired board space, the layout of
the antenna and favorable transmission line routing paths are extracted.
The configurations studied throughout this work were designed and implemented primarily
for the 24 GHz frequency range where an ISM band is available. The implemented patch, slot,
dipole and SWR antennas were manufactured using low cost PCB technologies to save cost
and also show the feasibility of employing PCBs for the realization of planar antennas at these
high frequencies. Nevertheless, the developed concepts are applicable to different substrate
technologies, antenna configurations and operating frequencies. In general, substrate materials
used for RF applications can be considered linear and isotropic. As a result, the antenna itself
is a linear and isotropic system. Therefore, it is geometrically and electrically scalable.
The approach for determining the electromagnetic antenna boundary and the method for
calculating coupling to transmission lines could be implemented in software for automated
and fast analyses. For this purpose, the field distribution of the designed antenna, the
geometrical layout of the antenna and the antenna parameters are imported into the software.
The software then deduces the electromagnetic antenna boundary. After this, the user can
route different transmission line paths (with specified transmission line parameters) while the
software calculates the coupling by field integration in real time. As a result, different routing
paths can be evaluated on-the-fly.
It is expected that planar antennas will play a significant role in future compact wireless
systems operating at millimeter-wave frequencies. However, the design and integration of
antennas remains simulation intensive. Therefore, the development of closed form
expressions for the field decay on the substrate and ground plane near patch, slot and dipole
antennas would facilitate on-the-fly estimations of the electromagnetic interactions.
Furthermore, an implementation of these models even in RF circuit simulators would seem
imaginable.
Appendices
– 101 –
Appendix 1 - Overview of Full-wave Electromagnetic Field Simulations
Analytical closed form solutions to the wave equation are only available for simple radiating
structures. The accurate calculation of fields for more complex radiating structures, such as
planar antennas, requires Maxwell’s equations to be solved numerically. Commercially
available full-wave solvers are based on the finite element method (FEM), finite difference
(FD) method, finite integration (FI) method and the method of moments (MoM) in both time
and frequency domains [106, 107]. The solver used in this work is based on the FEM in the
frequency domain, which is implemented in the commercially available software suite High
Frequency Structure Simulator (HFSS™) from Ansys (formerly Ansoft).
The FEM in the frequency domain solves the inhomogeneous vector wave equation for the
electric field obtained from substituting the first two of Maxwell’s equations (1) and (2)
assuming time harmonic fields.
10E j E jJ
ωε ω
µ
∇× ∇× − + =
(123)
The material constants can be set complex to account for dielectric and magnetic losses. The
matrix equation is derived such that the residual is minimized for the entire domain. For this
purpose, (123) is multiplied with a vector weighting function
i
G
and integrated over the
entire domain V to form the weighted residual equation
( )
FE
.
( )
10
i
V
F E E j E j J G dV
ωε ω
µ
= ∇× ∇× − + =
∫∫∫
(124)
Commonly tetrahedral elements Tk are used as finite elements to discretize the computation
domain because they can be naturally fitted to many geometrical shapes. The interpolating
functions
k
n
N
for each finite element Tk are chosen so that the electric field inside the element
can be described.
6
1
k kk
nn
n
E NE
=
=∑
(125)
Appendices
– 102 –
n references the edges of the tetrahedron, which are connected through the four vertices. Two
and three tangential components of the electric field are stored at the edges and vertices,
respectively, yielding a total of 24 complex values per tetrahedron.
Antennas are considered an open boundary problem. Solving differential equations, however,
requires the specification of boundary conditions. Reflection-free truncation of the
computation volume is an inevitable measure to reduce the computational cost that would be
necessary to simulate an open boundary problem with conventional boundary conditions such
as perfect electric conductor (PEC) or perfect magnetic conductor (PMC) boundaries. These
enforce surfaces with a reflection coefficient of 100%. They would have to be placed at a
large distance away from the radiating structure to ensure that the reflected wave is attenuated
enough to not disrupt the field configuration of the simulated structure. Therefore, a perfectly
matched boundary condition (PML) is implemented in FEM solvers to provide reflection-free
terminations of the computation volume. The complex anisotropic material of the PML is
chosen to ensure reflection-free matching of the PML to the free space impedance for all
incident angles, polarizations and frequencies [108].
Figure 74: Concept of PML boundary conditions at the sides of the computational domain to provide low
reflections absorbing boundaries.
A PML configuration is matched to a vacuum with the matching condition:
0
0
[]
[]
µµ
εε
=
(126)
The anisotropy of the permeability and permittivity are described with tensors, [µ] and [ε], in
order to ensure impedance matching and attenuation in z direction.
Appendices
– 103 –
0
[] [ ]
ε εΛ
=
(127)
0
[] []
µ µΛ
=
(128)
The tensor entries must obey the following condition:
1
00
[] 0 0
00
s
s
s
Λ
−
=
(129)
Furthermore, the entries are complex to ensure attenuation.
s a jb= −
(130)
The imaginary part b is used to model the electric and magnetic conductivities i.e., the losses,
and the real part a models the phase of the wave propagation in the PML. The PMLs are
truncated by either PECs or PMCs and must be thick enough to ensure high attenuation of the
reflected wave. It is interesting to note that the imaginary parts of the z components of the
above tensors are negative (different leading sign to the x and y components) implying the
existence of electric -κeEz and magnetic -κmHz sources within the PML materials.
