Modeling of Stray Magnetic Couplings in
Power Electronic Devices
vorgelegt von
M. Eng.
Takashi Masuzawa
ORCID: 0000-0002-5317-646X
an 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. Roland Thewes
Gutachter: Prof. Dr. Klaus-Dieter Lang
Gutachter: Prof. Dr. Eckart Hoene
Gutachter: Prof. Keiji Wada
Tag der wissenschaftlichen Aussprache: 25. Februar 2022
Berlin 2023
1
Acknowledgment
Firstly, I would like to sincerely thank Prof. Hoene for his kind instruction and help in
this research. His advice is always suggestive and I obtained a lot of knowledge and insight
through it. This research could not be finished without his support.
Next, I would like to deeply thank Prof. Klaus-Dieter Lang to be my dissertation’s
supervisor. His suggestions and help in my study are greatly appreciated.
I would also like to appreciate all my colleagues at Fraunhofer IZM especially Stefan
Hoffmann, Oleg Zeiter, Adam Kuczmik, Yujia Yang, Christoph Marczok, Gudrun Feix, Kirill
Klein, Stefan Junk, Andre Domurat-Linde for their help, discussions and friendship.
Regarding my stay at Fraunhofer IZM. I would like to thank DENSO
CORPORATION for giving me this great opportunity to stay at this state-of-the-art research
institute. I could gain a lot of excellent experience both professionally and privately through it.
Finally, I would like to express my deepest thanks to my parents, my wife: Yuriko and
my son: Ikuma for their dedicated support. All the support they have given me was always the
source of my power and strength. Through this two and half year stay in Germany apart from
hectic life in Japan, I realized the importance of family once again. Thank you!
Sincerely,
Takashi Masuzawa
February 2023
2
Abstract
Nowadays, a demand for a higher efficiency and power density of power electronic
devices is growing rapidly, and therefore there is a strong tendency to apply high switching
frequency and high-density integration technologies to the power electronic devices. However,
as a trade-off, those technologies can cause an increase of Electromagnetic Interference (EMI),
thus simultaneously satisfying a conversion performance and an EMI performance defined by
Electromagnetic compatibility (EMC) standards have become an extremely difficult task in a
product design process.
EMC filters with passive components are used to attenuate the EMI and playing a key
role to comply with the EMC standards. And hence a design of EMC filters is an important
part of the product design process. On the other hand, apart from an effect of EMI attenuation,
an EMC filter can lead to additional space requirements and costs, and thus it must be
optimally designed: the smallest size and the lowest cost have to be realized.
To realize an optimal design of an EMC filter, stray components, especially stray
magnetic couplings in power electronic devices which have a significant effect on a filter
performance, should be taken into account properly. Although the stray magnetic couplings
are strongly affected by a layout of PCB tracks and bus bars, and a placement and geometry
of the components, they have been determined in a product design process mostly based on
product designer’s experience in the past.
To solve this issue, some modeling methods of stray magnetic couplings have been
investigated, and some simulation technologies utilizing those modeling methods have been
reported. Nevertheless, there is no investigation applying the simulations to an actual product,
because it is not practical to consider the huge number of stray magnetic couplings existing in
power electronic devices. Thus, so far, a practical and efficient modeling method of stray
magnetic couplings has been strongly needed.
This doctoral dissertation presents a remarkably efficient modeling method of stray
magnetic couplings in a power electronic device that focuses on a dominant magnetic field.
The dominant magnetic field is derived from a fundamental circuit and electromagnetic theory,
3
and the influence of stray magnetic couplings caused by the dominant magnetic field is
theoretically clarified. And then, it is shown that the proposed method is superior to
conventional methods with respect to complexity of the modeling by using several EMC
filters with different configurations.
Moreover, the proposed modeling method is applied to an actual product, to verify its
effectiveness for an EMI filter design in a product design process.
4
Zusammenfassung
Hohe Schaltfrequenzen sind in der Leistungselektronik das wirksamste Mittel, um die
Leistungsdichte von Schaltungen zu steigern und die Anwendung von
Integrationstechnologien jenseits der bestückten Leiterplatte zu ermöglichen. Die Einhaltung
der elektromagnetischen Verträglichkeit (EMV) wird dabei aber schwieriger, da einerseits mit
höheren Schaltfrequenzen die Wirkung parasitärer Effekte stärker wird, andererseits mit einer
höheren Integration die Interaktionen zwischen Schaltungsteilen zunehmen. Damit wird die
Einhaltung der jeweiligen Produktanforderungen im Entwicklungsprozess sehr schwierig.
EMV Filter mit passiven Bauteilen werden für die Reduktion der Störungen
verwendet und sind der Schlüssel für die Einhaltung der EMV Normen. Der Entwurf der
Filter ist ein wichtiger Teil des Entwurfsprozesses, dessen optimales Ergebnis wesentlich über
das benötigte Volumen und Kosten entscheidet.
Für die Filterwirkung sind in der Leistungselektronik parasitäre elektromagnetische
Effekte von entscheidender Bedeutung, neben den offensichtlicheren kapazitiven Kopplungen
sind das vor allem die magnetischen Kopplungen zwischen Bauteilen und Leiterbahnen.
Durch das erhebliche Volumen der passiven Bauteile zeigen diese neben der
Leiterbahnführung einen dominanten Einfluss, der nur sehr erfahrenen Entwicklern
gegenwärtig ist.
Um diese Fragestellung zu lösen, werden in dieser Arbeit Methoden zu ihrer
Modellierung und Simulation erforscht. Sie basieren auf Vorarbeiten und erweitern diese, um
sie auf praxisrelevante Problemstellungen mit ihrer hohen Komplexität anwendbar zu machen.
Das geschieht, indem die hohe Zahl der magnetischen Kopplungen auf die dominant
Wirksamen zurückführt. Dafür werden aus einer kombinierten Anwendung der Schaltungs-
und Feldtheorie die entscheidenden Einflüsse abgeleitet und die Komplexität der
Aufgabenstellung stark reduziert. Es wird anhand von verschiedenen Filtern in
unterschiedlichen Konfigurationen gezeigt, dass die entwickelte Methode den bisher
gezeigten in Bezug auf Lösungsaufwand klar überlegen ist und die gemachten
Vereinfachungen zulässig sind.
5
Schließlich wird das Verfahren an einem aktuellen Produkt erprobt, womit die
Anwendbarkeit im Sinne der Zielstellung der Arbeit nachgewiesen wird.
6
Table of contents
General introduction
Overview of EMC in power electronics
Organization of this dissertation
Chapter 1: State of the art
1.1. Generation mechanism of EMI
1.1.1 Conducted noise and radiated noise
1.1.2 Differential mode and common mode noise
1.2. EMI attenuation techniques
1.2.1 Power semiconductor switch
1.2.2 Active noise canceller
1.2.3 Passive EMI filter
1.3. EMI filter design
1.3.1 Theory of EMI attenuation
1.3.2 EMI filter simulation
Chapter 2: Stray component in power electronic device
2.1. Stray impedance of passive component
2.2. Stray coupling in power electronic device
2.2.1 Stray capacitive coupling
2.2.2 Stray magnetic coupling
2.2.3 Modeling of conducting structure and coil
2.2.4 Modeling of capacitor
7
Chapter 3: Simplification method of stray magnetic coupling
3.1. Complexity of considering stray magnetic coupling
3.2. Basic idea of simplification method
Chapter 4: Application of simplification method to EMI filter circuit
4.1. Application to simple filter circuit
4.1.1 First device under test
4.1.2 Second device under test
4.2. Investigation and extension of the proposed simplification method
4.2.1 Extension of simplification method
4.2.2 Consideration of magnetic material
4.2.3 Result using improved simplified modeling method
4.3. Further discussion on modeling of filter coil
4.3.1 Leakage magnetic flux from fully-wound coil
4.3.2 Influence of stray capacitance on generated magnetic flux from filter coil
4.3.3 Design procedure of EMC filter
4.4. Application to EMC filter for a SiC solar inverter
4.4.1 Tested EMC filter
4.4.2 Consideration of magnetic material
4.4.3 Comparison of filter performance
8
Chapter 5: EMI design of actual product using simplification method
5.1. Configuration of EMI filter
5.2. EMI filter simulation using simplification method
5.2.1 Identification of major stray magnetic coupling
5.2.2 Comparison of filter performance
5.3. Design refinement of EMI filter
5.4. Experimental verification
Chapter 6: Conclusion and future work
6.1. Conclusion
6.2. Future work
9
Abbreviation
ADAS Advanced driver assistance systems
CFRP Carbon fiber reinforced plastic
CISPR Comité international spécial des perturbations radioélectriques
CM Common mode
ECU Electronic control unit
EMC Electromagnetic compatibility
EMI Electromagnetic interference
EMS Electromagnetic susceptibility
EPC Equivalent parallel capacitance
EPR Equivalent parallel resistance
ESL Equivalent series inductance
ESR Equivalent series resistance
EUT Equipment under test
FEM Finite element method
GaN Gallium nitride
GND Ground (electrical)
IOT Internet of things
LISN Line impedance stabilization network
MOM Method of moments
PCB Printed circuit board
SiC Silicon carbide
10
General introduction
Overview of EMC in power electronics
An EMC technology is increasingly becoming important as a fundamental technology
to prevent electromagnetic disturbances in electronic devices. The electromagnetic
disturbance arises from unintended electromagnetic noise generated by switching operations
of semiconductors, and the electromagnetic noise can propagate through space and connecting
cables. Accordingly, it can reach to other devices and result in malfunction. To avoid such a
critical issue, strict EMC standards have been set based on the two technical aspects: EMI and
Electromagnetic susceptibility (EMS). Fig. 1 shows an overview of EMC standards and
relevant organizations, and basically all commercial products are required to comply with
these standards.
Fig.1 Overview of EMC standards and relevant organizations
IEC
TC77 CISPR
SC77A: LF Phenomena
SC77B: HF Phenomena
/A: measurement
/B: ISM
/C: overhead lines
/D: vehicles
/E: broadcast receivers
/F: household appliances
/G: information technology
IEC 61000-X CISPR XX
International European
ETSI CENELEC
EN300 XXX
EN50 XXX
EN55 XXX
EN6X XXX
TC210
11
For a power electronic device, complying with EMI standard is especially critical and
has been a difficult task, because it principally controls high voltage and high current with a
switching operation of higher than kHz ordering frequency which can generate a high level of
electromagnetic noise. Fig. 2 shows a waveform of a drain-source voltage Vds, a gate voltage
Vgs and a drain current Id during a switching operation of a power semiconductor. Where the
horizontal axis is time and the vertical axis is the Vds and the Id. The voltage of higher than
700 V is controlled within one hundred nanosecond and it is seen that the waveform also
contains the voltage ringing with higher harmonic components. The rapid change and ringing
of high voltage and high current generate a high level of electromagnetic noise, and
accordingly, the generated noise can cause connection failure, malfunction of devices and
insulation degradation of motor windings.
Fig.2 Waveform of Vds, Vgs and Id during switching operation
Power density of power electronic devices is growing rapidly as described in
Fig.3[1][2]. Where the horizontal axis is the year and the vertical axis is the power density.
According to the predicted trend, power density become doubled over every four years and is
assumed to be increased up to around 50 kW/L in 2017. To realize such an extremely high-
power density, application of loss reduction techniques is strongly required as well as higher
integration technologies and sophisticated thermal design.
