Frequency Domain EMI-Simulation and Resonance Analysis of a

Frequency Domain EMI-Simulation and Resonance Analysis of a
Frequency Domain EMI-Simulation and Resonance
Analysis of a DCDC-Converter
P. Hillenbrand*, M. Böttcher, S. Tenbohlen
J. Hansen*
Institute of Power Transmission and High Voltage
Technology (IEH), University of Stuttgart
Stuttgart, Germany
[email protected]
Automotive Electronics
Robert Bosch GmbH
Schwieberdingen, Germany
[email protected]
Battery Cables & LISNs
Electromagnetic compatibility (EMC) in the field of full
and hybrid electrical vehicles is a rising topic [1]. Prediction
of conducted and radiated emissions of traction inverters is
important for car and component manufacturer especially in an
early development stage of the product. Therefore, there are
plenty of simulation models to estimate both kinds of
emissions. These models can be grouped in two parts:
transient simulations [2] and frequency domain simulations [38]. With the ability to model time-variant and non-linear
elements, transient simulations cover potential EMC issues
more accurately than frequency domain simulations. However,
simulation time steps need to be very short at high frequencies
and sharp rise and fall times, and the total simulation time
needs to be quite long to reach a steady state of the system.
The simulation time thereby rises with the dimensions of the
test setup. Concerning the dimensions of the CISPR 25 test
setup simulation models in frequency domain are absolutely
necessary to predict emissions above 30 MHz in practical time
durations [1].
There are several frequency domain simulation models for
inverter EMI in the literature, which approximate non-linear
source characteristics by linear modelings. On the one hand,
there are physics-based equivalent circuit models, e.g. [5].
These models are often used to simulate either common-mode
(CM) [6] or differential-mode (DM) [7] noise, i.e. they are
linear & time invariant
Motor Cables & Load
nonlinear & time variant
Battery Cables & LISNs
Keywords— conducted emissions, behavioral voltage sources,
multi-port network model, equivalent network
valid if one of both can be identified as dominating. Under
these circumstances, the switches are replaced by a single CM
or DM noise source. The main advantage of these models is
their simplicity, which allows a profound understanding of all
relating phenomena. On the other hand, there are modularterminal-behavioral (MTB) models like [3], [4]. These “blackbox” models can produce very accurate simulation results with
little information about the internal structure of the modeled
device. However, they are less suitable to get a good
understanding of the source and propagation of the emissions
and cannot be used to optimize a device towards lower EMI.
This contribution presents a “white-box” model to combine
the advantages of physics-based equivalent circuit models and
MTB models. Therefore, the nonlinear semiconductor
switches of a given converter are replaced by behavioral
voltages sources, Fig.1. Similar to a MTB model, the voltage
sources are characterized during operation of the converter.
Motor Cables & Load
Abstract—This paper proposes a frequency domain model to
predict conducted electromagnetic interferences (EMI) caused by
a converter. In the model, the nonlinear and time-variant
semiconductor switches of the converter are replaced by voltage
sources characterized by measurements during operation of the
converter. A vector network analyzer (VNA) measurement
method is presented to characterize the disturbance path from
the voltage sources to the line impedance stabilization network
(LISN). The approach shows that the main resonances of the
disturbance voltage at the LISN are caused by the coupling path,
which is linear and time-invariant. Based on this knowledge, a
frequency domain simulation of the coupling path is performed.
The simulation reproduces the measured coupling path very well.
Based on the analysis of the electromagnetic potential at selected
resonance frequencies, an electrical circuit is designed that
accurately describes EMC root-causes of the converter.
Fig. 1. Replacement of nonlinear and timevariant lowside and highside
switches by two ideal voltage sources in frequency domain.
The coupling path from each of the two voltage sources
towards the LISN is measured with a VNA and combined with
the measured voltage sources. This method is used to analyze
whether the replacement of the switches by the measured
sources is valid or not. Afterwards, a 3D geometry model is
presented to simulate the coupling path. Based on the
simulation model, a physics-based equivalent circuit is derived
by analyzing the electromagnetic potential at selected
resonance frequencies. The resulting circuit provides accurate
simulation results of the conducted emissions and can be used
for root-cause analysis of the converter EMI.