The radiating structure is surrounded by a 3D box. Additional PML edge elements are
introduced at the edges and sides to ensure a complete reflection-free outer box surface. The
impedance matching condition (126) is also applied to these elements. Figure 75 shows a
possible 2D configuration comprising one corner element.
Figure 75: Concept of PML edge elements at the corner of the box.
Appendices
– 104 –
High frequency models are excited by applying an exciting field distribution somewhere
inside or on the surface of the computation domain. For practical applications the excitation
(source) is a microstrip or coaxial mode on a transmission line. Since these modes are
boundary conditions for the source regions, they must be computed before the field
distribution inside the computational volume is solved. In the frequency domain, a harmonic
time dependency
~
jt
e
ω
is assumed. The electric field pattern for mode n is described as:
( ) ( )
,,, ,
zjz
nn
E xyz E xye
αβ
ω
−−
=
(131)
The computation of the S-parameters requires an accurate determination of the time averaged
power density
( )
,,S xyz
propagating in and out of the port for each desired mode. Hence, a
high accuracy of the 2D port field solution
( )
,
n
E xy
is vital. The time averaged total complex
power P of the mode can be evaluated at the cross section of the port.
( )
0
,,P S x y z z dxdy= =
∫∫
(132)
Concerning the stability of the computed field solution of the FEM, an adaptive mesh
refinement is employed in the field solver. The simulation process is divided into a number of
steps. First, a geometrical model of the antenna is set up with the 3D modeler. Material
parameters, boundaries and excitations are defined. A solution setup is created with a solution
frequency corresponding to the expected resonance frequency of the antenna. Next, a
frequency sweep is defined covering the entire frequency range of analysis.
After the simulation is started, the field patterns that exist on the defined cross section of the
ports are solved with a 2D full-wave solver. These patterns are used as boundary conditions
for the excitation. Then the initial mesh is seeded in the computational domain and the field
quantities and S-parameters are computed when the structure is excited with the solution
frequency. To obtain a stable solution, the mesh is refined, and the solution is computed
again. The maximum change ΔS is calculated:
( )
1
max
NN
ij ij
S SS
∆
−
= −
(133)
Appendices
– 105 –
From here on, the mesh is refined after each pass until a convergence criterion is met. Once a
stable solution is found, the sweep is executed, which extrapolates the field solution at the
solution frequency over the desired frequency range.
Appendix 2 - Examination of Numerical Solution Accuracy
Numerical computation results are approximations of the solutions to the wave equation.
Therefore, measurements need to be conducted on manufactured prototypes in order to give a
validation of the simulation results. It was observed in the studies in Section 2.2.3 that the
dynamic range of the field magnitudes is several orders of magnitudes down to -50 dB from
the values of the fields underneath the patch antenna. Furthermore, differences at the order of
1 dB were evaluated. Therefore, the accuracy and stability of the numerical full-wave
simulations need to be quantified. This includes the following: (1) quantification of the
influence of the automatically generated and refined mesh on the computed fields after each
pass; and (2) quantification of the influences of the solver settings (port mode refinement,
mesh refinement and absorbing boundary conditions) on the computed fields.
For these quantifications, the simulated magnetic field magnitude in region 1 of the probe fed
patch antenna is used (see Figure 20). In all simulations, the adaptive mesh refinement
process was used to ensure stability of the computed solution. At least eight passes with a
mesh refinement of 30 % were computed. Furthermore, it was ensured that at least three
consecutive passes with a maximum change of the S-parameters of 0.01 were computed. A
wave port was used as an excitation to feed the antenna from coaxial feeding line.
Figure 76 shows the results of the adaptive mesh refinement i.e., the change of the magnetic
field strength at three defined distances (0.125 λ0, 0.425 λ0 and 0.725 λ0 from the patch
center). It is observed that after the fourth pass the change in magnetic field strength is less
than 0.5 dB indicating that the field solution has converged.
The accuracy of the field pattern on the wave port can be specified within HFSS™. The
solver computes the solution for the 2D wave equation of the mode pattern for the electric and
magnetic fields independently. Then, the solutions are compared to each other through the
mode impedance and an error is determined. The triangular mesh on the port face is refined
until this error is below a defined value. For the quantification, two values of the port field
refinement are compared: 2 % and 0.01 %.
Appendices
– 106 –
Figure 76: Change in magnetic field strength on the ground plane of the patch antenna in region 1 in
dependency of the computed passes.
The mesh in the computation domain is generated and refined automatically by HFSS™.