0 200 400 600 800 1000
Id
Vds
Vgs
Vds [V] / Id[A]
Vgs [V]
Time [ns]
50
40
30
20
10
0
-10
1000
800
600
400
200
0
-200
12
Fig.3 Power density of power electronic devices[1][2]
As a way for loss reduction of the power electronic devices, application of higher
switching frequency and faster switching operation has been studied. And from this viewpoint,
a wide band gap semiconductor utilizing new materials such as Silicon Carbide (SiC) and
Gallium Nitride (GaN) is expected to be widely used over the next 10 years, because it can
realize very fast switching operation leading to a substantial switching loss reduction as well
as extremely low conduction loss. On the other hand, the fast switching operation can
intrinsically lead to increase of EMI level as described in Fig. 4 and 5, and therefore EMI
mitigation techniques are essential to take full advantage of the capability of the wide band
gap semiconductor.
(a) Conventional switching time
13
(b) Faster switching time
Fig.4 Time waveform with different switching times
Fig.5 Frequency spectrum envelope with different switching times
On the other hand, in terms of mass reduction, application of new material typified by
carbon fiber reinforced plastic (CFRP) is investigated and gradually spreading to mass
production products like latest hybrid/electric vehicles as shown in Fig. 6[3]. But however, due
to its lower conductivity compared to conventional materials like steel or aluminum, it could
arise critical EMI issues because of poor ground connection and lower shielding performance.
Therefore, more advanced EMI design techniques are required in these vehicles.
14
Fig.6 Internal structure of latest vehicle (BMW i3) [3]
With respect to the range of application of power electronic devices, it is increasingly
expanding and application to new systems represented by x-by-wire, advanced driver
assistance systems (ADAS) and Internet of things (IOT). In these systems, power electronic
devices are responsible for the main part of the control and power conversion, and thus EMI
issue should be more strictly treated compared to conventional ones, because, once the device
operates improperly or malfunction due to EMI issue, it will cause critical and fatal accidents
to itself and other connected devices.
In addition, recent demand for shortening of product development cycle is also a big
issue. Fig. 7 shows a relationship between the degree of freedom of design and cost required
for countermeasure at each stage of product development. Based on the relationship, degree of
freedom of design is high and thus cost required for countermeasure is quite low in an early
stage. On the other hand, cost required for countermeasure is extremely high due to the low
degree of freedom of design in a late stage. From this relationship, it can be said that once
critical EMI issues occur in a late stage, it can directly lead to huge amount of additional cost.
And in addition, the issue can necessarily get more serious and more difficult to be avoided in
the shortened product development cycle. Accordingly, it is concluded that significant
consideration on EMI design in an early stage, namely front-loading design methodology, is
more strongly needed.
15
Fig.7 Relationship between the degree of freedom of design and cost required
for countermeasure at each stage of product development
Organization of the dissertation
The purpose of this research is to establish an efficient product design methodology
utilizing a simple and accurate simulation technology in order to solve the above-mentioned
technical needs. Especially, a modeling method of stray magnetic couplings is detailed, and a
design process utilizing the proposed modeling method is also demonstrated.
This dissertation is composed of six chapters and the organization of this dissertation
is described as follows.
In chapter 1, the state-of-the-art technologies regarding generation mechanism of
EMI, EMI mitigation techniques and EMI filter design are described in order to provide
technical background necessary for understanding this research topic.
In chapter 2, stray components existing in power electronic devices are widely
discussed. Characteristic of actual passive components is completely different from ideal ones
Theoretical
design
Concept
design
Detailed
design
Mass production
design
Freedom of design Cost for countermeasure
Level of cost, freedom
Development process
16
in high frequency range due to stray impedance such as an equivalent series inductance (ESL)
and an equivalent parallel capacitance (EPC) mostly arising from its geometry. Likewise,
stray couplings caused by other components such as bus bars, PCB tracks and chassis in
devices also substantially affect EMI performance of the devices. Especially for high-power
power electronics devices which control large current, stray magnetic couplings have strong
influence, and thus a geometry and a placement of components is properly determined. In
terms of optimal design considering stray magnetic couplings, modeling of components and
EMI filter simulation have been investigated in the past research, and the state-of-the-art
simulation with elaborate modeling have shown a good agreement with measured results in
the wide frequency range.
In chapter 3, the proposed simplification method of stray magnetic couplings is
spelled out. As mentioned above, an accurate EMI filter simulation can be realized by
considering all stray magnetic couplings existing in a power electronic device. However, it is
not practical, because a product designer cannot determine which part of an EMC filter has to
be modified for better performance by using simulation with consideration of a huge number
of stray magnetic couplings. Furthermore, at an early stage of product design process, a
product designer has no detailed 3D geometry of a product. Therefore, a reduction of the
complexity of the modeling, namely an extraction of major couplings, is needed especially in
a product design process. To extract major couplings, mechanism of how stray magnetic
couplings are generated and how they can influence EMI performance of the power electronic
devices are investigated in detail. And then, based on the mechanism, a basic idea of the
proposed simplification method of stray magnetic couplings is derived, and the applicability
of the method is also mentioned.
To illustrate and validate the proposed simplification method, it is applied to several
EMC filters with configurations, and the simulated results with the method are compared to
the measured result in chapter 4. In addition, influence of magnetic material used for core and
how to simply consider the influence are specifically described.
In chapter 5, to verify the effectiveness of the proposed method in a product design
process, it is applied to an actual product. Firstly, an efficient and accurate EMC filter
simulation is carried out with the proposed modeling method, and secondly the most relevant
17
components which cause a major stray magnetic coupling are extracted. And then, an
improvement idea: which part of EMI filter should be changed for a better performance is
derived. Finally, the noise terminal voltage of the actual product is measured and compared
between the original design and improved one.
18
Chapter 1: State of the art
19
1.1 Generation mechanism of EMI
1.1.1. Conducted noise and radiated noise
Generation mechanism of EMI in power electronics can be considered as the
following idea of energy transfer: the EMI is generated and emitted by the emitter; and then
the EMI is transmitted to a receiver (victim) via a propagation path (transmission line). This
energy transfer can be categorized into the following two groups: conducted noise and
radiated noise. Conducted noise is an unintended electromagnetic energy transfer propagating
from an object to object and radiated noise is an unintended electromagnetic energy transfer
propagating via space in the form of electric and magnetic fields, as illustrated in Fig. 8.
Fig.8 Propagation path of conducted and radiated noise
In power electronic devices, radiated noise is generated from a chassis of the device
or a cable connecting to the device in the form of electric and magnetic fields. And mostly,
they arise from high frequency current and voltage which is strongly relevant to conducted
noise. In other words, radiated noise can be reduced by suppressing conducted noise, and
therefore the radiated noise is out of the scope of this work.
Signal line
Battery
DCDC
ECU
Inverter
Radio antenna
MG
12V
Noise source Receiver
Propagation
path
20
1.1.2. Differential mode and common mode noise
Fig. 9 shows the conduction path of high frequency current which is observed as a
conducted noise in the variable speed motor drive system. Along with a switching operation
of the power semiconductor, differential mode noise flows out via the power supply line and,
on the other hand, common mode noise flows out via a ground line[4]. Namely, the conducted
noise generated in power electronic devices can be divided into two modes: differential mode
and common mode by a difference in a conduction pathway[5].
Fig.9 Conduction path of high frequency current in variable speed motor drive system
Regarding a source of conducted noise in power electronic devices, the two
fundamental ones can be found as described in Fig 10[6]-[8]. First, the current commutation in
the DC-Link produces a voltage drop along the DC-Link capacitor and this voltage drop
mainly produces a DM noise. In other words, the source of differential noise is switching
ripple caused by switching operation of power semiconductor. Second, the voltage change at
the output node charges and recharges all capacitances connected to the output and the charge
and recharge of the capacitor mainly produces a CM noise. The unintended capacitance, so
called stray capacitances, will be explained in detail in chapter 5.
Power semiconductor
Battery Capacitor
Cooler
Motor
Common mode
Differential mode
21
Fig.10 Source of conducted noise in power electronic devices
Measurement of conducted noise is carried out with a Line Impedance Stabilization
Network (LISN) and a noise terminal voltage is measured as an object of regulation. In the
measurement of noise terminal voltage, the arrangement of the devices is clearly defined,
where the LISN is placed with a defined distance from the Equipment Under Test (EUT) and
conducted noise reaching LISN is measured by means of spectrum analyzer as a noise
terminal voltage. Fig.11 shows the internal configuration of the LISN used in noise terminal
voltage measurement defined by the EMC standards such as CISPR 11.
Fig.11 Internal configuration of the LISN used in noise terminal voltage measurement
Battery
Capacitor
Load
Power semiconductor
Noise
voltage Noise
current
39kW2mF
39kW2mF
250mH 50mH
50mH
250mH
7.5mF7.5mF
5W5W
0.47mF0.47mF
50W50W
Input Output
P
N
GND
P1
N1
GND
22
1.2 EMI attenuation techniques
Although many kinds of EMI attenuation techniques method for conducted noise
have been proposed so far[9], here characteristics of the four typical categories are described.
1.2.1. Power semiconductor switch
In order to reduce conducted noise at power semiconductor switch, various
techniques are proposed. A soft switching utilizing a resonance of voltage and current is one
of the techniques and it has been reported that it can realize EMI reduction simultaneously
with loss reduction[10][11]. Although sufficient EMI reduction effect can be realized by using
this technique, it is not practical to apply it to mass-production products due to considerable
additional cost and size caused by a complex circuit topology. And also, mitigation technology,
which reduces a peak value of the generated noise by varying a switching frequency, is well
known as spectrum-spreading technique[12][13]. This technique has been applied to many
products, but the total energy of the noise is not reduced, therefore the mitigation effect is
limited.
1.2.2. Active noise canceller
An active noise canceller has been widely studied as an effective noise reduction
technique[14][15]. Fig.12 shows a principle of an active noise canceller. Fig12 (a) is a common-
mode equivalent circuit of a motor drive system without an active noise canceller. A common
mode voltage change generated by the inverter Vinv originates a high frequency leakage
current In flowing through the motor, and part of the current that reach the measuring
terminals of the LISN become the noise terminal voltage Vn. On the other hand, with a noise
canceller as shown in Fig12 (b), the noise canceller detects the Vinv, and then applies the
voltage through a coupling transformer in order to reduce a high-frequency leakage current by
cancelling the Vinv. In addition, a cancelling technique by detecting the leakage current instead
of a common-mode voltage has been proposed[16].
Although sufficient noise reduction can be expected by utilizing an active noise
canceller, as far as we know, there have been few reports about a practical application to a
23
product. The reason for not using an active noise canceller is the size of the transformer used
in this topology. It is as large as a common mode choke coil with the same noise reduction,
and that is to say, no size saving can be obtained.
(a) Without active noise canceller
(b) With active noise canceller
Fig.12 Principle of an active noise canceller
1.2.3. Passive EMI filter
Passive EMI filter is an EMI mitigation technique widely applied to a product, and
many topologies of the filter have been presented and discussed[17]. Since an optimal design in
size and cost is a critical issue, a number of studies related to an optimal design method have
been reported[18]-[20]. In addition, since the characteristics of the EMI filter can be significantly
deteriorated by a wiring length and component placement and so on, an investigation focusing
Cstray
L R
Vinv
RLISN
in
Vn
MotorInverter
LISN
Motor
in
+
-
+
-
Cstray
L R
Vinv
RLISN
Vn
Inverter
Active noise canceller
LISN
24
on clarification of the unintended influence is becoming essential and constitute one of main
subjects of this work.
