Comparison of Distance Conversion Factors for H-field Emissions Limits

Comparison of Distance Conversion Factors for H-field Emissions Limits Jordi Solé-Lloveras#$, Marc García-Bermúdez#, Yasutoshi Yoshioka∧, Marco A. Azpúrua#$, Ferran Silva$ #EMC Barcelona, EMC Electromagnetic BCN S.L., Spain ∧Power System Control Research Department. Digital Innovation Laboratory. Fuji Electric Co., Ltd. Japan $Grup de Compatibilitat Electromagnètica, Universitat Politècnica de Catalunya, Spain {jordi.sole, marc.garcia, marco.azpurua}@emc-barcelona.com Abstract — Radiated electromagnetic emissions requirements are defined as field strength levels that must not be exceeded when measured at a standard reference distance from the equipment under test. However, when such emissions are measured by placing the antenna at a distance different from the reference one, conversion factors are employed to adjust the emissions limits accordingly. This paper compares five alternative proposals of distance conversion factors for magnetic field emissions limits in the frequency range from 150 kHz to 30 MHz. This analysis intends to identify commonalities and differences between independent proposals presented in research articles, technical reports, and standards. The results suggest the different proposals could be merged into a single set of H-field conversion factors. Moreover, throughout the application of conversion factors in real cases, it is confirmed that, for in situ testing, H-field limits defined for distances greater than 10 m are likely to be surpassed by the ambient levels specially for frequencies higher than 4 MHz. Keywords — conversion factors, emissions measurements, in situ testing, magnetic field, standards. I. INTRODUCTION Conducted emissions measurements are commonly used in the frequency range below 30 MHz to assess disturbances propagating through power and signal lines. However, they are not always sufficient to evaluate such potential interferences, particularly in applications where the dominant mechanism is magnetic field generation. Those applications include wireless power transfer (WPT), industrial induction heating, power line communication (PLC), and MRI systems. Moreover, for in situ testing, the methods utilizing Line Impedance Stabilization Networks (LISN) and radiofrequency current probes as transducers are not indicated. In fact, CISPR 16-2-1 [1] propose to use non-reactive pick-up devices such as high resistance voltage probes. Nonetheless, H-field measurements are preferred in most standards to evaluate the emissions in situ for this frequency range. Several standards define H-field emissions requirements, e.g., the ETSI EN 300 330 [2] for short-range devices (SRD), the EN 50121-2 [3] for railway systems, and the CISPR 11 [4] for industrial, scientific, and medical equipment when in situ testing is performed. Such H-field emissions limits are defined at a given reference distance, dref. In certain situations, the measurement distance, dmeas, necessarily differs from the reference distance, dref =dmeas. Therefore, the emissions requirements must be adjusted before the spectrum of the electromagnetic disturbance is compared with the corresponding limits. Distance conversion factors can be approached in two different ways. Some standards define conversion factors to transform the emissions requirements defined as limits at a given dref to the actual dmeas. On the other hand, other standards define conversion factors to transform the measurement data itself. In this paper, for sake of simplicity, we assume all conversion factors presented are employed to convert the emissions limits. For example, for electric field emission measurements above 30 MHz a correction equivalent to 20 dB/dec is applied. This factor approximately compensates for the free space path losses, assuming that far-field conditions are met. However, for magnetic field emissions measures in the 150 kHz -30 MHz band, any conversion factors should consider the near field effects and cannot be constant for all frequencies. Some standards propose an alternative approach rather than employing conversion factors when measuring at distances different than dref. For example, in CISPR 16-2-3 [5], it is proposed to conduct experimental measures with EUT (Equipment Under Test) active at different distances, and then, extrapolate the recorded strength values of magnetic field level to the standard or reference distance employing logarithmic regression. Nonetheless, this method is not feasible specially in in situ scenarios, where ambient noise is inherently time variant as well as the EUT emissions. In previous research, investigations were carried out to model, validate, and extract distance conversion factors for in situ H-field emissions measurements [6], [7]. Likewise, other proposals for distance conversion factors are found in the literature and standards. Consequently, this work aims to review