However, it is also possible to define a maximum cell size manually. In order to ensure that
the spatial field resolution is captured with high accuracy, a maximum mesh cell size of 0.3 λ0
was assigned on the substrate and ground plane. First order base functions were used to
describe the fields inside the mesh elements. The automatic mesh generated approximately
20000 mesh elements in the entire computation volume including the PML volumes. For the
manual mesh a total number of approximately 80000 mesh elements were generated after nine
passes with a maximum refinement of 30 %. For the quantification, the results of the
automatic mesh are compared to the manual mesh with a maximum cell length of 0.3 λ0 on
the substrate. Figure 77 shows the (a) automatically generated and refined mesh and (b)
manually generated and refined mesh. The results of both solutions are compared.
In all simulations, the PML boundary conditions implemented in HFSS™ were used.
However, radiation boundary conditions can also be specified. These boundary conditions
approximate the fields of the tangential field components on the boundary in a 1 D wave
equation. However, unlike PML boundaries, which ideally absorb plane waves at all
frequencies, incident angles and polarizations, radiation boundaries only absorb waves with
normal incidence effectively. For the quantification, a comparison between PML and
radiation boundaries is conducted.
Appendices
– 107 –
Figure 77: Comparison of the automatically (left) and manually (right) generated meshes on the substrate.
The change in field strength, resulting from the different solver settings, are compared to the
reference. Figure 78 shows the results. It is observed that a maximum change ΔH of less than
0.8 dB is observed for all three variations. Therefore, reproducibility and stability of the
computed field solutions is given.
Figure 78: Change in magnetic field strength on the ground plane of the patch antenna in region 1 for
different solver settings.
Finally, a simple test structure was fabricated and measured. Figure 79 shows a photo of the
planar test antenna. The antenna was designed to operate at 4.5 GHz in order to facilitate
accurate measurements of the electric field strength on the ground plane using electrically
short monopole probes. To ensure comparability with (quasi) millimeter-wave frequencies, a
Appendices
– 108 –
thick dielectric substrate was used (1.5 mm thick FR4 substrate). It has a similar electrical
thickness than the studied patch antenna in Figure 15.
Additionally, seven holes were drilled into the substrate. The holes have equal separation
distances from the patch antenna edges. Monopole probes with coaxial connectors were
inserted into these holes. The outer conductors of the coaxial connectors were soldered to the
ground plane. The monopoles themselves are the extension of the signal conductor of the
coaxial connectors.
Figure 79: Manufactured test board with patch antenna and monopole probes to measure the electric field
strength at different positions on the substrate.
The measured resonance frequency is at 4.45 GHz. The -10 dB impedance bandwidth is
140 MHz. Next, the coupling to the monopole probes, inserted into the holes in the grounded
substrate, was measured. The results are shown graphically in Figure 80.
Figure 80: Measured electric field strengths at the monopole probes on the test board of the patch
antenna.
Appendices
– 109 –
The magnitude of the coupling coefficient S21 is proportional to the electric field strength at
the position of the monopole probes. The measurement is scaled with an offset to match the
plot of the normalized electric field strength from the simulations. Altogether, seven
transmission measurements were conducted. The simulated and measured results are in good
agreement with the decay rate of the electric field.
In summary, the accuracy of the computed field simulations in this work has been quantified.
It is concluded that the obtained results are accurate on the order of 1 dB.
Appendix 3 – Microstrip Transmission Line Parameters
Figure 81 shows the cross section of a microstrip transmission line on the grounded substrate
configuration.
Figure 81: Configuration of a microstrip line on the grounded substrate configuration with dimensions.
The microstrip line is used as a feeding line for the antenna configurations and is also a
typical transmission line used signal distribution on PCBs. The width w was designed for a
characteristic impedance of 50 Ω. All the other parameters are fixed and governed by the
substrate configuration (h=250 µm, εr =3.75, tan(δ)=0.006, t=17.5 µm). The transmission line
parameters, shown in Table 10, were computed using a 2D quasi-static solver.
Line parameters Computed values
L' 295 pH/mm
C' 110 fF/mm
R' 76 mΩ/mm
G' 89 mS/mm
Z0 51.5 Ω + j0.1 Ω
β 0.86 mm
-1
Table 10: Computed transmission line parameters at 24 GHz.
A detailed overview of the transmission line parameters is given in Section 2.2.1.2. For the
target impedance of 50 Ω, w=500 µm was determined. The results show that the losses of the
Appendices
– 110 –
microstrip line are small. The imaginary part of Z0 is negligible compared to the real part. The
transmission line exhibits satisfactory low loss performance (ωL'>>R' and ωC'>>G') at
24 GHz. An overview of the fabrication and experimental characterization of this transmission
line is given in Appendix 4.
Appendix 4 - Prototyping and Measurement of Planar Structures
Throughout this work, the modeling and simulation results are validated with S-parameter
measurements. For this purpose, planar antennas, transmission lines and shielding structures
were manufactured and measured. This appendix gives an overview of the PCB
manufacturing technology and measurement techniques that were employed.
All the planar structures were designed on a high frequency substrate material (RO4350B®
from Rogers Cooperation) with two metallization layers suitable for low cost PCB
technologies. A 250 µm thick substrate was selected with favorable dielectric properties for
high frequency applications. The substrate was laminated with 17.5 µm thick copper on both
sides by the manufacturer. The relative dielectric constant εr and loss tangent tan(δ) are
approximately 3.75 and 0.006 in the frequency range considered in this work, respectively.