1.3 EMI filter design
1.3.1. Theory of EMI attenuation
In this section, theory of EMI attenuation with EMI filter is explained by taking a
typical LC filter topology widely used in a power electronic device as an example.
Incidentally, the filters discussed below are low pass filter designed to attenuate high
frequency noise. Fig. 13 shows the system configuration of DC motor controller. The DC
motor is connected to the output of H bridge circuit, and the battery is connected to the input.
Fig.13 System configuration of DC motor controller
In fig. 13, given that the voltage of the capacitor C1 is a noise voltage Vn, the
relationship between the noise voltage source and the noise current In can be described by Fig.
14, where ZC is an impedance of C1, ZL is an impedance of L and Zout is an impedance of all
components including a wiring at the battery side. Vn is influenced by the characteristic of C1:
a type, capacitance values and stray impedance such as ESR and ESL.
Battery
Motor CC1
In
L
LC filter
Vn
25
Fig.14 Relationship between the noise voltage source and the noise current
Normally, since the wiring length from the controller to the battery is in the range of a
few meters, an inductance of the wiring is around a few mH. Thus, at frequencies higher than
100 kHz, Zout is much bigger than ZC, the noise reduction effect of the filter Gf is defined by
the following equation between the output voltage Vout and the noise voltage source Vn.
n
out
fV
V
G=
(1)
And, since Vout is the voltage divided by the summation of the impedance of the coil
and the capacitor, Gf can be accordingly expressed by the following equation.
LC
C
fZZ
Z
G+
=
(2)
To obtain desired noise reduction effect in the frequency range defined by the EMI
standard, an appropriate combination of a coil and a capacitor should be selected. And thus,
an EMI filter simulation is normally used from this viewpoint. In next section, an overview of
a filter simulation is explained.
In
Vout
ZC
ZL
Zout
Vn
26
1.3.2. EMI filter simulation
Regarding EMC filter design, it is quite difficult that filter performance easily meets
an expected value designed using a simulation. Accordingly, filter components have to be
added and redesigned over again and again until a required performance can be reached. Since
those added components can directly lead to higher cost and larger size, and therefore an
accurate filter simulation to predict filter performance is strongly needed.
With respect to a filter simulation, it can be categorized into the following four levels.
Level 0 is the simplest simulation considering only ideal passive components in a
circuit simulation as described in Fig.15, and it allows the determination of nominal values of
filter components for frequencies at about 150 kHz.
Fig.15 Circuit schematic for Level 0 filter simulation
And Level 1 is a simulation considering non-ideal components with frequency
characteristic due to the parasitic impedance such as equivalent series resistance and
inductance (ESR and ESL) for the capacitor, and the frequency dependent behavior of ferrites
and winding capacitance for the inductor as described in Fig.15.
Level 2 is level 1 additionally considering stray impedance of lines and PCB tracks as
described in Fig. 16, and Level 3 is level 2 additionally considering stray magnetic couplings
as described in Fig.17.
Lleak1
k=1
Lleak2 Lleak : Leakage inductance
of filter coil
Inductance
Resistance
27
The calculation of the couplings is done by an electromagnetic simulation.
Calculation results consist of equivalent circuit elements corresponding to the effect of
magnetic field coupling, which are included in the circuit simulation. Investigation on
simulation level 3 has been reported[21]-[23], and it is said that simulation can accurately predict
filter performance and shows a good accordance with a measurement result. In next chapter,
the unintended components with significant influence on filter performance, namely stray
components, are described in detail.
Fig.16 Circuit schematic for Level 1 filter simulation
Fig.17 Circuit schematic for Level 2 filter simulation
k=1
Lleak2
Lleak1
Lleak : Leakage inductance
of filter coil
Inductance
Resistance
k=1
Lleak2
Lleak1
Lleak : Leakage inductance
of filter coil
Inductance
Resistance
28
Fig.18 Circuit schematic for Level 3 filter simulation
k=1
Lleak2 Lleak : Leakage inductance
of filter coil
Lleak1
Inductance
Resistance
Stray magnetic
coupling
29
Chapter 2: Stray component in power
electronic device
30
2.1 Stray impedance of passive component
Generally, the capacitor and the coil are expressed by the equivalent circuit described
in Fig. 19. Where RC is the equivalent series resistance ESR, LC is the equivalent series
inductance ESL and RL and CL represent the equivalent parallel resistance EPR and the
equivalent parallel capacitance EPC respectively.
(a) Capacitor (b)Coil
Fig.19 Equivalent circuit of capacitor and coil
The impedance of the capacitor ZC is expressed by the equation (3), and the
impedance of the coil is expressed by the equation (4).
( )
CLjRZ CCC
1-+=
(3)
( )
LCjRZ LLL
11/1 -+=
(4)
From the above equations (3) and (4), magnitude of the impedance of the capacitor
and the coil is expressed by the following equations.
( )
22 1CLRZ CCC
-+=
(5)
( ) ( )
22 1/11 LCRZ LLL
-+=
(6)
RCLC
C
RL
CL
L
31
Since a filter component contains a parasitic component as described above, they
should be considered in order to correctly estimate noise reduction effect. Regarding the
parasitic components, an EPC of the coil is on the order of pF and an EPR is on the order of
kΩ, therefore it is sufficient that only ESR and ESL of the capacitor should be taken into
account in the frequency range less than 30MHz.
Fig. 20 shows the relationship between frequency characteristic of an impedance of a
capacitor and the following parameters: capacitance C, ESL and ESR. Where the horizontal
axis is the frequency and the vertical axis is the impedance.
(a) Impedance change due to C
(b) Impedance change due to ESL
Frequency
Impedance
jL1/j
C
ESL=constant
Cchange
1/j
C
Frequency
Impedance
C=constant
ESL change
jL
32
(c) Impedance change due to ESR
Fig.20 Relationship between frequency characteristic of impedance of capacitor
and the following parameters: C, ESL and ESR
As indicated in the Fig.20, capacitance is a dominant impedance at frequency range
lower than the self-resonant frequency, and the ESL is a dominant impedance at frequency
range higher than the self-resonant frequency. The minimum value of the impedance is
defined by ESR.
Since a noise reduction effect is determined by an impedance ratio between a coil and
a capacitor, it is desirable that a capacitor has low impedance in the frequency range where a
noise reduction is needed. Namely, in order to obtain a greater noise reduction effect at the
same capacitance value, ESR should be small in the frequency range lower than the self-
resonant frequency, and ESL should be small in the frequency range higher than the self-
resonant frequency.
As previously stated, a capacitor with small ESL should be chosen in the frequency
range higher than self-resonant frequency. Additionally, influence of an inductance of a lead
of a capacitor and PCB pattern described in Fig. 21 should be properly treated.
Frequency
Impedance
j
L
1/j
C
C=constant ESL=constant
ESR change
Large to small
33
(a) Lead of capacitor (b) PCB pattern
Fig.21 Structures of lead of capacitor and PCB pattern related to stray inductance
The equivalent series inductance of a capacitor LC is expressed by the following
equation[24]. Where l is a length and a is a radius of lead of capacitor respectively
7
101
2
ln2-
-= a
l
lLC
(7)
Fig. 22 shows a calculation result of the inductance of capacitor lead with different
length l. Where a radius of the lead a is 0.25 mm. Where the horizontal axis is the length and
the vertical axis is the impedance. In order to reduce an inductance of a lead of a capacitor, it
is preferable to shorten a length of the lead as much as possible, or to use surface mount
components.
Fig.22 Calculation result of inductance of capacitor lead with different length
l
a
l
a
l
w
t
電流
i
Current
0
20
40
60
80
100
120
0 20 40 60 80 100 120
長さ [mm]
インダクタンス [nH]
Length l[mm]
Inductance [nH]
34
The equivalent series inductance of a PCB pattern LP is expressed by the following
equation[24]. Where l is a length, t is a thickness and w is a width of PCB pattern respectively.
7
105.0
2
ln2-
+
+
=tw
l
lLP
(8)
Regarding the equation (7) and (8), they are valid only for simple geometries like a
rectangular and cylinder. Therefore, a 3D simulation should be applied for more complicated
geometries in order to obtain an accurate result.
Fig. 23 shows a calculation result of the inductance of the PCB pattern with different
length and width. Where the thickness t is 70 mm. Where the horizontal axis is the length in
Fig (a) and the width in Fig (b), and the vertical axis is the impedance. In order to reduce an
inductance of the PCB pattern, it is preferable to shorten a length of the PCB pattern as short
as possible and to increase a width of the PCB pattern.
(a) With different length l
0
10
20
30
40
50
60
020 40 60 80 100 120
長さ [mm]
インダクタンス [nH]
Length l[mm]
Inductance [nH]
35
(b) With different width w
Fig.23 Calculation result of inductance of PCB pattern
2.2 Stray coupling in power electronic device
For power electronic devices with power up to 100 kW, size is an important issue.
Therefore, manufacturers make much efforts to minimize the size by integrating power
components, heat sink and control electronics. Accordingly, several problems arise due to
electromagnetic interaction between close components, and it can often lead to malfunction
and EMC problems. To reduce the interaction in the stage of development, information about
the electromagnetic fields generated from every component and conducting structure are
strongly required.
In this section, overview of the electromagnetic interactions, so-called a stray
capacitive coupling and magnetic coupling, is firstly discussed, and then a modeling method
to derive information on the two stray couplings are specifically explained.
2.2.1. Stray capacitive coupling
Fig. 24 shows the capacitive coupling between the overlapped PCB patterns in a
power electronic device. Common mode current flow out through the capacitive coupling, and
therefore it should be properly designed to be as small as possible from the viewpoint of
geometric configuration. However, it is intrinsically straightforward to consider stray
capacitive coupling compared to stray magnetic coupling. Because it exists between opposing
0
10
20
30
40
50
60
70
80
020 40 60 80 100 120
幅 [mm]
インダクタンス [nH]
Width w[mm]
Inductance [nH]
36
conductors such as above-mentioned PCB patterns and its location can be easily identified.
For this reason, stray capacitive couplings are out of the scope in this dissertation.
(a) Location of significant stray capacitance
(b) Equivalent circuit considering stray capacitance
Fig.24 Stray capacitive coupling between overlapped PCB patterns
2.2.2. Stray magnetic coupling
In contrast to stray capacitive coupling, stray magnetic coupling caused by the current
flow needs a more detailed analysis. Recent research points out a magnetic coupling between
components to severely influence a behavior of an EMI filter[25]-[27]. Even slight magnetic
coupling with coupling coefficient as low as 0.1 % can have significant influence and
dominate circuit behavior[28]. In Fig. 25, there is a parasitic magnetic field coupling caused by
large AC current between the power supply terminal and the inverter circuit. To weaken the
magnetic coupling, a magnetic shield was added and the conducted noise in AM band could
PCB patterns are overlapped in this area
Significant stray capacitance exist here
Upper layer Lower layer
Stray
capacitance
Motor
37
be successfully reduced by 15dB. With the miniaturization of the power electronic device,
similar problem could occur more often. Therefore, a magnitude and direction of magnetic
field generated from components and conducting structure have to be accurately predicted by
using an appropriate modeling.