and compare them to identify their commonalities and differences and to decide if some are advantageous or better fit specific situations/environments. The paper is organized as follows. Section II reviews the distance conversion factors in the literature and standards to summarize the existent proposals. Section III presents the comparative analysis, where the different distance conversion factors proposals are applied to standard emission limits to illustrate and quantify their differences. Section IV shows converted limits applied to real in situ measures, showing its Proc. of the 2025 International Symposium on Electromagnetic Compatibility (EMC Europe 2025), Paris, France, September 1–5, 2025 practical limitations, specially for high distances. Finally, the paper closes with a brief discussion about the applicability, usefulness, and intrinsic limitations of distance conversion factors. II. STATE OF THE ART The proposals listed in Table 1 are considered in our analysis of conversion factors for H-field emissions below 30 MHz. The reference distance defined for each proposal and the intended range of measurement distances for those factors are also mentioned. Table 1. Proposals of conversion factors. Proposal Section dref dmeas Solé et al.[6] II.A 10 m 3 m to 100 m Ishigami et al.[8] II.B 3 m and 10 m 1 m to 100 m ETSI [2] II.C 10 m 3 m, 10 m and 30 m Railway [3] II.D 10 m N/A PLC [9] II.E 30 m 3 m to 100 m A. In Situ H-field emissions tests The proposal by Solé et al. [6] derives and validates a set of distance conversion factors intended to be proposed for their consideration in new projects of electromagnetic compatibility standards for in situ testing, in particular, the CISPR 37 project. Simulations of loop-type field sources are employed to evaluate the change of the amplitude of the H-field components along a measurement axis. Then, an algorithm based on optimal changepoint detection [10] is developed to extract a piece-wise linear function to generate a set of simplified conversion factors as a function of the frequency and distance. Finally, results are validated experimentally. The cited paper presents factors for distances from 3 m up to 100 m after the consideration of different alternatives for combining the information from the components of the H-field vector. B. Analytical conversion factors Ishigami et al. [8] propose conversion factors from 1 m up to 10 m. Those factors are obtained using an analytical solution for the magnetic field strength produced by a loop antenna at a distance r,H(r), that is, H(r) = nIAe−jkr 4π−k2 r+jk r2+1 r3,(1) where Iis the loop current, nis the number of loop-turns, A is the loop area, k=2πf cis the wave number, and cis the light speed in vacuum. Conversion factors, CH, are computed using the ratio between the magnetic field obtained in two different distances, let us say, r1and r2, therefore, CH= H(r1) H(r2) .(2) Note that, those factors are independent of I,nand A. The theoretically predicted levels of magnetic emissions were checked at distances from 1 m to 10 m in a standardized test site. Later, complementary experiments compared the H-field emissions of an actual EUT at distances 3 m and 10 m. C. Short range devices and radio standards ETSI EN 300 330 [2] covers radio equipment considered as SRD or inductive loop transmitters and receivers operating in the range of 9 kHz to 30 MHz. These devices may include systems such as Radio Frequency Identification (RFID) or Near Field Communication (NFC). In addition to the typical EMC tests, this standard covers radio transmitter and receiver tests, for example, transmitting and spurious power and H-field. Although the reference distance for limits in this standard is 10 m, Annex H of this standard provides limit conversion factors to the fixed distances of 3 m and 30 m. Such factors are read from a plot and there are no references or explanations on how those factors were calculated. D. Railway applications Standard EN 50121-2 [3] scopes emission of complete railway systems. Emissions limits in the frequency range from 150 kHz to 30 MHz are defined for a reference distance of 10 m. Where such condition cannot be fulfilled, standard proposes the following equation to convert the results, E10 =Ex+ 20nlog10(x/10),(3) where E10 is the emissions level at 10 m,Exis the measured value at distance D. Finally, n, is a constant that depends on the frequency range: n= 1.8for frequencies from 150 kHz to 400 kHz,n= 1.65 for frequencies from 400 kHz to 1.6 MHz, and finally, n= 1.2for frequencies from 1.6 MHz to 30 MHz. The use of Ein (3), as per the corresponding standard, refers to either magnetic or electric field strength depending on the measured frequency range. This paper does not consider factors defined for frequencies above 30 MHz as they are for the emissions expressed in electric field units. As opposed to previous documents, in this standard the factor is proposed