# Geometry-Based Modeling of EMI of an LCL Filter in an AC-DC-AC Converter with WBG Power Semiconductors

Lennart Juenemann, Anja Schano, Mohamed Aziz, Ben Romdhane, Axel Mertens

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## ► To cite this version:

Lennart Juenemann, Anja Schano, Mohamed Aziz, Ben Romdhane, Axel Mertens. Geometry-Based Modeling of EMI of an LCL Filter in an AC-DC-AC Converter with WBG Power Semiconductors. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0011. hal-05069606

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Submitted on 15 May 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Geometry-Based Modeling of EMI of an LCL Filter in an
AC-DC-AC Converter with WBG Power Semiconductors

Lennart Juenemann, Anja Schano, Mohamed Aziz Ben Romdhane, Axel Mertens

Institute for Drive Systems and Power Electronics

Welfengarten 1

30167, Hanover, Germany

Tel.: +49 / 511 – 762 2862

E-Mail: lennart.juenemann@ial.uni-hannover.de

***Index Terms***—Electromagnetic interference (EMI), EMI modeling, Filter optimization, AC-AC converter, Frequency-domain analysis.

***Abstract***—This paper analyzes a grid-side LCL filter's parasitic behavior and gives its parasitic elements sensitivities. It presents a new model for capacitors, improving the accuracy of parasitic inductance predictions. Sensitivity analyses show that the arrangement greatly influences the filter's performance and electromagnetic behavior, even in the low-frequency range.

## I. INTRODUCTION

Electromagnetic interference (EMI) is more topical than ever due to wide-bandgap (WBG) power semiconductors' fast switching behavior. Due to their high costs, their use must be justified by system benefits such as the reduced size of passive components and filters or improved energy efficiency. The increasing cost of EMI filters works against this, underlining the importance of calculating EMI in advance.

The fast switching of silicon carbide (SiC) power semiconductors results in smaller switching losses than seen in typically used silicon (Si) devices [1]–[3]. Furthermore, the smaller switching losses lead to the ability to use higher switching frequencies, resulting in smaller passive filter components. Nevertheless, using SiC power semiconductors presents challenges. The fast switching results in the voltage and current waveforms having steeper rising and falling edges. The fast-changing currents can lead to voltage spikes even with a small parasitic inductance. Three effects increase the EMI spectrum: the steeper edges, the higher frequencies, and the higher amplitudes of the

spikes [4]–[6]. There are two critical consequences for AC-DC-AC converters. On the active front end (AFE) side, the grid operator has different standards for harmonics in the grid [7], [8]. The grid filter is needed to filter the harmonics and disturbances of the system. The machine-side inverter also impresses a common-mode voltage. This can lead to harmful currents in the machine elements, especially in the bearings [9].

AC-DC-AC converters with AFE have become more popular because of their bidirectional power flow, increasing energy efficiency. These systems also feature power factor correction [10].

This paper focuses on the EMI behavior of the grid-connected filter. After providing background information on the topic in Section II, the basic equivalent circuits of the filter components follow in Section III. The main part, Section IV, deals with the filter components and their arrangement. Finally, the main results are presented, and an outlook on future work will be given in Section V.

## II. BACKGROUND OF LCL FILTER AND EMI

The system under consideration is an AC-DC-AC converter equipped with an active rectifier and active inverter both using SiC power semiconductors. Typically, these systems are used with passive diode rectifiers or IGBTs. The higher switching frequencies and faster switching gradients of SiC power semiconductors increase the effort needed for EMI investigations. An LCL filter fulfills the aforementioned EMI requirements at the grid connection. The system is a low-voltage 400 V grid with a DC link voltage of 650 V and a rated power at the machine of 10 kW.

This work is part of the project EMV-Vor-LE, funded by the Federal Ministry for Economic Affairs and Climate Action based on a decision by the German Bundestag. Funding number: 22630N.
<figure><img src="image_3.png" /><figcaption>Fig. 1. AC-DC-AC converter with SiC power semiconductors</figcaption></figure>

The design of the LCL filter has been prepared by following the step-by-step design routine of [11]. By pursuing these guidelines, the values for the filter components are obtained. Since SiC power semiconductors offer the advantage of lower switching losses than Si semiconductors with the same rating, the switching frequency can be increased. With high switching frequencies, the values of the passive components can decrease. Fig. 2 shows the values of the two inductors of the LCL filter, where $L_1$ is the rectifier-side inductor, and $L_2$ is the one on the grid side.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Filter inductors for different switching frequencies of the rectifier</figcaption></figure>

The inductor $L_1$ sees the greater current change, which means that the inductance needs to be higher. With a switching frequency of 20 kHz, the inductor needs a value of 1.23 mH. Using the potential of SiC power semiconductors with 100 kHz switching frequency, the inductance decreases to about 0.25 mH.