(a) without magnetic shield (b) with magnetic shield
Fig.25 Example of EMC problem caused by stray magnetic coupling for an actual product
2.2.3. Modeling of conducting structure and coil
Stray magnetic couplings used in a filter performance simulation can be obtained
from geometry by means of 3D electromagnetic simulations[29]-[34]. Furthermore, effective
modeling methods of the relevant components for the 3D simulation have been reported in the
past investigations[35]-[37]. According to the investigations, geometry of conducting structures
and filter coils can be directly applied to the 3D simulation in most of cases. On the other
hand, in some cases, it is needed to consider influence of magnetic material in leakage
magnetic flux. With respect to this issue, simple and effective method to consider magnetic
material will be described later.
Fig. 26 Structure and simplified simulation model of filter coil[35]-[37]
38
2.2.4. Modeling of capacitor
3D simulation models of passive components have to be designed to accurately
obtain the stray magnetic field, and also it should avoid extensive calculation times due to
high complexity. From this viewpoint, in contrast to a filter coil, a geometry of a filter
capacitor requires a major modification, since an inner structure of a film capacitor used for a
filter capacitor is too complicated to be directly applied to the 3D simulation, as described in
Fig. 26. Hence, to obtain stray magnetic couplings, the modified capacitor model with the
simplified inner structure described in Fig. 27 is applied to the 3D simulation.
(a) X-ray photograph (side) (b) X-ray photograph (front)
(c) Illustration of inner structure
Fig. 26. Inner structure of filter capacitor[35]-[37]
Elektrode
(Metallisierung)
Dielektrikum
(Folie)
Metallisierte
Enden
Pin
i i
Metalized
end
Dielectric
(Film)
Electrode
(Metallization)
Pin
39
Fig. 27. Simplified model of filter capacitor[35]-[37]
An Inner structure of other type of capacitor used for a filter capacitor have to be
considered as well. Fig.28 shows an inner structure and simplified model of a tantalum
electrolytic capacitor.
(a) X-ray picture
(b) Model of current conducting path
Fig. 28 X-ray picture of inner structure of SMD tantalum electrolytic capacitor
and model of current conducting path
40
Chapter 3: Simplification method of stray
magnetic coupling
41
To realize an optimal filter design, stray magnetic couplings between components
should be properly taken into account in addition to a self stray impedance of the components,
as previously stated. And hence some modeling methods of stray magnetic couplings have
been investigated in the past[38], and some accurate simulations utilizing those modeling
methods have been reported[39]-[41]. However, it is not practical to consider a huge number of
stray magnetic couplings existing in a power electronic device, because a product designer
cannot determine which part of an EMC filter has to be modified for better performance by
using simulation with consideration of a huge number of stray magnetic couplings.
Furthermore, at an early stage of product design process, a product designer has no detailed
3D geometry of a product. Therefore, a reduction of the complexity of the modeling, namely
an extraction of major couplings, is strongly needed especially in a product design process.
With respect to an extraction of major couplings, the idea to identify major couplings has been
suggested[42], but however, since the idea is empirically developed using a specific prototype,
it is considerably ambiguous whether the idea is applicable to general EMC filter designs.
In this chapter, the basic idea of a proposed simplified modeling method of stray
magnetic couplings is introduced.
3.1 Complexity of considering stray magnetic coupling
Fig. 29 shows an EMC filter consisting of one coil, two capacitors and stray
inductances. Even in this simple filter, there are nine relevant stray inductances resulting in 36
stray magnetic couplings to be considered. The stray inductances originate from the PCB
tracks, the connecting cables, the leads of components, the leakage magnetic flux from the
coil, and so on. For example, the two stray inductances in the branch including the coil
correspond to the PCB tracks connected to the coil and the leakage inductance of the coil
respectively. The stray inductance in the branch including the capacitor is the combined stray
inductance of the capacitor and the PCB tracks connected to the capacitor.
42
Fig. 29 filter circuit considering stray inductance
3.2 Basic idea of simplification method
The EMC filter in Fig. 29 is assumed to be a part of the half-bridge circuit as shown
in Fig. 30. Either of the capacitors in the EMC filter is the DC link capacitor, which is a part
of the commutation cell. The noise current, the alternating current with high amplitude
flowing in the commutation cell, produces a voltage drop along the DC link capacitor. And
consequently, this voltage drop mainly produces a conducted noise which spreads to the
power supply lines through the EMC filter.
Although most of the conducted noise directly propagates to the power supply, a
considerable part can also indirectly propagate via magnetic couplings. The influence of the
indirect propagation will significantly increase, particularly when there is a large difference in
amplitude between the conducted noise at the input and the output of the EMC filter. As a
result, the filter performance of the filter is severely deteriorated by the indirect propagation.
Stray inductance
43
Fig. 30 Noise current in half-bridge circuit
The simplification method we propose is based on identifying current loops with high
amplitude and ones with low amplitude in the EMC filter. Current loops with high amplitude
radiate strong magnetic flux which is picked up by current loops with low amplitude.
Fig. 31 illustrates the basic idea of the simplification method. The equivalent circuit
of the half-bridge circuit is divided into three parts: the input loop, the high impedance area,
and the output loop. The input loop can be, for example, the commutation cell in the half-
bridge circuit composed of the current source Iin, the impedance of the current source Zin, the
impedance of the input capacitor (the DC link capacitor) ZCin, and the relevant stray
inductances[24]. The current Iin generates the large magnetic flux
in. And the output loop can
be, for example, the current loop composed of the impedance of the output capacitor ZCout, the
impedance of the power supply including connectors, cables and Line Impedance
Stabilization Network (LISN) Zout, and the relevant stray inductances.
DC link
EMC filter
Power
supply
Noise
current
Commutation cell
Load
44
Fig. 31 Basic idea of simplification method.
The magnetic flux
in generated from the input loop can cause a significant magnetic
coupling between the input loop and the output loop. And also, since the high impedance
components ZL like a filter coil connect the input loop to the output loop, the high impedance
area can be sensitive to a magnetic coupling with the input loop as well. An influence of a
magnetic coupling can be theoretically defined as an induced voltage. In Fig. 32, ehigh and eout
are the induced voltages caused by the magnetic couplings in the high impedance area and the
output loop respectively.
Fig. 32 Influence of magnetic coupling in EMC filter
Input High impedance Output
Iin
in Zout
Stray inductance
ZCin ZCout
ZL
EMC filter
Zin
Iin
Iout
ehigh eout
ZCout
ZCin
ZL
Ihigh
+
-+
-
Iout_out
Iout_high
Zout
Input High impedance Output
Zin
45
These induced voltages ehigh and eout cause the additional currents in the output loop
Iout_high and Iout_out, which deteriorate the performance of the EMC filter. Iout_high and Iout_out are
given by:
high
outCout
Cout
highout I
ZZ
Z
I+
=
_
(9)
outCout
outCout
L
Cinin
Cinin
high
outCout
Cout
ZZ
ZZ
Z
ZZ
ZZ
e
ZZ
Z
+
++
+
+
=
(10)
( )
outCoutLCinin
out
outout ZZZZZ
e
I++
=////
_
(11)
out
CoutL
Cinin
Cinin
CoutL
Cinin
Cinin
out
Z
ZZ
ZZ
ZZ
ZZ
ZZ
ZZ
e
+
++
+
+
+
=
(12)
Iout_high is the current flowing in the output loop caused by ehigh, Iout_out is the current
flowing in the output loop caused by eout, and Ihigh is the current flowing in the high
impedance area caused by ehigh.
Since the impedance of capacitors ZCin and ZCout and the impedance of the PCB tracks
Zin are generally much smaller than the impedance of the high impedance component ZL, the
following approximations can be applied.
L
outCout
outCout
L
Cinin
Cinin Z
ZZ
ZZ
Z
ZZ
ZZ
+
++
+
(13)
46
CoutLCoutL
Cinin
Cinin ZZZZ
ZZ
ZZ
+
+
(14)
LCoutL
Cinin
Cinin ZZZ
ZZ
ZZ ++
+
(15)
With the above-mentioned approximations (13)-(15), Iout_high and Iout_out can be
simplified as follows:
L
high
outCout
Cout
highout Z
e
ZZ
Z
I+
=
_
(16)
outCout
out
outout ZZ
e
I+
=
_
(17)
The influence of ehigh and eout can be compared using a ratio between the additional
currents in the output loop Iout_high and Iout_out expressed by (16) and (17). The ratio rIout is
described as:
out
high
L
Cout
outout
highout
Iout e
e
Z
Z
I
I
r==
_
_
(18)
Unless ehigh is much larger than eout, the ratio rIout is basically much smaller than one,
because ZL is much larger than ZCout from the viewpoint of a filter design; otherwise the EMC
filter has no effect on noise attenuation. Based on this premise, since the influence of ehigh is
negligible, the stray magnetic couplings in the EMC filter can be simplified as described in
Fig. 33, where Min-out is the major stray magnetic coupling between the input loop and the
output loop.
47
Fig. 33 Major stray magnetic coupling in EMC filter
ZCin ZCout Zout
Iin Iout
Input Output
Min-out
Zin
48
Chapter 4: Application of simplification
method to EMI filter circuit
49
In this chapter, the proposed simplified modeling method is applied to several
different EMC filters. And the filter performance of the EMC filter Pf is compared between a
measurement and a simulation to prove an effectiveness of the proposed simplification
method and clarify its limitation.
4.1 Application to simple filter circuit
Fig. 34 depicts a system configuration for a measurement of a filter performance Pf.
In this measurement, Pf is defined as the ratio of the output voltage A divided by the reference
voltage Ref, measured by means of Gain-Phase analyzer: Agilent 4395A. The range of
measuring frequency is set from 0.01-100 MHz. The nanocrystalline cores in Fig. 34 are used
to suppress common mode current flowing through the Gain-Phase analyzer. Regarding the
measurement of Pf, less than -100 dB is inaccurate due to the limit of signal to noise ratio.
Fig. 34 System configuration for a measurement of Pf
A
Ref
Input
Power splitter P
N
P
N
Tested filter
Nanocrytalline core
50
4.1.1. First device under test
The EMC filter used in the first application is illustrated in Fig. 35, and Fig. 36 shows
its equivalent circuit. In Fig. 36, a major stray magnetic coupling obtained based on the
aforementioned simplification and the following classical stray impedances are considered:
the equivalent series resistance (ESR) and the equivalent series inductance (ESL) of the
capacitors and the PCB tracks, the equivalent parallel resistance (EPR) and the equivalent
parallel capacitance (EPC) of the coil. Where Lleak1 and Lleak2 are leakage inductances of the
coil. The stray magnetic couplings and the classical stray impedances are obtained from 3D
geometries by means of the commercial simulation software: ANSYS Q3D Extractor[33].
Fig. 35 Tested EMC filter for first application
ZL: 1.1 mH
Cin:2.2 mFCout:2.2 mF
ZL: 1.1 mH
51
Fig. 36 Equivalent circuit of EMC filter used in circuit simulation
In Fig. 37, the filter performance Pf is compared between the measurement and the
simulation without and with consideration of the major stray magnetic coupling. Where the
horizontal axis is the frequency and the vertical axis is the filter performance. It can be seen in
Fig. 37 that the simulation considering the major stray magnetic coupling and the
measurement show a good agreement with the error of less than 5 dB in the frequency range
up to 70 MHz. On the other hand, the simulation result without consideration of the stray
magnetic couplings is totally different from the measurement result. From the result, it can be
concluded that the simulation using the proposed modeling has a sufficient accuracy to predict
the influence of the stray magnetic coupling.