A. Description of the Silicon Carbide MOSFETs Inverter
This contribution uses the test setup presented in [6] to
investigate the conducted emissions of an automotive inverter.
Similar to the case defined in CISPR 25, the setup consists of
two LISNs, the inverter, and a three-phase load (3~load)
which are mounted on a conductive table and connected to
each other using unshielded cables. In contrast to [6], the
investigated inverter uses silicon carbide (SiC) MOSFETs.
Fig. 2 pictures the main PCB of the Inverter (a) and the
cooling of the semiconductors (b). For simplicity reasons, the
inverter is reduced to one half-bridge, yielding a DCDCconverter configuration. One leg of the 3~load is connected to
the half-bridge, the remaining two legs are linked to HV-. The
3~load consists of three inductances which are connected to a
star and three discrete capacitances towards the housing of the
load. To limit the load current of the DCDC-converter, one
resistor is added in series with each of the three inductances.
Fig. 3. FFT of disturbance voltages VHV+ and VHV- at the LISN, measured in
time-domain during operation of the DCDC-converter. [env. = envelope]
Fig. 2. a) main PCB b) front perspective of the cooling of the inverter
The half-bridge consists of two SCT2080KE SiCMOSFETs (I) produced by RohmTM with a maximum drain
current of 40 A and a breakdown voltage of 1.2 kV. Both
switches are connected to a DC-link capacitor of 17.2 µF. The
capacitor is built up with seven 2.2 µF electrolyte capacitors
(II) and 18 100 nF ceramic capacitors (III) which are placed
very close to the switches. To minimize the influence of the
control electronics, battery supplied gate-units (IV) with
optical fiber- transmitted control signals are used at the top of
the main PCB.
B. Disturbance Voltage at the LISN during operation of the
The DC-voltage VDC applied to the DC link capacitor is set
to 192 V for all following measurements and simulations. The
half-bridge operates at a pulse width frequency of fPWM = 10.1
kHz, a duty cycle of 7 % and a blanking time of tb = 1.6 µs,
which avoids a short circuit of the DC-link capacitor during
During the operation of the inverter, the disturbance
voltages, VHV+ and VHV-, at the LISNs are measured using an
oscilloscope in time-domain. Afterwards, the measured data is
transformed into frequency-domain using an FFT-algorithm.
Fig. 3 shows the measurement results. The high frequencies
are measured with a 20 MHz high-pass filter to achieve a
sufficient signal-to-noise ratio.
To characterize the behavioral voltage sources VHS and VLS
shown in Fig. 1, the voltages across the high-side and low-side
switches of the converter are measured during operation. For
the model, both magnitude and phase of the voltage sources
are relevant. Because of that, both voltages are measured
simultaneously in time domain. In equal manner to the
measurement of the disturbance voltage at the LISNs, the
signals are measured with an oscilloscope and transformed
afterwards into frequency-domain. To minimize the influence
of the voltage probe, it is necessary to use a high-impedance
probe. It is advantageous if the probe shows a high pass
characteristic. Fig. 4 shows the measured magnitude of the
high-side and low-side voltage for the operating point
described in Section II B. For better differentiation, VLS is
displayed as the peak envelope of 50 adjacent data points.
Fig. 4. Voltage frequency spectrum of high-side and low-side switches
during operation of the DCDC-converter (VDC = 192 V, fPWM = 10.1 kHz, 7%
duty cycle) [env. = envelope]
The measurement results of the magnitudes, Fig. 4, show
that both voltages are very similar to the spectrum of a
trapezoidal pulse. Below 40 MHz the phase difference
between both voltages is close to zero. In this frequency range
the noise sources can be described as a common-mode source
concerning the orientation of the voltages pictured in Fig. 1.
Above 40 MHz the phase shift varies between 0 and 180 deg.
In this frequency range both common and differential mode
excitation are present.
50 Ω
Motor Cables & Load
50 Ω
Fig. 5. Measurement setup of the voltage transfer function form the high-side
switch to the LISN with short circuited low-side switch.