The manufacturing process of the planar test structures comprises a number of steps. First, the
copper was structured from both sides with a laser (Protolaser S from LPFK Laser &
Electronics) as defined by the layout. Then, holes were drilled at the positions where vias,
connecting the top and bottom layers, are to be placed. Next, a conductive paste
(ProConduct® from LPKF Laser & Electronics) was applied to fill the holes. The test
structures were then placed on a vacuum table to coat the inner sides of the drilled holes.
Finally, the test structures were placed into an oven for 30 minutes with a temperature of
160 °C to cure the vias. Once this process is completed, the test structures are ready for the S-
parameter measurements.
The measurements were conducted with a vector network analyzer (PNA 8361A from Agilent
Technologies), which is capable of measuring S-parameters up to 67 GHz. With the additional
S-parameter test set, four port S-parameter measurements can also be conducted. The planar
test structures were placed on the wafer chuck of a prober station. The LRRM (line, reflect,
reflect, match) and SOLT (short, open, load, thru) calibration techniques [109] were used to
set the reference planes to the ends of the measurements tips. The S-parameters can then be
measured from these reference planes. Figure 82 shows a photo of the GSG (ground, signal,
Appendices
– 111 –
ground) probes that were used to measure the structures. These probes have a pitch of
300 µm.
For the calibration of the network analyzer, an impedance standard substrate (106-683) from
Cascade Microtech was used. It contains all necessary standards including opens, shorts,
loads, thrus and lines.
Figure 82: Photo of a GSG probe to contact the measurement structures.
In order to contact the test structures with the GSG probe, an adapter structure was designed
and implemented. All the planar structures in this work comprise grounded microstrip-type
configurations. Therefore, the adapters were designed as planar pads, and the ground pads
were shorted to the ground plane with two vias. The adapters are depicted in Figure 83
together with two designed 50 Ω microstrip transmission lines (see Appendix 3) of different
lengths (1 mm and 5 mm), which were measured to show the transmission and reflection
characteristics of the adapters and the microstrip lines. The references planes are also shown,
indicating the position of the probe tips.
Figure 83: Measured transmission and reflection coefficient of the manufactured microstrip transmission
lines.
Appendices
– 112 –
Up to a frequency of approximately 27 GHz the reflection coefficients S11 are below -6 dB.
This implies that less than 25 % of the input power is reflected at the probe tips. The
transmission coefficients S21 of both lines are below 2 dB up to 35 GHz. Furthermore, the
transmission coefficients are similar for both line lengths.
References, List of Figures and List of Tables
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Transactions on Antennas and Propagation, vol. 43, 1995.
[109] S. A. Wartenberg, RF Measurements of Die and Packages: Artech House, 2002.
List of Figures
Figure 1: Illustration of a compact wireless module based on a low cost PCB configuration. .. 2
Figure 2: Coupling between: (a) two transmission lines; and (b) a patch antenna and a
transmission line at 24 GHz. ...................................................................................................... 3
Figure 3: Cross sections of the three fundamental antenna types: (a) patch antenna on
grounded substrate; (b) slot antenna in ground plane; and (c) dipole antenna on ungrounded
substrate. ..................................................................................................................................... 4
Figure 4: Classification of techniques for the reduction of undesired electromagnetic coupling
caused by surface waves. ........................................................................................................... 8
References, List of Figures and List of Tables
– 123 –
Figure 5: Cross sections of configurations for surface wave suppression: (a) conventional
substrate with ground plane; (b) integration of EBG structure; (c) integration of DGS; and (d)
modification of substrate material. ........................................................................................... 10
Figure 6: Illustration of the complex power density transfer to and from a planar antenna
configuration integrated on a PCB. The coordinate system is centered, and the plane z=0 is on
the ground plane. ...................................................................................................................... 13
Figure 7: Overview of approach to determine electromagnetic antenna boundary. ................ 14
Figure 8: Equivalent circuit model of an infinitesimal transmission line piece with the
distributed per-unit-length parameters. .................................................................................... 19
Figure 9: Grounded substrate used for the calculation of surface wave fields. ....................... 25
Figure 10: Solutions of the transcendental equations for different values of εr and h. ............ 27
Figure 11: Longitudinal electric field of TM0 surface wave with λ=16.67 mm (f=18 GHz). .. 28
Figure 12: Transverse electric field of TM0 surface wave with λ=16.67 mm (f=18 GHz). ..... 28
Figure 13: Overview of coupling mechanisms between planar antennas and board
components. .............................................................................................................................. 31
Figure 14: Illustration of distributed nature of capacitive and inductive coupling from a
resonant patch antenna. ............................................................................................................ 31
Figure 15: Model of patch antenna on a grounded dielectric substrate. .................................. 32
Figure 16: Parameterized transmission line model of a conventional rectangular patch antenna
for excitation with the TM100 mode. ......................................................................................... 34
Figure 17: Distribution of current density on the patch resonator with the "idealized" current
excitation. ................................................................................................................................. 36
Figure 18: Simulation of the propagating power density excited by the patch antenna on the
ground plane. ............................................................................................................................ 37
Figure 19: Simulation of the spatial complex power density excited by the patch antenna on
the ground plane in region 1. .................................................................................................... 37
Figure 20: Configuration of the coaxial probe feed and the inset distance s from the patch
edge. ......................................................................................................................................... 38
Figure 21: Simulation of the normalized magnetic field excited by the patch antenna on the
ground plane in region 1. .......................................................................................................... 39