Higher voltages, steeper voltage gradients, and high switching frequencies increase electromagnetic compatibility (EMC) issues. The spectrum at the inverter's output has higher amplitudes with higher frequency components. This effect is shown using the example of a trapezoidal voltage signal for a duty cycle of 0.5. In the envelope curves shown in Fig. 3, the voltage, dv/dt, and switching frequency have been varied.

Comparing the envelope curves, it stands to reason that EMI rises with switching frequency and switching gradient.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Comparison of different envelope curves [12]</figcaption></figure>

### III. PARASITICS IN CAPACITORS AND CHOKES

The equivalent circuits for the capacitor and the chokes are explained before analyzing the 3D models in *Ansys Q3D*.

1) *Equivalent Circuit and Parasitic Inductance of Capacitors:* Usually, a capacitor is modeled as an ideal capacitance. At higher frequencies, this is no longer valid. The contact pins and capacitor can be simplified to a resistance and an inductance. The equivalent circuit produces a C, R, and L serial circuit. Fig. 4 illustrates the circuit.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Equivalent circuit for a capacitor</figcaption></figure>

2) *Equivalent Circuit and Parasitic Inductance of Chokes:* As presented in the example of the capacitor, the ideal equivalent circuit diagram is insufficient. A choke also needs more elements in the equivalent circuit to better understand the actual effects. [13] describes an extended equivalent circuit, as depicted in Fig. 5.

The choke typically shows a resistive and inductive behavior up to the first resonant frequency. At the first resonance, the resistance $R_p$ indicates the quality of the resonant circuit, which represents the high-frequency losses in the ferrite core and copper winding. The resistance measures the losses of the winding and the core. The choke shows a capacitive behavior for frequencies higher than the resonant frequency. The reason for this is the winding's parasitic capacitance. The other circuit elements represent the distributed parasitic behavior of
<figure><img src="image_7.png" /><figcaption>Fig. 5. Extended equivalent circuit and resulting impedance against frequency [13]</figcaption></figure>

the choke and allow the modeling of even higher frequencies. Using [13], it is possible to derive a new calculation rule for this choke:

$$EPC_{L1} = \frac{4}{9} \left( \frac{3z_1}{3z_1+z_4} \right)^2 (C_{L,1,2} + C_{L,2,3}) + \left( \frac{2z_4}{3z_1+z_4} \right)^2 C_{L,3,4} \quad (1)$$

$EPC_{L1}$ is the equivalent parallel capacitance (EPC) - $C_0$ in Fig. 5. $C_{L,n,m}$ is the parasitic capacitance from the winding layer to another layer. $z_x$ describes the number of turns of each layer. The adapted plate capacitor formula can calculate the capacitance of each layer:

$$C_{L,n,m} = \varepsilon_0 l_{w,n,m} z \frac{d_D}{d_w}. \quad (2)$$

A non-orthocyclic winding with the average winding length $l_{w,n,m}$ is used. $d_D$ is the side length of the conductor, and $d_w$ is the distance between two layers, which is set to 0.6 mm.

## IV. MODELING OF THE LCL FILTER

This section describes the LCL filter model, divided into capacitor and choke models.

1) **Parasitic Model of the Capacitors:** Two capacitors are used in parallel to reach a low parasitic inductance in the capacitors. Also, the capacitors are wired in antiparallel. This leads to decoupling, which improves the filter's performance [14]. The authors of [14] compare a model of a film capacitor and a measurement, which shows low deviations. For further improvement, the construction of film capacitors is analyzed in more detail. The detailed view is shown in Fig. 6.

The manufacturing process consists of winding the capacitors. This is the reason why the oval shape is created. It is noticeable that the wrap does not fill the entire volume. If this is not mapped correctly, there may be differences in the parasitic inductance. Two

<figure><img src="image_8.png" /><figcaption>Fig. 6. Section through the real capacitor (left) and model in Ansys Q3D (right).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Old model [14] and new model in Ansys Q3D</figcaption></figure>

models are compared to show the difference between the parasitic inductances.

In Fig. 7, the left model is the conventional modeling of [14]. The new model is mapped on the right with the accurate shape and correct dimensions. The length of the contact pins is for mounting on a two-layer PCB. One capacitor's parasitic inductance and resistance are simulated in Ansys Q3D. Fig. 8 compares these results with the impedance measurement.