We obtain the transfer function as the ratio of the measured
and the input voltage,
𝑇𝐹HS→LISN+ = out
Port 1
100 nF
Port 3
50 Ω
Port 2
50 Ω
Motor Cables & Load
In a real test setup, it is hardly possible to estimate all
essential parasitic elements to create a detailed equivalent
circuit of the test setup. Therefore, a VNA measurement
method is presented to characterize the frequency behavior of
the linear time-invariant (LTI) system components without
knowing any specific element. Based on the principle depicted
in Fig. 1, both switches are regarded as ideal voltage sources.
According to the superposition principle, the effect of one
ideal voltage source can be calculated individually with all
other voltage sources short-circuited. Consequently, the LTI
system between the voltage sources and the LISN can be
represented by voltage transfer functions. One transfer
function for each voltage source VHS and VLS is measured for
one LISN port with the principle shown in Fig. 5. During
excitation at one switch, the other switch is short-circuited
through the gate unit.
100 nF
isolated from the measurement table with one port directly
connected to the switch and the other port connected to the
LISN with an analog fiber optic link. Here, the critical aspects
are the bandwidth of the fiber optic link and the isolation of
the VNA supply. More accurate measurements can be
achieved with three single ended VNA ports in the setup
pictured in Fig. 6. Port 1 and port 2 are connected to drain and
source of the high-side switch, respectively, and port 3 is
connected to the LISN.
Fig. 6. VNA measurement setup with three single ended ports.
In this test setup, the transfer function can be calculated
from the scattering parameter data [S]. One possible way is the
mixed-mode calculation presented in [10], where two singleended ports are transformed to one differential port. In this
scenario the port impedance of the differential port has to be
considered, which is equal to the sum of two single-ended
ports. With the correct port impedance, the voltage transfer
function can be calculated from the reflection at the
differential port between port 1 and 2 and the response at
port 3. A simpler way is the direct calculation of the transfer
function using the admittance matrix [Y] calculated by
equation (2) with the unit matrix [E].
[Y] =
([E] + [S])−1 ∙ ([E] − [S])
The transfer function is independent of the impedance
between port 1 and port 2. Consequently, a virtual ideal
current source of 1 A is used as excitation at the switch.
According to Kirchhoff’s current law, the potentials at the
ports can then be described with (3), and calculated with (4),
as follows:
In the literature different measurement methods are
described to measure a voltage transfer function with the help
of a VNA. For the existing test setup we considered that the
differential excitation at the switch has to be galvanically
isolated from the single-ended measurement at the LISN. The
traditional approach for this problem is to convert the balanced
port to a single-ended port using a balun. The two major
disadvantages of this technique are non-ideal isolation and
limited bandwidth of the balun, particularly when
characterization over a wide frequency range is necessary
[10]. Another possibility is to run the VNA galvanically
[Y] ∙ ⃗φ
⃗ = I → ⃗φ
⃗ = [Y]−1 ∙ I,
(φ2 ) = [( ⋮
𝑌13 −1
⋮ )] ∙ (−1)
The voltage transfer function defined in (1) can then be
calculated with the resulting potentials and equation (5):
φ2 −φ1
Measurement setup and calculation can be checked by
applying a DC-voltage to the converter. A voltage of less than
10 V mostly changes the voltage dependent capacitance of the
switch and the scattering parameter data significantly.
However, with a correct calculation and measurement setup,
the voltage transfer function should remain identical. Fig. 7
shows the measurement result of the transfer functions of the
low-side and high-side voltage source towards LISN+.
Fig. 7. Measurement result of the transfer functions measured with a VNA
With the information of the voltage sources and the
disturbance path towards the LISN, it is possible to calculate
the disturbance voltage spectrum at the LISN by (6). Fig. 8
shows the calculation result compared to the measured
disturbance voltage during the operation of the converter.
disturbance voltage at the LISN are caused by the linear and
time-invariant disturbance path. This is investigated further in
the following simulation.