But whereas, there can be an exception: an accuracy of a simulation using the
proposed simplified modeling deteriorates for a certain structure of an EMC filter. In the next
section, the limitation of the proposed simplification method is investigated in detail using an
EMC filter with different structure.
Lleak1
k=1
Lleak2
Inductance
Resistance
Min-out
52
Fig. 37 Comparison of Pf between simulation and measurement
4.1.2. Second device under test
Fig. 38 shows the EMC filter used for the second application with the following
differences compared to the EMC filter used in the previous section: the larger input loop, the
longer distance between the two capacitors, and the smaller output loop. As a result of these
differences, the induced voltages eout and ehigh become higher and lower respectively, in other
words, a ratio between Iout_high and Iout_out is increased and not much smaller than one.
Fig. 39 depicts a comparison of the filter performance Pf of the EMC filter between
the measurement and the simulation. Where the horizontal axis is the frequency and the
vertical axis is the filter performance.
-140
-120
-100
-80
-60
-40
-20
0
0.01 0.1 1 10 100
Sim. w/o coupling
Sim. w/ 1 coupling
Measurement
0
-20
-40
-60
-80
-100
-120
0.01 0.1 1 10 100
Filter performance Pf[dB]
Frequency [MHz]
-140
53
Fig. 38 Tested EMC filter with different structure
Fig. 39 Comparison of Pf between simulation and measurement using different EMC filter
Larger input loop
Smaller output loop
Longer distance
-120
-100
-80
-60
-40
-20
0
0.01 0.1 1 10 100
Sim. w/ 1 coupling
Measurement
0
-20
-40
-60
-80
-100
-120
0.01 0.1 1 10 100
Filter performance Pf[dB]
Frequency [MHz]
54
In Fig. 39, it can be found that there is a considerable difference of 16 dB between the
simulation and the measurement. And hence, it can be concluded that the indispensable
premise used for the aforementioned simplification of modeling is no longer effective.
Namely, the influence of the induced voltage in the high impedance area ehigh has to be
considered as well as eout in order to realize an accurate simulation of a filter performance Pf
of the tested EMC filter.
In the next section, the limitation of the proposed simplification method is
theoretically investigated, and a major stray magnetic coupling to be additionally considered
for an accurate simulation is discussed.
4.2 Investigation and extension of the proposed
simplification method
4.2.1. Extension of simplification method
Fig. 40 depicts the tested EMC filter considering the influences of the magnetic field
generated from the input, where ZLdif1 and ZLdif2 are impedance of the leakage inductances of
the filter coil.
Fig. 40 Tested EMC filter including influence of magnetic field
Iin
Iout
ehigh1 eout
ZCout
ZCin
ZLdif1
Ihigh
+
-+
-
Iout_out
Iout_high
Zout
Input High impedance Output
ZLdif2 ehigh2
+-
Zin
55
In Fig. 40, the ratio between the output currents Iout_high and Iout_out is given by:
out
highhigh
LdifLdif
Cout
outout
highout
Iout e
ee
ZZ
Z
I
I
r21
21_
_+
+
==
(19)
The induced voltage eout is generated by the stray magnetic coupling between the
input loop and the output loop Min-out, and the induced voltage ehigh is dominantly generated by
the stray magnetic coupling between the filter coil and the input loop Min-L. Therefore, eout and
ehigh can be respectively described as follows:
dt
dI
Me in
outinout -
=
(20)
dt
dI
Me in
Linhigh -
(21)
And by using (20) and (21), rIout is given by:
out
highhigh
LdifLdif
Cout
outout
highout
Iout e
ee
ZZ
Z
I
I
r21
21_
_+
+
==
outin
LinLin
LdifLdif
Cout
M
MM
ZZ
Z
-
-- +
+
=21
21
(22)
Note that a magnetic material used for a core of a filter coil should be properly
considered in a calculation of a stray magnetic coupling. Although a software developed for
research has been reported which can deal with a magnetic material[43], most of commercial
simulation software to obtain partial impedances cannot consider a magnetic material, or even
56
if it is possible, a simulation considering a magnetic material can lead to an immense increase
of computational time and a poor convergence of simulation. And thus, a magnetic
characteristic of a magnetic material has to be considered in a simple way. A simple method to
consider a magnetic is specifically explained in the next section.
Moreover, since the structure of the EMC filter is symmetric, the following two
relations can be applied to (22).
LdifLdifLdif ZZZ == 21
(23)
LinLinLin MMM --- == 21
(24)
Fig. 41 describes the EMC filter circuit considering one conventional major stray
magnetic coupling and two additional ones derived using (23) and (24).
Fig. 41 EMC filter circuit considering major stray magnetic couplings
ZCin ZCout Zout
Iin Iout
Input Output
Min-out
ZLdif1
Min-L
ZLdif2
Min-L
Zin
57
Accordingly, rIout can be defined again as follows:
outin
Lin
Ldif
Cout
outout
highout
Iout M
M
Z
Z
I
I
r
-
-
== 2
2
_
_
(25)
Fig. 42 depicts a calculated rIout using (25). Where the horizontal axis is the frequency
and the vertical axis is the ratio of output current. It can be seen that rIout is mostly larger than
one in the frequency range from 10 kHz to 100 MHz; the induced voltage ehigh has a larger
influence than eout at most frequencies. This fact in Fig. 42 corroborates that the necessity of
consideration of ehigh to realize an accurate simulation of the tested EMC filter.
Fig. 42 Calculated ratio of output current rIout
4.2.2. Consideration of magnetic material
Leakage magnetic flux generated from a filter coil can be divided into two main parts
as shown in Fig. 43[44].
0.01
0.1
1
10
100
1000
10000
100000
0.01 0.1 1 10 100
0.1 1 10 100
0.01
10000
1000
100
10
1
0.1
0.01
100000
Ratio of output current rIout
Frequency [MHz]
58
In the past study[44], it is concluded that a main leakage flux is the leakage flux 2.
However, the flux 1 is much larger than the leakage flux 2 for the filter coil used in the
previous section, as can been seen from Fig. 44: the simulation result of the magnetic flux line
generated from the filter coil by differential mode current at the frequency of 1 MHz. It
indicates that the conclusion in the past study[44] is applicable to a limited structure of an EMC
filter. In other words, a major leakage flux must be carefully considered, since it is strongly
dependent on a structure of a filter coil.
The magnetic path of the leakage flux 1 is composed of the small core part with a
high permeability and the large air-gap part with a low permeability, and hence the total
effective permeability
m
eff is strongly correlated to a structure of the winding and the core,
similarly to a solenoid coil.
In the past study[45][46], it is concluded that leakage magnetic flux from a typical
common mode choke coil generated by differential mode current is nearly equal to that from a
solenoid coil. That is because the magnetic fluxes inside the core, that are generated by the
differential currents in both of the windings, repel each other and flow outside of the core as
shown in Fig. 44.
Fig. 43 Major leakage magnetic flux from filter coil
Leakage flux 1
Leakage flux 2
59
Fig. 44: Magnetic flux line of filter coil
Figure 45 illustrates the idea of the approximation. The winding of the coil can be
described as the solenoid coil with the same effective magnetic length l and the same cross
section A in this approximation.
The effective magnetic length l is given by:
360
2
rl =
(26)
60
Fig. 45 Magnetic flux line of filter coil
Figure. 46 shows the effective permeability of the core as a function of
, a ratio of
rod length divided by rod diameter, with different curves for material permeability
m
i, where
is given by:
2
l
A
=
(27)
Table 1 shows a value of A, l,
and
m
i used in the calculation of the effective
permeability
m
eff.
Table 1 Obtained values for calculation of
m
eff
r
A
A
l
A[m2]
ｌ
[m]
m
i
2
1005.2 -
5
1096.8 -
9.1
10000
61
Using the values in Table. 1, the obtained effective permeability
m
eff is 6.5 as shown in
Fig. 46. Where the horizontal axis is the
and the vertical axis is the
m
eff.
Fig. 46 Effective permeability of core as a function of
[45][46]
Since a mutual inductance is theoretically proportional to an effective permeability of
a core
m
eff, the magnetic coupling considering the core is given by:
aireffcore MM
m
=
(28)
Where Mcore and Mair are a magnetic coupling with and without the core respectively.
6.5
62
The obtained
m
eff is validated by comparing a magnetic flux distribution using FEM
simulation HFSS[34]. The simulation model is shown in Fig. 47, and the simulation condition
is shown in Table 2. In Fig. 47, a current source injects a test signal between the taps of the
two windings while the other two taps are connected. Accordingly, the discussed magnetic
leakage flux is excited: a flux generated from the differential inductance of the coil.
Fig. 47 Model for simulation of magnetic flux distribution
Table 2 Simulation condition
Fig. 48 compares the simulated result of magnetic flux distribution generated from
the filter coil between with the core and without the core.
XY
Z
Current I
Short circuit
3mm
Measuring plane of magnetic flux distribution
Frequency [MHz] Current for with core [A] Current for without core [A]
1 1 6.5 (=
m
eff)
63
Fig. 48 Distribution of magnetic flux from filter coil
The results illustrated in Fig. 48 shows a good agreement. The leakage inductance
itself is theoretically proportional to a permeability, and hence it can be concluded that the
calculation method of
m
eff using the aforementioned approximation is sufficiently accurate for
considering an effect of a magnetic material in a simulation aiming at an optimal filter design.
4.2.3. Result using improved simplified modeling method
Fig. 49 shows the improved equivalent circuit of the EMC filter considering the three
major stray magnetic couplings and the classical stray impedances. Where Lleak1 and Lleak2 are
a leakage inductance of the filter coil.
In Fig. 50, the filter performance Pf is compared between the measurement and the
two simulations: circuit simulation considering classical stray impedances and one major
stray magnetic coupling Min-out, and circuit simulation considering classical stray impedances
and three stray magnetic couplings: two Min-Ls and one Min-out. Where the horizontal axis is the
frequency and the vertical axis is the filter performance. The Min-out is obtained by means of
ANSYS Q3D Extractor[33]. On the other hand, in terms of the two Min-Ls, the value of stray
magnetic coupling obtained by ANSYS Q3D Extractor[33] is multiplied by
m
eff which is
calculated based on the aforementioned approximation, in order to consider the influence of
the magnetic core.
With core (I: 1A) Without core (I: 6.5A)
X
Z
[Wb/m2]
4
102-
4
101-
5
102-
5
101-
6
102-
5
105-
6
105-
64
Fig. 49 Improved equivalent circuit of EMC filter considering major stray magnetic couplings
and classical stray impedances
Fig. 50 Comparison of filter performance Pf
Lleak1
k=1
Lleak2
Inductance
Resistance
Min-out
Min-L
Min-L
-120
-100
-80
-60
-40
-20
0
0.01 0.1 1 10 100
Sim. w/ 1 coupling
Sim. w/ 3 couplings
Measurement
0
-20
-40
-60
-80
-100
-120
0.01 0.1 1 10 100
Filter performance Pf[dB]
Frequency [MHz]
65
In Fig. 50, it can be seen that additionally considering the two additional stray
magnetic couplings can produce a substantial improvement of 13 dB in accuracy in the
frequency range up to 8 MHz, compared to the simulation considering only Min-out. But
whereas, there is still the considerable difference of 20 dB in the frequency range higher than
8 MHz. With respect to the observed difference, it is assumed that the difference originates
from a different magnetic flux distribution generated from the filter coil between in low
frequency and high frequency. This change in magnetic flux distribution is particularly
discussed in the following section.