Figure 22: Simulation of the normalized magnetic field excited by the patch antenna on the
ground plane in region 2. .......................................................................................................... 39
References, List of Figures and List of Tables
– 124 –
Figure 23: Illustration of far-field waves radiated by a planar antenna configuration including:
(a) the space wave mode; and (b) the surface wave mode. ...................................................... 41
Figure 24: Graphical illustration of the reactive power density, the threshold value for
determining the electromagnetic antenna boundary as well as the antenna parameters. ......... 43
Figure 25: Simulation model and dimensions of the 24 GHz inset fed patch antenna. ........... 45
Figure 26: Measurement of the reflection coefficient S11 of the patch antenna and comparison
to full-wave simulation. The top view of the manufactured antenna with the feeding line and
contact pads is also shown. ...................................................................................................... 46
Figure 27: Simulation model and dimensions of the 24 GHz edge fed slot antenna. .............. 47
Figure 28: Measurement of the reflection coefficient S11 of the slot antenna and comparison to
full-wave simulation. The top view of the manufactured antenna with the feeding line and
contact pads is also shown. ...................................................................................................... 47
Figure 29: Simulation model and dimensions of the 24 GHz center fed dipole antenna. ........ 48
Figure 30: Measurement of the reflection coefficient S11 of the dipole antenna and comparison
to full-wave simulation. The top view of the manufactured antenna with the feeding line and
contact pads is also shown. ...................................................................................................... 49
Figure 31: Comparison of the simulated electric field distributions on the ground planes in the
vicinity of the: (a) patch antenna; (b) slot antenna; and (c) dipole antenna. ............................ 49
Figure 32: Comparison of the simulated magnetic field distributions on the ground planes in
the vicinity of the: (a) patch antenna; (b) slot antenna; and (c) dipole antenna. ...................... 50
Figure 33: Comparison of the simulated radiation patterns (gain) of the patch, slot and dipole
antenna in two principle elevation planes. ............................................................................... 51
Figure 34: Simulated reactive power density on the ground plane of the planar antennas. ..... 52
Figure 35: Comparison between the physical and additional electrical sizes of the planar
antennas. ................................................................................................................................... 54
Figure 36: Illustration of the planar antennas with microstrip transmission lines routed inside
electromagnetic antenna boundary of the (a) patch and (b) slot antennas. .............................. 55
Figure 37: Effects on the resonance frequencies of the antennas for different transmission line
separation distances d. .............................................................................................................. 56
Figure 38: Effects on the insertion loss of the microstrip transmission line routed inside the
antenna boundaries. .................................................................................................................. 56
Figure 39: Illustration of the planar antennas with reduced ground plane sizes. ..................... 57
References, List of Figures and List of Tables
– 125 –
Figure 40: Simulation results of the effects of reduced ground plane sizes on the antenna
gains. ........................................................................................................................................ 58
Figure 41: Overview of method to calculate coupling from antenna fields to transmission
lines. ......................................................................................................................................... 61
Figure 42: Illustration of method to calculate coupling from antenna fields to transmission
lines. ......................................................................................................................................... 61
Figure 43: Configuration of a microstrip transmission line on a grounded substrate. ............. 62
Figure 44: Simulation of the magnetic field distribution of the patch antenna split up into the
two tangential components on the ground plane. ..................................................................... 68
Figure 45: Overview of the different cases used to study the coupling between the three planar
antennas and the microstrip transmission lines. ....................................................................... 69
Figure 46: Comparison of full-wave simulation with field integration (coupling model) results
for the patch, slot and dipole antenna with l= λ/4 and d=λ/4. .................................................. 70
Figure 47: Comparison of full-wave simulation with field integration (coupling model) results
for case 1. ................................................................................................................................. 71
Figure 48: Comparison of full-wave simulation with field integration (coupling model) results
for case 2. ................................................................................................................................. 72
Figure 49: Comparison of full-wave simulation with field integration (coupling model) results
for case 3. ................................................................................................................................. 72
Figure 50: Comparison of full-wave simulation with field integration (coupling model) results
for case 4. ................................................................................................................................. 73
Figure 51: Overview of the patch antenna with the two transmission line routing cases with
multiple bends. The x-y coordinates specify the segments of the transmission line. ............... 73
Figure 52: Comparison of full-wave simulation with field integration (coupling model) results
with spectral response for case 1. ............................................................................................. 74
Figure 53: Comparison of full-wave simulation with field integration (coupling model) results
with spectral response for case 2. ............................................................................................. 75
Figure 54: 3D simulation models used to study the coupling to the ports for two transmission
lines, (a) and (b), with and without the microstrip transmission line, respectively. ................ 76
Figure 55: Test structures and 3D simulation models used for experimental verification of the
simulated coupling between the patch antenna and the microstrip transmission lines. ........... 77
Figure 56: 3D simulation models of the coupled patch antennas including: (1) E-plane case;
and (2) H-plane case. ................................................................................................................ 79
References, List of Figures and List of Tables