A coupling path simulation is performed using a two-step
computer simulation. First, a geometry model is created,
which exhibits the key geometric features of the measurement
setup. This model comprises the measurement table, LISNs,
load box, wiring, a PCB model, and models of the packages of
the switches as well as the styrofoam (blue), on which the
setup is placed, Fig. 9. Excitation ports are set at the end
points of all wires, at the positions of all capacitors, and
between source and drain of each switch. The model is
discretized by a tetrahedral mesh. Based on model order
reduction, a broadband frequency-domain electromagnetic
field computation is performed, resulting in a multi-port
network model which characterizes the electromagnetic
properties of the geometry model. Secondly, this model is
applied in a circuit simulator, where S-Parameter data of the
DC-link capacitors, of 3~load and LISNs are attached to the
multiport model. As in the measurements, one of the switches
is short-circuited (represented by the RDS,on of the closed
switch), and the other is equipped with a broadband voltage
source in frequency domain. The simulations are carried out in
the CST Studio Suite [9] on an HP Z820 Workstation with
128 GB RAM. The electromagnetic simulation takes about 12
minutes in the frequency range from 0.3 to 110 MHz.
However, the subsequent circuit simulation needs several
seconds only.
VHV+,calc = TFHS→LISN+ ∙ VHS +TFLS→LISN+ ∙ VLS (6)
LISN & DC-Supply
4x4 S-Parameter
50 Ω
50 Ω
3x3 S-Parameter
2.2 uF electrolyte capacitor
1x1 S-Parameter
100 nF ceramic capacitor
1x1 S-Parameter
Fig. 9. 3D-geometry of the simulation model.
Fig. 8. Comparison of measured and calculated disturbance voltage
[env. = envelope].
The calculation of the disturbance voltage reproduces the
measurement very well in the complete frequency range from
0.15 to 110 MHz. This proves the validity of replacing the
semiconductor switches by measured voltage sources. The
magnitudes of the disturbance voltage at the LISN show a
similar shape compared to the measured transfer functions.
This allows the conclusion that the main resonances of the
The computed transfer function by the above described
model is shown in Fig. 10, in comparison with the measured
one. The mismatch is a smaller than 5 dB from 0.3 to
110 MHz. In the model, a short circuited switch is represented
by its on-resistance (RDS,on). This value has a strong influence
to the magnitude of the TF below 1 MHz. For this model, the
value is measured outside the test setup with a different gateunit which causes the small deviations at lower frequencies.
Taking advantage of the electromagnetic simulation, we
now use the computer model to study the resonances A and B
in the spectrum displayed in Fig. 10. In particular, we use the
the wire ends in the loadbox there are 2 nF capacitors located;
the inductances corresponding to the resonances are the wires
and the PCB, with PCB plus and minus short-circuited due to
the excitation (one switch is short circuited, the other switch is
attached to a voltage source with no series impedance). At
resonance B (shown in Fig. 12), the positive maximum of the
potential is the PCB itself, whereas the negative one is the
entire ground structure, i.e., table, loadbox, and cooler.
Fig. 10. Comparison of measured and simulated transfer functions.
Fig. 12. Electromagnetic potential of resonance B: The PCB with attached
wires resonates with the entire ground structure of loadbox, table, and cooler.
Both are approximately surfaces of equal potential, shortened at LISN side.
Based on this insight we derive a PHREEC topology and
circuit as in Fig. 13: We set circuit nodes at each end of the
wires (N1, N3, N4, N6), as well as one on the loadbox in
between the wire ends (N5) and one on top of the cooler (N1),
Fig. 12. Computing the partial inductance matrix of this
system, we obtain two partial inductances for the wires and
one inductance for the ground return path. The partial
inductances are calculated as LCable_U (N2-N6), LCable_W (N3-N4)
and LGround (N1-N5) including the inductive coupling to each
other. Finally, the capacitance values CLoad,U and CLoad,W are
known by loadbox construction, and the capacitances CHV+,
CU, and CHV- are computed by a static solver. The computed
capacitances include the capacitances of the switches, the PCB
and the connected cable.
27.5 pF
481.5 nH
2.13 nF
37.9 pF
The electromagnetic potential at the resonances A and B is
shown in Fig. 11 and Fig. 12 and is computed by the CST
Studio Suite. At resonance A (shown in Fig. 11) we recognize
the wires to carry maximum and minimum potential. In fact, at
measurement table
414.8 nH
Fig. 11. Electromagnetic potential of resonance A: the wires with their load
box capacitances resonate with each other. Loadbox, cooler, and table are of
almost constant potential.