The aforementioned extended simplification method is also applicable to an EMC
filter with a shield. Fig. 51 shows the tested EMC filter with the shield between the input and
output loop. Due to an influence of the shield, the induced voltages eout become lower[47]-[49].
And, in other words, a ratio riout is not much smaller than 1 as described in Fig. 52. Where the
horizontal axis is the frequency and the vertical axis is the ratio of output current.
Fig. 53 shows the equivalent circuit of the EMC filter with the filter between the
input and the output loop. Where Lleak1 and Lleak2 are a leakage inductance of the filter coil.
Fig. 51 Tested EMC filter with shield between input loop and output loop
66
Fig. 52 Calculated ratio of output current rIout
Fig. 53 Equivalent circuit of EMC filter with shield between input and output loop
0.01
0.1
1
10
100
1000
10000
100000
0.01 0.1 1 10 100
Frequency [MHz]
0.1 1 10 100
0.01
10000
1000
100
10
1
0.1
0.01
100000
Ratio of output current rIout
Lleak1
k=1
Lleak2
Inductance
Resistance
Lleak1. leak2 : leakage inductance
of filter coil
Min-out
Min-L
Min-L
Shield
67
In Fig. 54, the filter performance Pf is compared between the measurement and the
simulation considering classical stray impedances and three stray magnetic couplings: two
Min-Ls and one Min-out. Where the horizontal axis is the frequency and the vertical axis is the
filter performance. The two Min-Ls are obtained by the same steps as the second tested EMC
filter. Meanwhile, Min-out is obtained by means of FEM simulation software HFSS[34]. ANSYS
Q3D Extractor[33] uses a field solver based on the method of moments (MoM), and thus it
cannot directly consider skin effect inside conductors. That is to say, the software can not
accurately calculate the influence of the shield in the stray magnetic coupling Min-out.
And, similarly to the second tested EMC filter, additionally considering the two
additional stray magnetic couplings realize an accurate simulation and it shows a good
agreement between the simulation and the measurement result in the frequency range up to
100 MHz.
Fig. 54 Comparison of filter performance Pf
68
4.3 Further discussion on modeling of filter coil
4.3.1. Leakage magnetic flux from fully-wound coil
As previously stated, leakage magnetic flux generated from a filter coil can be
divided into two main parts and a major leakage flux is strongly dependent on a structure of a
filter coil. In contrast to a partly-wound coil used for the aforementioned investigation, the
main leakage flux generated from a fully-wound coil is the leakage flux 2, as shown in Fig. 55
and Fig. 56. As can be seen from Fig. 56, leakage magnetic flux 2 flow outside of the core and
is not influenced by the core, and in other words, it is not necessary to consider the
permeability of the core in this case.
The simulation model is shown in Fig. 57, and the simulation condition is shown in
Table 3. In Fig. 57, a current source injects a test signal between the taps of the winding.
Fig. 55 Major leakage magnetic flux from fully-wound filter coil
Leakage flux 1 Leakage flux 2
69
Fig. 56 Magnetic flux line of filter coil
Fig. 57 Model for simulation of magnetic flux distribution
XY
Z
Current: I
3mm
Measuring point of magnetic flux distribution
70
Table 3 Simulation condition
Fig. 58 compares the simulation result of magnetic flux distribution generated from
the filter coil between with the core and without the core. The results illustrated in Fig. 58
shows a good agreement, and hence it can be concluded that leakage magnetic flux 2 is few
dependent of the presence of the magnetic material.
Fig. 58 Distribution of magnetic flux from fully-wound filter coil
In relation to the leakage magnetic flux 2, the past study has suggested that the
winding of the coil can be divided into two parts[50]. And, by focusing on the dominant
leakage flux, the winding of the coil can be simplified as shown in Fig. 59.
Frequency [MHz] Current [A]
1 1
With core (I: 1A) Without core (I: 1A)
X
Z
[Wb/m2]
5
101-
6
105-
6
101-
7
101-
6
102-
7
102-
7
105-
71
(a) Dominant leakage flux from winding
(b) Simplified model of winding focusing on dominant leakage flux
Fig. 59 Basic idea for simplification of winding
Next a simulation is executed to validate the correctness of the proposed
simplification of a winding. The simulation model is shown in Fig. 60, and the simulation
condition is the same as Table 3. In Fig. 47, a current source injects a test signal between the
taps of the winding.
Dominant leakage flux
Current: I
Current: I
72
Fig. 60 Model for simulation of magnetic flux distribution
Fig. 61 shows a comparison of the simulation result of magnetic flux distribution
generated from the filter coil between with the complete and simplified winding. The both
results match pretty well and it shows that the proposed simplification is effective for this type
of winding.
Fig. 61 Comparison of magnetic flux distribution
XY
Z
Current: I
3mm
Measuring point of magnetic flux distribution
Complete winding Simplified winding
X
Z
[Wb/m2]
5
101-
6
105-
6
101-
7
101-
6
102-
7
102-
7
105-
73
4.3.2. Influence of stray capacitance on generated magnetic flux from filter coil
The previous study has suggested that the magnetic flux distribution can be strongly
affected by a displacement current flowing through a stray capacitance of filter coil[51][52]. In
other words, a magnetic flux distribution can change dramatically in the vicinity of a self-
resonant frequency of a filter coil, because the current path is completely different between
the inductive region and the capacitive region as described in Fig. 62. Where the horizontal
axis is the frequency and the vertical axis is the magnitude of impedance.
Fig. 62 Difference of current path between inductive and capacitive region
The simulations of leakage magnetic flux are executed to compare magnetic flux
distribution under different frequencies. The simulation model is shown in Fig. 47, which is
the same as the aforementioned investigation. The simulation condition is listed in Table 4
and Fig. 63 illustrates the relationship between the magnitude of impedance and the
simulation frequencies. Where the horizontal axis is the frequency and the vertical axis is the
magnitude of impedance.
0.1
1
10
100
1000
10000
100000
10000 100000 1000000 10000000 100000000
Z_DIF_sim
Z_DIF_sim
100000
Magnitude of impedance[W]
0.01 0.1 1 10 100
Frequency [MHz]
10000
1000
100
10
1
0.1
Frequency [MHz]
0.1 1 10 100
0.01
10000
1000
100
10
1
0.1
100000
Magnitude od impedance [W]
Inductive Capacitive
Current i
Current i
74
Table 4 Simulation condition
Fig. 63 Relationship between magnitude of impedance and simulation frequencies
Fig. 64 shows a comparison of the simulation result of magnetic flux distribution
generated from the filter coil at the simulation frequency of 1 MHz, 10 MHz, 50 MHz and
150 MHz. The simulation results at 1 MHz and 10 MHz show a good agreement, but however
it starts to change as frequency increase toward the self-resonance frequency. And accordingly,
it shows the completely different distribution in the capacitive region. The results of this
investigation reveal that a dedicated modeling method is needed to accurately predict stray
magnetic couplings, especially for a filter coil used in the frequency range higher than its self-
resonance frequency.
Frequency [MHz] Current [A]
1, 10, 50, 150 1
0.1
1
10
100
1000
10000
100000
10000 100000 1000000 10000000 100000000
Z_DIF_sim
Z_DIF_sim
100000
Magnitude of impedance[W]
0.01 0.1 1 10 100
Frequency [MHz]
10000
1000
100
10
1
0.1
Frequency [MHz]
0.1 1 10 100
0.01
10000
1000
100
10
1
0.1
100000
Magnitude od impedance [W]
Inductive Capacitive
(a) 1 MHz
(b) 10 MHz
(c) 50 MHz
(d) 150 MHz
75
(a) 1MHz (b)10 MHz
(c) 50MHz (d)150 MHz
Fig. 64 Simulation result of magnetic flux distribution generated from the filter coil
at the different simulation frequencies
76
4.3.3. Design procedure of EMC filter
This section shows a procedure to optimally design an EMC filter considering the
aforementioned major stray magnetic coupling Min-out and Min-L. In this procedure, the
following steps can be taken:
1) Current loops with a high amplitude and those with a low amplitude in a circuit are
identified as input loop and output loop.
2) Relevant components are placed to make the cross section of the identified input loop
and output loop as small as possible, since both of the major stray magnetic couplings
Min-out and Min-L are decreased by reducing the cross section.
3) In order to clarify major stray magnetic couplings to be considered, rIout is calculated
in the frequency range where ZL is much larger than ZCout.
4) When rIout is much smaller than one, the placement of relevant components is
iteratively changed until Min-out reaches a minimal value. Otherwise the placement of
are iteratively changed until the both of Min-out and Min-L reach a minimal value.
4.4 Application to EMC filter for a SiC solar inverter
In this chapter, to clarify its applicability and its problems to be solved for application
to actual products, we apply the proposed modeling method to an EMC filter for a SiC solar
inverter[53].
4.4.1. Tested EMC filter
Fig. 65 depicts the EMC filter for the SiC solar inverter used in the verification. And
Fig. 66 shows the circuit schematic of the tested EMC filter used for the three-phase grid
connection. The filter is composed of the three output inductors Lout, the two common mode
choke coils LCM, the nine X-capacitors CX, and the two Y-capacitors CY. This EMC filter has
26 stray inductances resulting in 325 stray magnetic couplings.
77
Fig. 65 Tested EMC filter for SiC solar inverter.
Fig. 66 Circuit schematic of the tested EMC filter.
EMC filter
VEMI
R
50Ω
A
50Ω
Lout1
Lout2
Lout3
CX1*
CY1
CX2*
CY2
LCM1 LCM2
CX3*
50Ω
50Ω
800 mH
2.2 mF
220 nF
1.2 mH (CM) 1.2 mH (CM)
2.2 mF
100 nF
1 mF
800 mH
800 mH
Uin
Vin
Win
Uout
Vout
Wout
CM: Common mode
78
4.4.2. Consideration of magnetic material
As previously stated, the effective permeability
m
eff related to the leakage magnetic
flux from the coil can be easily derived by using the approximation, where necessary[45][46].
Whereas it is assumed that the leakage magnetic flux from the coil generated by
common mode current is not significantly influenced by the core, because the magnetic fluxes
inside the core do not repel each other. Similarly, to the common mode choke coil, it is also
assumed that the leakage magnetic flux from the output inductor is not significantly
influenced by the core for the same reason.
To validate the assumption, a distribution of magnetic flux from the output inductor is
compared between ones with and without the core by means of 3D Finite Element Method
(FEM) simulation software: ANSYS HFSS [34].
The output inductor is built using a Hitachi Metals AMCC-40 core with an air gap of
1.1 mm. The number of turns of the winding is 48. The horizontal and vertical wire sizes of
the winding are 6 mm and 2 mm respectively. Fig. 67 shows the simulation model. The input
current is 1 A, and the simulating frequency is 1 MHz.
Fig. 67 Model for simulation of magnetic flux distribution.
X
Y
Z
Current: I
X-Y plane
X-Z plane
79
Fig. 68 presents the comparison of the simulated magnetic flux distribution on X-Y
and X-Z planes between the output inductors with and without the core.