to correct the measured values and not the limit. Therefore, for sake of simplicity, the sign of the factor has been reversed for the later sections. E. Power Line Communications Standard EN 50065-1 scopes power line communication (PLC) systems signaling on low-voltage electrical installations in the frequency range from 3 kHz to 148.5 kHz. CENELEC TC219/WG9 is working on extending such range beyond, up to a frequency of 526.5 kHz. In an internal test report of the former group [9], magnetic field decay in function of distance is studied for a PV system comprising two rows of 25 photovoltaic (PV) panels connected to a single PV inverter via two Maximum Power Point Tracking (MPPT) interfaces. Devices within this system communicate by employing a custom communication system based on Huawei’s PLC technology (IEEE 1901.1). Regarding the system, the layout of internal cables connecting the two MPPT and the PV panels form two Proc. of the 2025 International Symposium on Electromagnetic Compatibility (EMC Europe 2025), Paris, France, September 1–5, 2025 different loops, each of one encompassing half of the PV panels. H-field is assessed in three axes: in front of the first loop, in front of the second loop, and in the middle of the former two axes. Considering findings of preliminary tests and comparisons made for different combinations of PLC operations over the different MPPT loops, magnetic fields are measured at distances varying from 3 m to 30 m considering the configuration of the system providing the highest radiated emissions. By complementing the analysis of the levels of the PLC signal contribution to the H-field with additional characterization using a signal generator, it was observed experimentally that the roll-off of the H-field strength with distance valid for these empirical observations obeys the following equation, H2=H1+ 30 log 10(d1/d2),(4) where d1is the distance where measures are taken, with the associated magnetic field value, H1. Such value can be extrapolated to H2at the reference distance, d2. This equation is proposed for frequencies from 148.5 kHz to 526.5 kHz. III. ANALYSIS To study the qualitative and quantitative differences between the factors, a couple of magnetic field emissions limits have been selected, and these conversion factors will be applied to this limits for a given distance. Two scenarios will be studied. First of all, CISPR 37 draft limit proposed at 10 m will be converted to 3 m employing the conversion factors from former section. Secondly, CISPR 11 limit proposed at 30 m will be converted to 10 m following the same methodology. A. Limit conversion from 10 m to 3 m The first limit selected is proposed in the draft of CISPR 37[11], a standard project focusing on in situ testing and being developed by CIS/B WG7. The limit, stablished for a reference distance of 10 m, is shown in Fig. 1. It is important to remark that this limit originated from CISPR 11 H-Field limit defined at 30 m, which was later converted to 10 m employing factors proposed in first draft of CISPR 37. CISPR 37 draft limit converted to 3 m by means of the conversion factors of proposal of Section II is depicted in Fig. 2. As expected, all the proposals of conversion factors deliver differently adjusted limits. Analyzing Fig. 2, it can be observed that for frequencies up to 4 MHz, a good match is shown between the factors by "Ishigami et al." and “ETSI” proposals. On the other hand, the factors of “Railway” and “PLC” show close correspondence but significantly differ from the previously mentioned cases. "Solé et al." factors produce a limit fitting between the two previous pairs of proposals. Above 20 MHz, all proposals produce a limit within a margin of ±3 dB. The transition from the near-field to the far-field is almost completed at these frequencies and distances for the type of sources assumed. In this condition, the influence of some effects, such as the Fig. 1. H-field emissions limits according to the CISPR 37 draft (10 m). H-field [dBµA/m] Fig. 2. CISPR 37 limit (10 m) converted to 3 m. geometry of the source antenna, is less dominant. Therefore, variations across different proposals at higher frequencies are reduced. Finally, more relevant differences are found in the range from 4 MHz to 20 MHz in between all proposals. This is primarily caused by the transition zone between the near-field and far-field, where the proposed factors become more sensitive to the differences in the assumed source type used for each case. B. Limit conversion from 30 m to 10 m The second study case will be the limit proposed in CISPR 11 [4] for Class A Group 1 equipment, which is depicted in Fig. 3. The standard defines in situ H-field limits for a reference distance of 30 m. To study the difference between the conversion factors proposals, the limit will be converted from a reference distance of 30 m to 10 m. As commented previously, this limit converted to 10 m