38.6 pF
method proposed in [11] to discover the root-cause of these
resonances. The resonances are explained with the aid of a
physically reduced equivalent electrical circuit (PHREEC),
i.e., an electrical circuit in which the capacitances and
inductances correspond to those parts of the model geometry,
which are the root-causes of the resonances. The derivation of
the PHREEC’s topology is hereby essential. In an electrical
circuit, the circuit nodes are locations of constant potential; by
contrast, on a location 𝑥 within a 3D-structure, the
electromagnetic potential 𝜑(𝑥 ) is, along with the vector
potential 𝐴(𝑥 ), a continuous quantity [14]. However, at
resonance frequencies, we can often localize maxima and
minima of the electromagnetic potential clearly. In this case,
the approximation of the 3D- structure by a PHREEC is
admissible, and we set a single circuit node each in maximum
and minimum [11]. Finally, the value of the capacitances that
causes the resonance can be estimated by an electrostatic
solver [9] or by the method explained in [12]. The partial
inductances that span the corresponding loops are computed
using the algorithm described in [13].
2.15 nF
202.0 nH
MU-W = 0.317
MGround-U = 0.344
MGround-W = 0.344
Fig. 13. Equivalent circuit derived from potential analysis of modes A and B.
Fig. 13 shows the resulting equivalent circuit which
combines the involved elements of resonance A and B. The
circuit is further extended by the elements of the LISN as well
as the battery cables and implemented in a Spice simulation.
Fig. 14 compares the transfer function from the high-side
switch to the LISN based on the circuit simulation and the 3D
Fig. 14. Comparison of simulated transfer function with 3D-geometry model
compared to the simulation of the derived equivalent circuit
measurement and the simulation are very sensitive with
respect to small resistances, which can differ in measurement
and simulation models.
This paper proposes a new frequency-domain model for
conducted EMI of a converter. The model is designed by
replacing the nonlinear and time-variant semiconductor
switches of the converter by behavioral voltage sources,
characterized by measurements during operation of the device.
To verify the approach, voltage transfer functions from the
sources to the LISN are measured with a VNA in the real test
setup. Combining the transfer functions with the voltage
sources allows the reproduction of the disturbance voltage at
the LISN and justifies the method. Subsequently, the transfer
functions are simulated based on a 3D-model. A geometry
model of the complete CISPR 25 test setup is combined with
S-Parameter data of the LISNs, load and discrete parts of the
inverter. The simulation reproduces the measured coupling
path very well. Based on the resonances of the electromagnetic
potential, a physical equivalent circuit is developed which
accurately describes the root-causes of the EMI resonances.
Looking at resonance A and B, the results show a similar
shape of the voltage transfer function. The slight deviations of
the resonance frequencies are caused by the inaccurate
position of the nodes N1 to N6 and the higher Q factor of the
resonances in the circuit simulation are caused by the
approximation of the load capacitances without series
resistance and series inductance. Above 50 MHz, the circuit
does not match the 3D-simulation since the next resonance at
about 70 MHz is not considered in the PHREEC topology
Based on the circuit presented in Fig. 13, the resonances A
and B can be explained in detail. Resonance A is caused by a
series resonance of LCable_U, LCable_W, Cload,U and Cload,W with a
resonance frequency of 6.2 MHz. At the resonance frequency,
there is a local maximum of the differential mode current
between both motor cables. This current result in a large
voltage drop between N2 and N5 due to the higher inductance
of LCable_U compared to LCable_W. This phenomenon is also
known as DM-to-CM conversion. The LISN and the battery
cables are connected in parallel to these two points and show
therefore a high voltage drop at that frequency. Secondly,
resonance B is caused by a CM-resonance of both motor
cables connected in parallel, the inductance of the ground
path, and the capacitances inside the inverter. This resonance
between the inverter and the 3~load is well described in [6],
but is shifted towards higher frequencies because of the much
smaller parasitic capacitances inside the inverter investigated
in this work.
It is also interesting to note that below 600 kHz, the circuit
model shows identical behavior as the 3D-model, as both
differ here from the measurement. Precisely, apart from a
rough estimation of LISN wire inductances, the circuit and the
3D-model do not share any common information in this low
frequency range. Here, reflection at the high-side switch is
very close to 1 caused by very low inductance of the DC-link
capacitor and the short circuited low side-switch. Hence, the
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