– 126 –
Figure 57: Simulation results of the coupling coefficient S21 between the patch antennas at
24 GHz. .................................................................................................................................... 80
Figure 58: Physical and electrical concept of the mushroom-type EBG structure .................. 81
Figure 59: Illustration of the Brillouin zone (left) for an EBG unit cell (right). ...................... 82
Figure 60: Full dispersion diagram for the space and surface wave modes of the EBG cell. .. 83
Figure 61: Model of E-plane patch antennas with integrated EBG for the suppression of
coupling. ................................................................................................................................... 84
Figure 62: Simulation results of the coupling coefficient S21 between the E-plane coupled
patch antennas in dependency of the separation distance a. .................................................... 85
Figure 63: Simulation results of the coupling coefficient S21 between the E-plane coupled
patch antennas in dependency of the separation distance a. .................................................... 86
Figure 64: Configuration and dimensions of the designed SWR patch antenna. ..................... 87
Figure 65: Surface current distribution: on the excited (a) conventional patch antenna; and on
the (b) SWR antenna. The arrows indicate the direction of the current anti nodes. ................ 88
Figure 66: Measurement results of the reflection coefficient S11 of the SWR patch antenna and
comparison to full-wave simulation. ........................................................................................ 89
Figure 67: Simulation of the reactive power density on the ground plane of the SWR patch
antenna. .................................................................................................................................... 90
Figure 68: 3D simulation models of the coupled antennas: (1) conventional patch antennas;
and (2) SWR patch antennas. ................................................................................................... 90
Figure 69: Simulation results of the coupling coefficient S21 between two conventional patch
antennas and two SWR patch antennas. ................................................................................... 91
Figure 70: Photos of the test structures used to measure the coupling: (1) conventional patch
antennas; (2) patch antennas with EBG structure; and (3) SWR patch antennas. ................... 92
Figure 71: Comparison of coupling measurement results: (a) conventional patch antennas; (b)
patch antennas with EBG structure; and (c) SWR patch antennas. ......................................... 92
Figure 72: Overview of the SWR patch antenna with the two microstrip transmission line
routing cases with multiple bends. The x-y coordinates specify the absolute routing path of the
transmission line. ...................................................................................................................... 94
Figure 73: Overview of an optimized design process for planar antenna integration including
the approaches, methods and results proposed in this work. ................................................... 96
Figure 74: Concept of PML boundary conditions at the sides of the computational domain to
provide low reflections absorbing boundaries. ...................................................................... 102
References, List of Figures and List of Tables
– 127 –
Figure 75: Concept of PML edge elements at the corner of the box. .................................... 103
Figure 76: Change in magnetic field strength on the ground plane of the patch antenna in
region 1 in dependency of the computed passes. ................................................................... 106
Figure 77: Comparison of the automatically (left) and manually (right) generated meshes on
the substrate. ........................................................................................................................... 107
Figure 78: Change in magnetic field strength on the ground plane of the patch antenna in
region 1 for different solver settings. ..................................................................................... 107
Figure 79: Manufactured test board with patch antenna and monopole probes to measure the
electric field strength at different positions on the substrate. ................................................. 108
Figure 80: Measured electric field strengths at the monopole probes on the test board of the
patch antenna. ......................................................................................................................... 108
Figure 81: Configuration of a microstrip line on the grounded substrate configuration with
dimensions. ............................................................................................................................. 109
Figure 82: Photo of a GSG probe to contact the measurement structures. ............................ 111
Figure 83: Measured transmission and reflection coefficient of the manufactured microstrip
transmission lines. .................................................................................................................. 111
List of Tables
Table 1: Summary of the spatial field decay rates near excited planar antennas. .................... 41
Table 2: Comparison of the simulated parameters of the planar antennas at 24 GHz. ............ 51
Table 3: Comparison of the calculated threshold values. ......................................................... 52
Table 4: Deduced dimensions of the electromagnetic antenna boundary of the antennas. ...... 53
Table 5: Comparison of the calculated, simulated and measured coupling values between the
patch antenna and microstrip transmission lines at 24 GHz. ................................................... 77
Table 6: Deduced electromagnetic antenna boundary values of the SWR patch antenna and
comparison to the conventional patch antenna. ....................................................................... 90
Table 7: Evaluated coupling values of the three configurations. ............................................. 93
Table 8: Comparison of shielding effectiveness and required board space between EBG
structure and SWR patch antenna. ........................................................................................... 93
Table 9: Comparison of simulated coupling to the transmission lines for cases 1 and 2. ........ 95
Table 10: Computed transmission line parameters at 24 GHz. .............................................. 109
– 128 –
Short Biography and List of Publications
Florian Ohnimus was born in Lüneburg, Germany. He received the Dipl.-
Ing. degree in electrical engineering (with honors) in 2007 from the
Technical University of Berlin (TUB), Germany. Since April 2007, he has
been working as a research engineer in the RF and High-Speed System
Design Group (RSD) at the Fraunhofer Institute for Reliability and
Microintegration (IZM) and the Berlin Center of Advanced Packaging
(BeCAP). Mr. Ohnimus is recipient of the Studienpreis des Jahres 2007 from the TUB, the
Erwin-Stephan-Preis 2008 and the Best Paper Prize of the Loughborough Antennas and
Propagation Conference 2010.