employing CISPR 37 draft conversion factors, which do not appear in this document, creates the H-field limit defined in the CISPR 37 draft standard. Therefore, it is decided to plot such limit as well to compare with the proposals discussed in this paper. Results are shown in Fig. 4. Proc. of the 2025 International Symposium on Electromagnetic Compatibility (EMC Europe 2025), Paris, France, September 1–5, 2025 Fig. 3. H-field emissions limits according to the CISPR 11 (30 m). Fig. 4. CISPR 11 limit (30 m) converted to 10 m. In this scenario, more coincidence among all conversion factors is observed regarding previous case. Partly, this is because, for measurement distances greater than 10 m, the predicted field levels are less sensitive to near-field effects than the 3 m distance situation. That said, the proposal by Solé et al., based on simulations and practical experiments, and the proposal from Ishigami et al., primarily based on analytical equations, largely coincide. Such proposals also coincide with CISPR 37 limit. Minor changes are observed in the transition frequencies between 1.5 MHz and 6 MHz due to the algorithm used to extract the factors in "Sole et al." proposal. On the other hand, for "ETSI" proposal, a very good agreement is also observed specially in frequencies below 2 MHz and frequencies above 10 MHz. Finally, for "PLC" and "Railway" proposal results diverge from other cases except on frequencies above 10 MHz, where far-field condition is assumed. IV. APPLICATION TO IN SITU SCENARIOS In this section, converted limits will be applied to different ambient noise measures taken at five different locations. The places and dates where measures were taken are summarized in Table 2. Measures are recorded in situ, on an open area where nearby electronic devices and communication systems are present. Emissions from such devices and systems will appear overlapped to the instrument noise floor. To evaluate the converted limits, the maximum and minimum values from Section III.A, and then, maximum and minimum values from Section III.B will be used. All proposals have been taken into account, excepting the "PLC" proposal, which factor does not cover the complete frequency range. Table 2. H-field ambient noise measures. Measure City Country Date M1 Aachen Germany August, 2024 M2 Zaragoza Spain February, 2024 M3 Barcelona Spain January, 2024 M4 Madrid Spain February, 2024 M5 Tokyo Japan February, 2025 The first case analyzes CISPR 37 limit (10 m) converted to 3 m employing the maximum and minium conversion factors studied on Section III.A. Data of 5 ambient noise measures, CISPR 37 limit, and the limit converted to 3 m employing former conversion factors are shown in Fig. 5. Fig. 5. Ambient H-field measures and maximum and minimum values of CISPR 37 (10 m) limit converted to 3 m. CISPR37 draft limit defined at 10-m is also plotted. When comparing the measures with the limit defined by CISPR 37 at 10 m at frequencies lower than 4 MHz, the margin from the ambient noise level to the limit level is enough (at least 6 dB), except where some noise of external equipment or broadcasting communication systems (such as AM radio) are present. Nonetheless, for frequencies above 4 MHz, the only measure with enough margin is "M4". When applying the maximum and minimum of the conversion factors to the limit (blue and red traces respectively), similar behavior can be observed. In this case, for frequencies below 10 MHz, both cases show enough margin to the ambient noise level for all the ambient noise measures. Nonetheless, for frequencies above 10 MHz when employing the minimum value of converted limits (red trace), margin of most of the ambient noise measures is less than 6 dB. Proc. of the 2025 International Symposium on Electromagnetic Compatibility (EMC Europe 2025), Paris, France, September 1–5, 2025 For the second case, CISPR 11 limit defined at 30 m will be studied. In this case, data of the ambient noise measures, CISPR 11 limit, and such limit converted to 10 m employing factors proposed on Section III.B are shown in Fig. 6. Fig. 6. Ambient H-field measures and maximum and minimum values of CISPR 11 (30 m) limit converted to 10 m. CISPR 11 defined at 30 m is also plotted. In this case, the limit proposed at CISPR 11 offers little margin even for "M4" and is practically below the ambient noise of the remaining sites. When converting the limit to 10 m and for frequencies below 4 MHz there is enough margin in most cases from the ambient noise level to the limit. However, for frequencies above 4 MHz, levels in the limit might still be low to ensure a reasonable margin. It is important to remark that former analysis is conducted for situations where dmeas < dref. This means that, after utilizing the conversion factor, the resulting limits have amplitudes higher than the original limit. It is important to consider, that, in the opposite case, where dmeas > dref, amplitude