<figure><img src="image_10.png" /><figcaption>Fig. 8. Impedance of the capacitor models and the measurement</figcaption></figure>

The measurement is performed with the precision impedance analyzer Wayne Kerr 6500 B [15]. Up to 200 kHz, the capacitive behavior is dominant. The simulation uses the rated value of the capacitance, which is why
the impedance behaves the same in both simulations and measurement. At about 480 kHz, the C, L, and R serial resonant circuit has its base frequency. The measurement and new model show nearly the same base frequency. The difference from the old model is about 200 kHz. The effective resistance to be read off shows a value of 3 mΩ in the new model. With 8 mΩ, the measured value is more than twice the simulated value. The reason for this is the resistance of connections and contacts. The old model shows a minor serial resistance since the cross-sectional area is bigger, leading to a lower resistance. Above the base frequency, another highly damped resonance is noticeable at about 3 MHz in the measurement. The model only consists of an C-L-R circuit, meaning a second resonance is not mappable in this configuration.

2) *Parasitic Model of the Chokes:* Typically, chokes are modeled as an inductance with a parallel capacitance and parallel resistance. When using a choke with multilayer windings, the parasitic capacitance between the layers is not negligible in the high-frequency range. The rectifier-side choke $L_1$ is shown in different views in Fig. 9.

<figure><img src="image_11.png" /><figcaption>Fig. 9. Different views of the modeled choke $L_1$</figcaption></figure>

As described earlier, the choke is made from four ferrite cores. The winding has a rectangular profile with 200 insulated strands. The model does not include the strands because these would enormously increase the modeling effort and simulation time.

In the first approach, the focus is placed on the winding without considering the ferrite cores. The level of modeling is investigated by comparing different orders of equivalent circuits. The first order uses a simple C, L and R parallel circuit. The higher-order model increases the level of detail (Fig. 10). Each layer has its own resistive and inductive components, with a parasitic layer-to-layer capacitance in parallel. The comparison is shown in Fig. 11.

Both models show promising results in the frequency range up to the resonant frequency. The simulation shows a slightly lower inductance due to simplifications in the model and due to the measurement connections.

<figure><img src="image_12.png" /><figcaption>Fig. 10. Equivalent circuit of the fourth-order order model of the choke</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Impedance of the choke winding with first-order equivalent circuit, fourth-order equivalent circuit, and measurement (without core)</figcaption></figure>

The higher-order model matches the resonant frequency even better. Since the damping is not considered here (no $R_p$), the impedance amplitude does not match the measurement - the layers' parasitic capacitance results in more resonances. The measurement shows three extra resonances up to 30 MHz. Furthermore, these resonances show a high damping, which is also not considered in the simulation. The higher-order model shows two undamped series resonances and two undamped parallel resonances resulting from layer-to-layer capacitance. The analytically calculated, simulated, and measured layer-to-layer capacitances and the resulting $EPC_{L1}$ are shown in Tab. I for choke $L_1$.

<table><caption>TABLE I
COMPARISON OF THE EPC OF THE CHOKE</caption><thead><tr><td>Method</td><td>Value EPC<sub>L1</sub> in pF</td><td>Relative deviation</td></tr></thead><tbody><tr><td>Analytical</td><td>131.25</td><td>0.2 %</td></tr><tr><td>Simulation Q3D</td><td>118.39</td><td>10.6 %</td></tr><tr><td>Measurement</td><td>130.98</td><td>-</td></tr></tbody></table>

In the next step, the cores are considered in the
measurement. The results are shown in Fig. 12. The magnetic cores add additional – desired – impedance, so the filter’s attenuation rises. The number of resonances follows the same behavior without the ferrite cores, but the resonances are even more damped. From this, it is concluded that the core influences the damping but adds no extra resonance to the frequency spectrum.

<figure><img src="image_14.png" /><figcaption>Fig. 12. Measurement of the impedance of the choke winding and the choke with cores</figcaption></figure>

In Fig. 13, the measurement results are compared. Again, the course of simulation and measurement up to the first resonant frequency is the same. In the fourth-order model, the damping from the measurement was included, which is realized by the resistance $R_p$. Since the

<figure><img src="image_15.png" /><figcaption>Fig. 13. Impedance of the choke with a first-order equivalent circuit, fourth-order equivalent circuit, and measurement (with core</figcaption></figure>

3) Arrangement of the Filter Components: The different filter components need to be arranged on the PCB. The arrangement influences the couplings between the components and, therefore, the attenuation quality. This is why, in the first step, the couplings are investigated.

<figure><img src="image_16.png" /><figcaption>Fig. 14. Different arrangements of the filter components</figcaption></figure>

Fig. 14 shows different arrangements. The distance between the components is fixed. The chokes have two arrangements each: the winding facing the capacitors or the cores facing the capacitors. In this filter, the so-called opposite current direction (OCD) technique is used [14], [16]. This technique minimizes capacitor coupling because the magnetic fields cancel each other out. Tab. II summarizes the coupling between the components.