Publications related to Dissertation
• F. Ohnimus, G. Fotheringham, I. Ndip, E. Engin, S. Guttowski, H. Reichl, K.-D. Lang, “Integration of
Planar Antennas Considering Electromagnetic Interactions at Board Level, IEEE Transactions on
Electromagnetic Compatibility, March, 2011.
• F. Ohnimus, I. Ndip, E. Engin, S. Guttowski, H. Reichl, “Modeling and Analysis of Electromagnetic Field
Distribution in Vicinity of Patch Antennas at Millimeter-wave Frequencies”, presented at IEEE International
Symposium on Microelectronics (IMAPS), San Jose, USA, November, 2009.
• F. Ohnimus, I. Ndip, E. Engin, S. Guttowski, H. Reichl, “Study of Shielding Effectiveness of Mushroom-
type Electromagnetic Bandgap Structures in Close Proximity to Patch Antennas”, presented at IEEE
Loughborough Antennas and Propagation Conference, Loughborough, UK, November, 2009.
• F. Ohnimus, I. Ndip, E. Engin, S. Guttowski, H. Reichl, “Comparison of Electromagnetic Field Distribution
in Vicinity of Patch and Slot Antennas”, presented at IEEE Loughborough Antennas and Propagation
Conference, Loughborough, UK, November, 2009.
• F. Ohnimus, U. Maaß, I. Ndip, S. Guttowski, H. Reichl, “Planar Antenna Design and Integration for
Millimeter-wave Communication Systems”, presented at Wireless Congress, Munich, October, 2009.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Integration of Planar Millimeter-wave Antennas considering
Electromagnetic Reliability Aspects”, Smart System Integration and Reliability - Honorary Volume on the
Occasion of Herbert Reichl's 65th Birthday: Goldenbogen Verlag, Dresden, 2010.
Publications, Workshops and Talks related to other Research Activities
• F. Ohnimus, C. Hoherz, M. Hampicke, I. Ndip, S. Guttowski, K.-D. Lang, D. Lumbeck, M. Kreitmair,
“Integration and Evaluation of Electrically Small 868 MHz PCB Antennas for Wireless USB Stick”,
– 129 –
accepted for presentation at IEEE European Microwave Conference (EuMC), Manchester, UK, October 9-
14, 2011.
• F. Ohnimus, I. Ndip, A. Podlasly, A. Ostmann, T. Fritzsch, J. Wolf, S. Guttowski, K.-D. Lang, “Design and
Comparison of Efficient and Compact Patch Antennas for 24 GHz Radar and Communication Systems“,
presented at Smart Systems Integration Conference (SSI 2011), Dresden, Germany, March 22-23, 2011.
• G. Fotheringham, C. Tschoban, F. Ohnimus, I. Ndip, S. Guttowski, K.-D. Lang, U. Fotheringham, M. Letz,
“Extraction of Dielectric Properties of Glass Substrates for RF Applications up to 40 GHz using a Split-
Cylinder-Resonator“, presented at Smart Systems Integration Conference (SSI 2011), Dresden, Germany,
March 22-23, 2011.
• F. Ohnimus, U. Maaß, G. Fotheringham, B. Curran, I. Ndip, T. Fritzsch, J. Wolf, S. Guttowski, K.-D. Lang,
"Design and Comparison of 24 GHz Patch Antennas on Glass Substrates for Compact Wireless Sensor
Nodes", International Journal of Microwave Science and Technology, Hindawi, December, 2010.
• F. Ohnimus, R. Erxleben, C. Tschoban, I. Ndip, M. Niedermayer, H. Scholtz, T. Bonin, S. Guttowski, K.-D.
Lang, “Design and Characterization of a Low Profile Miniaturized UHF PIFA for Compact Wireless Sensor
Nodes”, presented at IEEE Loughborough Antennas and Propagation Conference, Loughborough, UK,
November, 2010.
• F. Ohnimus, J. Haberland, C. Tschoban, I. Ndip, K. Heumann, C. Kallmayer, S. Guttowski, K.-D. Lang,
“Design and Characterization of a Small Encapsulated UHF RFID Tag for Wood Log Monitoring”,
presented at IEEE Loughborough Antennas and Propagation Conference, Loughborough, UK, November,
2010.
• G. Fotheringham, F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, „RFID - Theoretische Konzepte und
Anwendungsbeispiele, Jahrbuch Oberflächentechnik“, Galvanotechnik: Leuze Verlag, Ausgabe 10/10,
Oktober, 2010.