of converted limits will be lower than the original ones. Therefore, it is expected that resulting limits have amplitudes almost below the ambient noise levels in most cases. Furthermore, it might be that the equipment under test emissions becomes undetectable at such distances, and the test outcome is not conclusive. V. CONCLUSION Different proposals of conversion factors for H-field limits have been compared. Each proposal is independent and obtained by different methods and sources, such as simulation, experiments, or theoretical equations. Emissions limits, such as CISPR 37 limits for a 10 m distance or CISPR 11 limits for a30 m, are converted employing former conversion factors and compared among others. Despite the fact that some conversion factors show similar behavior specially in far-field range, several discrepancies are observed in frequency ranges where the near-field is transitioning to far-field. Furthermore, although the factors are derived from proposals whose scope may be different, they all deal with the same effect (magnetic field), which is why a consensus should be reached in order to have specific factors even if they are only valid for certain conditions (e.g., for a particular size of equipment or at certain distances). Then, ambient noise measures taken on five different locations for in situ tests are compared with already proposed limits for reference distances of 10 m and 30 m. Measures are also compared with such limits converted to other distances and the margin from the limit to the ambient measure level is analyzed. In most cases, and specially above 4 MHz, such margin is extremely low or inexistent due to the restrictiveness of limits. Therefore, application of factors for large distances is inconvenient for real in situ tests due to the limits are surpassed by ambient noise levels, and therefore, making any measurement of emissions from the EUT non conclusive. ACKNOWLEDGMENT We want to thank Prof. Kawamata, Prof. Ishigami, Cedric Lavenu, Ricardo Fiorelli, Ming Ye, Diannming Liu and Xiaona Liu for participating in the cited research regarding conversion factors. We also want to thank Johannes Nieuwenhuizen for his valuable comments. This work was supported in part by the project 21NRM06 EMC-STD which has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States, and in part by the “Ministerio de Ciencia e Innovación” of Spain, through the Project DIN2021-012003 under Grant MCIN/AEI/10.13039/50110001103 and Project PID2022-137495OB-C32/MCIN/ AEI/10.13039/501100011033 /FEDER, UE. REFERENCES [1] CISPR 16-2-1:2014 - Specification for radio disturbance and immunity measuring apparatus and methods - Part 2-1: Methods of measurement of disturbances and immunity - Conducted disturbance measurements. Geneva, Switzerland, 2014. [2] European Telecommunications Standards Institute (ETSI), “Short Range Devices (SRD); Radio equipment in the frequency range 9 kHz to 25 MHz and inductive loop systems in the frequency range 9 kHz to 30 MHz. Harmonised Standard covering the essential requirements of article 3.2 of Directive 2014/53/EU,” ETSI, Tech. Rep. EN 300 330 V2.1.1, 2017. [Online]. Available: https://www.etsi.org/deliver/etsi_ en/300300_300399/300330/02.01.01_60/en_300330v020101p.pdf. [3] European Committee for Electrotechnical Standardization (CENELEC), Railway applications – Electromagnetic compatibility – Part 2: Emission of the whole railway system to the outside world, 2017. [4] CISPR 11:2015 - Industrial, Scientific and Medical Equipment - Radio-Frequency Disturbance Characteristics - Limits and Methods of Measurement. Geneva, Switzerland, 2015. [5] CISPR 16-2-3:2016 - Specification for radio disturbance and immunity measuring apparatus and methods - Part 2-1: Methods of measurement of disturbances and immunity - Radiated disturbance measurements. Geneva, Switzerland, 2016. [6] J. Solé-Lloveras, Y. Yoshioka, M. Añón-Cancela, T. Kootz, F. Silva, and M. A. Azpúrua, “Distance conversion factors for in situ h-field emissions tests,” IEEE Open Journal of Instrumentation and Measurement, vol. 4, pp. 1–10, 2025. DOI: 10 . 1109 / OJIM . 2024 . 3509543. Proc. of the 2025 International Symposium on Electromagnetic Compatibility (EMC Europe 2025), Paris, France, September 1–5, 2025 [7] J. Solé-Lloveras, M. A. Azpúrua, Y. Yoshioka, and F. Silva, “Experimental validation of correction factors for in situ h-field measurements below 2 mhz,” in 2024 International Symposium on Electromagnetic Compatibility – EMC Europe, 2024, pp. 203–208. DOI: 10.1109/EMCEurope59828.2024.10722398. [8] S. Ishigami, T. Itsukaichi, K. Kawamata, and Y. Yoshioka, “Proposal of the theoretical conversion factor for the interpolation of measured radiated emission levels,” in 2022 International Power Electronics Conference (IPEC-Himeji 2022ECCE Asia), 2022, pp. 301–305. DOI: 10.23919/IPEC-Himeji2022-ECCE53331.2022.9807129. 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