In Fig. 68, there is no significant difference in the distribution of the magnetic flux
between the simulation results with the core and without the core. Moreover, the common
mode choke coil is not the main part of the output loop. Thus, we reach a conclusion that it is
not necessary to consider
m
eff of the output inductor and the common mode choke coils for the
filter performance simulation conducted in the next section. On the other hand, it is highly
likely that
m
eff needs to be considered by using the above-mentioned approximation for the
simulation in differential mode. In future work, the influence of
m
eff needs to be investigated
in more detail.
Fig. 69 shows the circuit schematic of the tested EMC filter with the highlighted
input loop, output loop, and stray magnetic couplings Min-out and Min-L. Common mode noise
is critical and thus it has to be suppressed by the tested EMC filter. Therefore, the highlighted
loops and stray magnetic couplings are extracted focusing on the path of common mode
current.
(a) With core (b) Without core
4
102-
5
102-
6
102-
7
102-
4
102-
5
102-
6
102-
7
102-
[Wb/m2]
80
(c) With core (d) Without core
Fig. 68 Distribution of magnetic flux: X-Y plane in (a) and (b); X-Z plane in (c) and (d).
Fig. 69 Circuit schematic with the highlighted input loop, output loop,
and major stray magnetic couplings.
Fig. 70 presents calculated rIout using (29), where the simulated values of Min-out and
Min-L are 3.2 nH and 0.25 nH respectively. Where the horizontal axis is the frequency and the
vertical axis is the ratio of output current.
4
102-
5
102-
6
102-
7
102-
4
102-
5
102-
6
102-
7
102-
[Wb/m2]
VEMI
R
50Ω
A
50Ω
Lout1
Lout2
Lout3
CX1*
CY1
CX2*
CY2
LCM1 LCM2
CX3*
50Ω
50Ω
Uin
Vin
Win
Uout
Vout
Wout
CM: Common mode
Min-out
Min-L
81
outin
Lin
L
Cout
outout
highout
Iout M
M
Z
Z
I
I
r
_
_
_
_==
(29)
Fig. 70 Calculated ratio of output current rIout.
It can be seen that calculated rIout is smaller than 0.1 in the frequency range from 0.02
MHz to 30 MHz. Therefore, it is concluded that the influence of the induced voltage in the
high impedance area ehigh is negligible in this frequency range. This fact in Fig. 70
corroborates that the major stray magnetic coupling in the tested EMC filter is Min-out.
4.4.3. Comparison of filter performance
To verify the effectiveness of the proposed modeling method, the filter performance
of the EMC filter is compared between a measurement and a simulation.
Fig. 71 depicts a system configuration for a measurement of a filter performance Pf in
common mode. In this measurement, Pf is defined as the ratio of the output voltage A to the
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
0.01 0.1 1 10 100
10
1
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.01 0.1 1 10 30
Frequency [MHz]
Ratio of output current rIout
82
reference voltage Ref. The range of measuring frequency is set from 0.01 MHz to 30 MHz.
The nanocrystalline cores in Fig. 71 are used for the aforementioned reason.
Fig. 71 System configuration for measurement of Pf.
Fig. 72 shows the circuit simulation model with the highlighted input loop, output
loop, and major stray magnetic coupling Min-out. The software used for the circuit simulation is
Portunus[54]. The major stray magnetic coupling incorporated into the circuit simulation model
described in Fig. 72 is obtained from the 3D geometry by using the PEEC method software:
FASTHENRY[29].
Fig. 73 depicts the 3D simulation model including the output inductor, the common
mode choke coil, the X and Y-capacitors, the connecting wires and the PCB tracks. The
inductor and the coil have no core based on the conclusion in the preceding section.
A
Ref
Power splitter UVW
GND
UVW
GND
Tested EMC filter
Nanocrytalline core
83
CY1
N1
GND
A
R:=50
L:=L_LCM
L:=L_LCM
L:=L_LCM
R:=R_LCM
N23
R:=R_LCM
R:=R_LCM
N19
N24
C:=7p
C:=7p
C:=7p
CX23 CX22 CX21
CY2
CX13 CX12 CX11
L:=2.5u
L:=2.5u
L:=2.5u
C:=21p
R:=1.1k
C:=21p
R:=1.1k
C:=21p
R:=1.1k
L:=720u
L:=720u
L:=720u
C:=18p
R:=8k
N43
N45
N53
C:=18p
R:=8k
C:=18p
R:=8k
N54
N50
N51
N4
N21
N9
N17 N28 N27 N8 N12
N20
GND
E
+
E1
AC:=1.0
R:=50
GND GND
R:=50
N6
R
R:=50
N2
GND
N26
L:=L_LCM
L:=L_LCM
L:=L_LCM
R:=R_LCM
N230
R:=R_LCM
R:=R_LCM
N190
N240
C:=7p
C:=7p
C:=7p
N16N31
N30
N18
lcy1 lcy2
lcx21lcx22lcx23
N10
N15
lcx11lcx12lcx13
N25
N29
lzu1
lzu2
lzu3
Resistance
Matrix
Resistance
Matrix
R_M325_LCM7_ND48
Inductance
Matrix
Inductance
Matrix
L_M325_LCM7_ND48
Ck=30fF
C:=30f
N7 N3
Ref A
Input Output
Min-out
Fig. 72 Circuit simulation model with the highlighted input loop, output loop,
and major stray magnetic coupling.
84
Fig. 73 Simulation model of tested EMC filter.
Fig. 74 shows a comparison of the filter performance Pf in common mode between
the measurement and the simulation with the following three conditions: considering the
classical stray impedances (ESR and ESL of a capacitor and EPR and EPC of a coil),
considering the classical stray impedances and all the stray magnetic couplings (325
couplings), considering the classical stray impedances and only the major stray magnetic
couplings (1 coupling) derived with the proposed modeling method. Where ESR is an
equivalent series resistance, ESL is an equivalent series inductance, EPR is an equivalent
parallel resistance, and EPC is an equivalent parallel capacitance. And the horizontal axis is
the frequency and the vertical axis is the filter performance.
In Fig. 74, the measurement result and the simulation results considering all the
couplings and only the major coupling show a good agreement in the frequency range up to
10 MHz. On the other hand, the simulation without consideration of the stray magnetic
coupling inaccurately predicts the filter performance with the difference of more than 100 dB
compared to the measurement result. Most importantly, the simulation using the proposed
modeling method realizes a comparably accurate prediction in comparison with the
simulation using the conventional modeling method, even though the number of the
considered stray magnetic couplings is dramatically reduced from 325 to just one. Regarding
the difference in the frequency range higher than 10 MHz, it is assumed that it is caused by
Common mode
choke coil
Output inductor
85
the following three elements: 1) the connections between the shielded cables and the tested
EMC filter forming a small loop, which can be affected by magnetic flux, 2) the residual
common mode current flowing through the measuring instrument, and 3) the changed
distribution of magnetic flux of the coils due to the stray capacitances over their self
resonance frequencies[51][52].
Fig. 74 Comparison of Pf between simulation and measurement.
-200
-150
-100
-50
0
0.01 0.1 1 10
Filter performance Pf [dB]
frequency [MHz]
Sim. w/o couplings
Sim. w/ 325 couplings
Sim. w/ 1 coupling
Measurement
0
-50
-100
-150
-200
0.01 0.1 1 10 30
Filter performance Pf[dB]
Frequency [MHz]
86
Chapter 5: EMI design of actual product
based on proposed simplification method
87
5.1 Configuration of EMC filter
As stated in previous chapters, an accurate prediction of EMC filter performance can
be simply realized by using the proposed simplification method of a stray magnetic coupling.
In this chapter, to validate its effectiveness in a product design process, it is applied to
a prototype of an actual product. Firstly, a filter simulation considering a major stray magnetic
coupling is carried out as well as previous chapters. And then, a design refinement for
improving EMC performance is investigated focusing on components which cause the major
stray magnetic coupling. Finally noise terminal voltage of LISN is compared between before
and after an application of the design refinement.
Fig. 75 shows a placement of EMC filter and DC capacitor in the tested prototype of
the product and Fig. 76 illustrates its circuit schematic. The EMC filter consists of two filter
coils and one filter capacitor as shown in Fig. 76.
Fig. 75 Placement of EMI filter and DC capacitor in tested prototype of the product
EMC filter and DC capacitors
88
Fig. 76 Circuit schematic of EMI filter and DC capacitor
5.2 EMC filter simulation using simplification method
5.2.1. Identification of major stray magnetic coupling
Although 3D simulation has be carried out to identify major stray magnetic coupling,
the complete model of the product cannot be applied due to a huge amount of computational
time brought by its complex geometry. To solve this issue, the 3D model needs to be
simplified according to the following steps.
Firstly, to reduce the number of components in a simulation model, a path of a noise
current which generates stray magnetic couplings has to be identified. Fig. 77 shows the
identified path of the noise current and it can be seen that the current flow through the
switching devices, the DC link capacitors, the shunt resistors and the connecting PCB patterns,
and the current causes the influence on the LC filter and the components connecting to the
battery. That is to say, the other components irrelevant to stray magnetic couplings can be
removed.
2.5 mH
2.5 mH
2.2 mF
3 *330 mF
DC capacitor
Filter coil
Filter capacitor
Relay
89
Fig. 77 Noise current in the tested prototype
And next, to reduce the number of minute shapes in a simulation model, especially
minute shapes of PCB patterns have to be simplified. As described in Fig. 78, the small edges
in PCB patterns can be removed, because it has no influence on distribution of the noise
current. Similarly, the via holes included in the current path can be united and the via holes
excluded in the current path can be removed. With respect to the DC link capacitors, they are
simplified in the same way mentioned in the Chapter 2.
(a)Complete model (b)Simplified model
Fig. 78 Comparison of PCB pattern between complete model and simplified model
90
Fig. 79 depicts a 3D simulation model used for an identification of major stray
magnetic couplings using ANSYS Q3D extractor[33].
Fig. 79 Simplified 3D simulation model used for extraction of major stray magnetic coupling
Fig. 80 shows the simulation results of the current distribution in the input loop and
the output loop. The current flowing in the input loop generates major stray magnetic
couplings, and the simulated value of Min-L and Min-out shown in Fig. 81 are 0.9 nH and 0.1 nH
respectively. Regarding the Min-L, it is obtained by means of ANSYS Q3D extractor[33] in
consideration of the filter core using the aforementioned approximation.
91
Fig. 80 Simulation results of current distribution in input loop and output loop
Fig. 81 Major stray magnetic couplings in tested EMC filter for EPS-ECU
5.2.2. Comparison of filter performance between measurement and simulation
Fig. 82 presents calculated value of rIout using (29). Where the horizontal axis is the
frequency and the vertical axis is the ratio of output current. It can be seen that calculated rIout
is higher than 1 in the frequency range lower than 0.2 MHz. As previously stated, influence of
the Min-L is not negligible in the frequency range. But however, influence of magnetic
1st layer
2nd layer
Input loop Output loop
2.5 mH
2.5 mH
2.2 mF
3 *330 mF
Min-out
Min-L
Input loop Output loop
92
coupling is theoretically proportional to frequency and have no sufficient influence in EMC
filter performance in the frequency range, as can be seen from the investigations in the
preceding chapters such as Fig. 37 and Fig. 74. From this fact, we conclude that the major
stray magnetic coupling in the tested EMC filter is Min-out.
outin
Lin
L
Cout
outout
highout
Iout M
M
Z
Z
I
I
r
_
_
_
_==
(29)
Fig. 82 Calculated ratio of output current rIout.