<table><caption>TABLE II
COUPLING COEFFICIENTS OF FILTER ARRANGEMENTS 1 TO 6</caption><thead><tr><th></th><th>k<sub>C1C2</sub></th><th>k<sub>L1C1</sub></th><th>k<sub>L1C2</sub></th><th>k<sub>L2C1</sub></th><th>k<sub>L2C2</sub></th><th>k<sub>L1L2</sub></th></tr></thead><tbody><tr><td>1</td><td>0.31544</td><td>0.00209</td><td>0.00169</td><td>0.02009</td><td>0.02034</td><td>0.00011</td></tr><tr><td>2</td><td>0.31983</td><td>0.00213</td><td>0.00174</td><td>0.00458</td><td>0.00980</td><td>0.00021</td></tr><tr><td>3</td><td>0.29943</td><td>0.00926</td><td>0.00425</td><td>0.01309</td><td>0.01986</td><td>0.00022</td></tr><tr><td>4</td><td>0.31631</td><td>0.00550</td><td>0.00809</td><td>0.01990</td><td>0.02039</td><td>0.00034</td></tr><tr><td>5</td><td>0.34231</td><td>0.00598</td><td>0.00573</td><td>0.02076</td><td>0.05172</td><td>0.00036</td></tr><tr><td>6</td><td>0.32146</td><td>0.00537</td><td>0.00815</td><td>0.00509</td><td>0.01010</td><td>0.00041</td></tr></tbody></table>

The coupling coefficients rise if the magnetic field encounters a large area. For example, in arrangements 3 and 5, the winding of one choke faces one capacitor’s bigger area, which leads to high couplings. Fig. 15 shows the influence on the attenuation of the arrangement of the filter components. The attenuation is the ratio of the output current to the input current. Arrangement 1 shows the highest attenuation over the whole frequency range. This is because, in that arrangement, the windings of the chokes face the capacitors’ small sides. The distance from the ferrite is at its maximum here.

A sensitivity analysis for the different parasitic elements follows. Fig. 16 shows the attenuation for different parasitic elements considered. First, the ideal case shows the resonance of the LCL components (ideal). There is no impact on the filter’s attenuation above the resonant frequency. Next, the capacitors’ ESL is considered (PE capacitors). This results in lower attenuation from a
<figure><img src="image_17.png" /><figcaption>Fig. 15. Simulation of the influence of the component arrangement on the filter attenuation</figcaption></figure>

frequency of 1 MHz upwards. The additional impedance decreases the effect of the capacitors. Considering the EPC and the damping resistor of the chokes (PE chokes), the attenuation worsens above 5.5 MHz. The additional resonance increases the attenuation in the range from 1 MHz up to 8 MHz. Adding all magnetic couplings between the components – as pictured in arrangement 1 – creates an additional resonance (arrangement 1). This leads to a much smaller attenuation in the frequency range from 100 kHz to 1 MHz if the OCD technique is not used (arrangement 1 - OCD).

<figure><img src="image_18.png" /><figcaption>Fig. 16. Simulation of the influence of parasitic elements (PE) on the attenuation</figcaption></figure>

Finally, the construction of the filter is presented in Fig. 17 and a comparison of the filter impedance from the simulation and the measurement in Fig. 18. For the construction, arrangement 4 was used to meet specific

construction space requirements.

<figure><img src="image_19.png" /><figcaption>Fig. 17. Construction of the LCL filter with arrangement 4</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 18. Measurement and simulation of the impedance magnitude</figcaption></figure>

Simulation and measurement show the same behavior up to about 200 kHz. The global course of the simulation fits the measurement in the higher frequency range. The measurement shows a resonance at a frequency of about 15 MHz, already seen in the choke measurement.

## V. CONCLUSION

This paper analyzes parasitic behavior in the frequency range up to 30 MHz in detail and gives sensitivities for the components' arrangement and their parasitic effects. A new model for film capacitors has been implemented, improving the accuracy of parasitic inductance predictions. The arrangement of filter components has a significant influence on the resulting attenuation. For harmonic filters, the lower frequency range – in this case from 100 kHz upwards – the arrangement and parasitic elements of the components impact the attenuation. Another finding is that the winding-to-core capacitance is absent in the frequency range under consideration. Optimizing the filter and predicting the behavior is necessary to meet the EMI standards. In future work, the
prediction of damping factors will be analyzed. Lastly, building a three-phase system to explore the interactions is necessary. The knowledge gained will be applied to motor filters.

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