• I. Ndip, F. Ohnimus, K. Löbbicke, M. Bierwirth, C. Tschoban, S. Guttowski, H. Reichl, K. D. Lang, and H.
Henke, "Modeling, Quantification, and Reduction of the Impact of Uncontrolled Return Currents of Vias
Transiting Multilayered Packages and Boards," IEEE Transactions on Electromagnetic Compatibility, vol.
52, pp. 421-435, May, 2010.
• I. Ndip, F. Ohnimus, K. Löbbicke, C. Tschoban, M. Bierwirth, S. Guttowski, H. Reichl, "Equivalent Circuit
Modeling of Signal Vias Considering their Return‐Current Paths", presented at IEEE Asia‐Pacific
International Symposium on Electromagnetic Compatibility, Beijing, China, April 12‐16, 2010.
• I. Ndip, K. Löbbicke, M. Bierwirth, C. Tschoban, B. Curran, R. Erxleben, F. Ohnimus, U. Maaß, G.
Fotheringham, S. Guttowski, H. Reichl, "Managing the Return-Currents of Signal Vias in Organic and
Silicon Substrates", presented at Smart Systems Integration Conference (SSI 2010), Como, Italy, March 23-
24, 2010.
• F. Ohnimus, G. Fotheringham, I. Ndip, S. Guttowski, H. Reichl, “Comprehensive Design Method for RFID
Tags based on EM Field Simulations”, presented at Ansys/Ansoft Workshop, Leipzig, November 18-20,
2009.
• F. Ohnimus, A. Podlasly, J. Bauer, A. Ostmann, I. Ndip, S. Guttowski, H. Reichl, “Electrical Design and
Characterization of Elevated Antennas at PCB-Level”, presented at IEEE Electrical Components and
Technology Conference (ECTC), San Diego, USA, May, 2009.
– 130 –
• G. Fotheringham, F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Parameterization of Bent Coils on Curved
Flexible Substrates for RFID Applications”, presented at IEEE Electrical Components and Technology
Conference (ECTC), San Diego, USA, May, 2009.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Design Challenges and Techniques for Passive RFID Tag
Antennas”, presented at Semiconductor Conference Dresden, April 29-30, 2009.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “An Efficient and Broadband Slot Antenna for 60 GHz
Applications”, presented at IEEE Conference on Electrical Design of Advanced Packaging and Systems
(EDAPS), Seoul, South Korea, December, 2008.
• I. Ndip, F. Ohnimus, S. Guttowski, H. Reichl, “Minimizing Electromagnetic Interference in Power-Ground
Cavities”, presented at IEEE Conference on Electrical Design of Advanced Packaging and Systems
(EDAPS), Seoul, South Korea, December, 2008.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Design and Characterization of Integrated Antennas for
Communication Applications”, presented at Inspiring Engineering - Ansoft Global Application Workshop
for High Performance Electronic Design, Munich, November 10, 2008.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Design and Analysis of a Bent Antenna-Coil for a HF RFID
Transponder”, presented at IEEE European Microwave Conference (EuMC), Amsterdam, Netherlands,
October, 2008.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Entwurf integrierter Antennen für Kommunikations- und
Radaranwendungen”, presented at Wireless Communication and Information (WCI), Berlin, October 15-16,
2008.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Entwurf Integrierter Antennen für Kommunikations- und
Radaranwendungen”, presented at RadioTecC 2008, Adlershof, Berlin, October 15-16, 2008.
• U. Maaß, F. Ohnimus, B. Curran, I. Ndip, S. Guttowski, H. Reichl, “Auswirkungen von Toleranzen der
Aufbau- und Verbindungstechnik auf das elektrische Verhalten integrierter HF-Komponenten”, GMM-
Fachtagung Zuverlässigkeit und Entwurf, Ingolstadt, 29.9.-1.10., VDE Verlag, 2008.
• I. Ndip, F. Ohnimus, S. Guttowski, H. Reichl, “Modeling and Analysis of Return-current Paths for
Microstrip-to-Microstrip Via Transitions”, presented at IEEE Electronics System-Integration Technology
Conference (ESTC), Greenwich, London, UK, September, 2008.
• I. Ndip, A. Ostmann, F. Ohnimus, U. Maaß, S. Guttowski, H. Reichl, “Elektrischer Entwurf von System-in-
Package, Leiterplatten und Integrierten Komponenten für HF/High-Speed Anwendungen”, Workshop
SMT/Hybrid/Packaging, Nuremberg, June 5, 2008.
• F. Ohnimus, I. Ndip, S. Guttowski, H. Reichl, “Modeling and Simulation of Integrated Antennas for RFID
and Wireless Communication Applications”, Workshop on Antenna Simulations for Industrial Applications,
Kaiserslautern, September 11, 2007.
• I. Ndip, F. Salhi, U. Maaß, G. Fotheringham, F. Ohnimus, S. Guttowski, and H. Reichl, “Optimal Electrical
Design of System Packages and Integrated Components using the M3-Approach”, presented at IEEE
Electronics Packaging Technology Conference (EPTC), Nevada, USA, June, 2007.