Fig. 83 depicts a system configuration for a measurement of a filter performance Pf.
In this measurement, Pf is defined as the ratio of the output voltage A to the reference voltage
Ref. The range of measuring frequency is set from 0.01 MHz to 100 MHz. The
nanocrystalline cores in Fig. 83 are used for preventing common mode current from flowing
through the measurement instrument.
0.0001
0.001
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100
1000
100
10
1
0.1
0.01
0.001
0.0001
0.01 0.1 1 10 100
1=
Iout
r
Range where affected
by stray magnetic coupling
Ratio of output current rIout
Frequency [MHz]
93
Fig. 83 System configuration for measurement of Pf.
Fig. 84 shows the circuit simulation model with the highlighted major stray magnetic
coupling Min-out. The software used for the circuit simulation is Simplorer[55].
A
Ref
Input
Power splitter P
N
P
N
Tested filter
Nanocrytalline core
94
0
LCDIF1 3nH
Rn2
3mOhm
Rp2
0.97476mOhm
Ln2
2.5nH
Lp2
1.91nH
CDIF1 300uF
RCDIF1 0.009ohm
+
VVMref Rout 50ohm
Rin
50ohm
E1
+
VVMout
Rref 50ohm
Lp3
3.05nH
Rp3
1.684mOhm
RCDIF2 0.0048ohm
CDIF2 2.2uF
LCDIF2 2.3nH
Lp1
(8/2) nH
Rp1
2.5mOhm
Rn1
1mOhm
Ln1
(11/2) nH
Rp4
1.7946mOhm
Lp4
26nH
Ln4
12.31nH
Rn4
1.807mOhm
R1 0.009ohm
C1 300uF
L1 3nH L2 3nH
C2 300uF
R2 0.009ohm
R3
1mOhm Linput 1fH Loutput 1fH
C4
13pF
R5
7000ohm
L5
2.5uH
L6
2.5uH
R6
7000ohm
C5
13pF
L_GND 1nH
L3 (3*10) nH
R4 10mOhm
Min-out : 0.1 nH
Input loop Output loop
Fig. 84 Circuit simulation model with major stray magnetic coupling.
95
Fig. 85 shows a comparison of the filter performance Pf between the measurement
and the two simulations: with and without consideration of the major stray magnetic coupling
Min-out. Where the horizontal axis is the frequency and the vertical axis is the filter
performance. From Fig. 85, it can be seen that the measurement result and the simulation
results with consideration of the major coupling show a good agreement in the almost whole
frequency range.
In the next section, a design refinement using this accurate filter simulation to
improve performance of the EMC filter is discussed.
Fig. 85 Comparison of Pf between simulation and measurement
-120
-100
-80
-60
-40
-20
0
20
40
0.01 0.1 1 10 100
40
0
-40
-100
-120
0.01 0.1 1 10 100
20
50 dB
-20
-60
-80
Measurement
Sim. w/o coupling
Sim. w/ 1 coupling
Filter performance Pf[dB]
Frequency [MHz]
96
5.3 Design refinement of EMC filter
As described earlier, major stray magnetic coupling Min-out has a dominant influence
in a performance of the tested EMC filter, and thus it has to be reduced in order to realize a
better filter performance.
According to a detailed investigation using 3D simulation with ANSYS HFSS[34], it
was found that the Min-out mainly existed between the relay, the shunt resistor and the DC
capacitors as shown in Fig. 86. With respect to magnetic field generated from the PCM tracks,
it is mostly cancelled by the eddy current flowing in GND layer located closed to the path of
the noise current.
Fig. 86 Placement of major stray magnetic coupling Min-out in tested EMC filter
A design refinement was investigated focusing on the placement and the geometry of
these components, but however the same components, the same placement area and circuit are
used in order to fairly evaluate the effectiveness of the design refinement.
And accordingly, an optimal design refinement was derived: it was found that Min-out
can be most reduced by change shape of the shunt resistor from U-shaped to flat-shaped.
Fig. 87 depicts a comparison of simulation results of a magnetic flux distribution
97
generated from input loop between before and after the design refinement. And it can be seen
that the magnetic flux after the design refinement is significantly reduced compared to before.
(a) Before design refinement (b) After design refinement
Fig. 87 Simulation result of magnetic flux distribution
Fig. 88 shows the circuit simulation model with the reduced major stray magnetic
coupling Min-out. The Min-out is significantly reduced by the aforementioned design refinement
from 0.1nH to 0.02 nH.
98
0
LCDIF1 3nH
Rn2
3mOhm
Rp2
0.97476mOhm
Ln2
2.5nH
Lp2
1.91nH
CDIF1 300uF
RCDIF1 0.009ohm
+
VVMref Rout 50ohm
Rin
50ohm
E1
+
VVMout
Rref 50ohm
Lp3
3.05nH
Rp3
1.684mOhm
RCDIF2 0.0048ohm
CDIF2 2.2uF
LCDIF2 2.3nH
Lp1
(8/2) nH
Rp1
2.5mOhm
Rn1
1mOhm
Ln1
(11/2) nH
Rp4
1.7946mOhm
Lp4
26nH
Ln4
12.31nH
Rn4
1.807mOhm
R1 0.009ohm
C1 300uF
L1 3nH L2 3nH
C2 300uF
R2 0.009ohm
R3
1mOhm Linput 1fH Loutput 1fH
C4
13pF
R5
7000ohm
L5
2.5uH
L6
2.5uH
R6
7000ohm
C5
13pF
L_GND 1nH
L3 (3*10) nH
R4 10mOhm
Min-out : 0.02 nH
Input loop Output loop
Fig. 88 Circuit simulation model with reduced major stray magnetic coupling.
99
Fig. 89 shows a comparison of the simulation result of the filter performance Pf
between before and after the design refinement. Where the horizontal axis is the frequency
and the vertical axis is the filter performance. As can be seen from in Fig. 89, the Pf is
improved by 25 dB at the frequency of about 1 MHz owing to the design refinement.
In the next section, noise terminal voltage of LISN is measured and compared
between before and after the design refinement to verify its effectiveness on EMC
performance of the tested EPS- ECU.
Fig. 89 Comparison of Pf between before and after design refinement
5.4 Experimental verification
Fig. 90 shows an experiment setup for a measurement of noise terminal voltage. The
noise terminal voltage of LISN is measured by means of a spectrum analyzer Agilent E4407B
and the range of measuring frequency is set from 0.01-100 MHz. And the motor current and
the switching frequency are 30 Amps and 10 kHz respectively.
-100
-80
-60
-40
-20
0
20
40
0.01 0.1 1 10 100
Before design refinement
After design refinement
-25 dB
Filter performance Pf[dB]
Frequency [MHz]
40
0
-40
-100
20
-20
-60
-80
0.01 0.1 1 10 100
100
Fig. 90 Experiment setup for measurement of noise terminal voltage.
Fig. 91 shows a comparison of the measured value of the noise terminal voltage
between before and after the design refinement. Where the horizontal axis is the frequency
and the vertical axis is the noise terminal voltage. As can be seen from in Fig. 91, the noise
terminal voltage is reduced by 20 dB at the frequency of about 1 MHz owing to the design
refinement. Since it agrees well with the filter performance improvement shown in Fig. 89, it
is concluded that the reduction of the noise terminal voltage is due to the filter performance
improvement.
On the other hand, we can observe the difference in the frequency range higher than 5
MHz. With respect to the observed difference, it is assumed that the difference originates from
a common mode current flowing through a stray capacitance and a measuring instrument,
because an influence of a common mode current theoretically becomes greater as a frequency
becomes higher. That is to say, in the case that noise suppression in the frequency range
higher than about 5 MHz is required, it is recommended that a propagation path of common
mode current is more carefully considered in addition to stray magnetic couplings[56]-[58].
Polystyrene foam
-+
Battery
1500
GND plane
ECU
: Motor line
: Batery line
: GND line
Motor
LISN
101
Fig. 91 Comparison of noise terminal voltage between before and after design refinement
1.00E+01
2.00E+01
3.00E+01
4.00E+01
5.00E+01
6.00E+01
7.00E+01
8.00E+01
9.00E+01
10000 100000 1000000 10000000 100000000
LISN－
Before design refinement
After design refinement
Noise terminal voltage [dmB]
Frequency [MHz]
0.01 0.1 1 10 100
-20 dB
90
70
50
20
10
80
60
40
30
102
Chapter 6: Conclusion and future work
103
6.1 Conclusion
EMC filters with passive components are used to attenuate the EMI and playing a key
role to comply with the EMC standards. On the other hand, apart from EMI attenuation, it can
lead to an additional cost and size, and therefore an optimal design in size and cost is strongly
needed and hence lots of works has been done for it. To realize an optimal design of an EMC
filter, stray magnetic couplings in power electronic devices should be taken into account
properly, and hence an accurate and a straightforward method to consider influence of stray
magnetic couplings in a filter simulation is strongly needed so that a product designer can
practically utilize it in a product design process.
This doctoral dissertation focuses on a modeling of stray magnetic couplings and tries
to explore several important issues. The author’s wish is to clarify a mechanism of EMC
performance deterioration caused by stray magnetic couplings and find helpful and practical
approach applicable to EMC problems caused in an actual product. The contributions of this
dissertation can be summarized as follow:
1) Identification of generation mechanism of stray magnetic coupling
Firstly, a generation mechanism of stray magnetic coupling was investigated, and it
was revealed that stray magnetic couplings was caused by an alternating current with high
amplitude flowing in the commutation cell. The alternating current with high amplitude
radiates strong magnetic flux leading to a number of problematic magnetic couplings existing
in an EMC filter.
2) Clarification of influence of stray magnetic coupling on EMC filter performance
An influence of stray magnetic couplings was explained using an equivalent circuit
divided into three parts: the input loop, the high impedance area, and the output loop. The
magnetic flux generated from the input loop cause a significant magnetic coupling between
the input loop and the output loop, and also between the input loop and the high impedance
area. The influence of the magnetic coupling can be theoretically defined as an induced
voltage, and accordingly it reveals the influence can be described as just two induced voltages.
3) Extraction of major stray magnetic coupling with dominant influence
Based on that how the induced voltages deteriorate a performance of an EMC filter, a
104
simplification method of stray magnetic couplings was theoretically studied. And, as a result,
a formula to extract a major stray magnetic coupling was derived.
4) Simplified modeling of passive component focusing on stray magnetic coupling
Past and current technologies were studied, and straightforward modeling method of
passive components such as a capacitor, a coil was proposed. Moreover, an influence of a
magnetic material used for a filter core was specifically investigated. And consequently, a
straightforward calculation method of effective permeability was derived.
6.2 Future work
Future work will focus on a development of multi-physics modeling and simulation.
In this doctoral dissertation, EMC issues was focused and an EMC design utilizing simulation
technologies was mainly discussed. But however, since power electronics intrinsically poses
multidisciplinary consideration, a designer has to deal with not only EMC but also other
technical fields such as structure, thermal and reliability in a design process[59]-[62]. Moreover,
individual technologies in power electronics have been studied for long years and already
reached a mature phase today, and therefore a technology advantage is expected to be brought
by combination of different technologies[63]. From this viewpoint, the importance of multi-
physics modeling and simulation will drastically increase and it will be indispensable.
105
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