# Enhanced Impedance Measurement to Predict Electromagnetic Interference Attenuation Provided by EMI Filters in Systems with AC/DC Converters

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## Abstract

**:**

## Featured Application

**The proposed enhanced single-probe method can be used to measure the impedance of energized devices or systems, which is usually not possible with traditional direct measurement methods. The online impedance measure is helpful in filter design/selection, system monitoring, and fault diagnosis. In addition, the obtained online impedances allow the prediction of converter-generated electromagnetic interference in both DC, AC single-phase, and AC three-phase systems, as well as estimation of the insertion loss of EMI filters, which is beneficial to filter assessment and design.**

## Abstract

## 1. Introduction

## 2. Enhanced Single-Probe Method and Verification

#### 2.1. Enhanced Single-Probe Method

_{x}), as shown in Figure 1a, is presented. In the proposed setup, the bulk current injection (BCI) probe is connected to one port of the vector network analyzer (VNA) through a coaxial cable. A short wire connecting the unknown impedance is wound on the core of the BCI probe forming multiple turns. In each of these turns, the wire enters the probe inner window from a side, crosses the probe leaving the opposite side, and runs back to the entering side. The turn number of this looped wire is called N

_{turns}. Inside the BCI probe, there is a feeding winding whose number of turns is N

_{probe}(this number is out of the operator’s control since it is related to the probe manufacturer and model). It is worth noting that it is possible to use not only BCI probes but also current monitor probes, as they are basically the same instrument, and many models are declared for both purposes by manufacturers. However, their design is usually optimized for one of the two scopes. Monitor probes have a high number of turns N

_{probe}in order to reduce the loading impedance ($50/{N}_{probe}^{2}$ Ω) on the clamped cable, which would perturb the circuit under test. Conversely, BCI probes usually have a very low N

_{probe}to be effective in inducing a longitudinal voltage source onto the clamped cable.

_{turns}instead of only one turn [21], and to specifically make the number of wire turns N

_{turns}exactly equal to the turns N

_{probe}of the feeding winding inside the BCI probe. The sensitivity analysis in Section 2.2 will support this choice.

_{m}) seen at a-a’ can be extracted from the measured scattering parameter (S

_{11}) by [28]:

_{0}is the internal reference impedance of the VNA.

**T**of the two-port network (port a-a’ and b-b’) accounts for the BCI probe and the two-turn loop wire and its parasitic components:

_{x}can be computed from [25]:

_{x}can be expressed in terms of S

_{11}and three coefficients (k

_{1}, k

_{2,}and k

_{3}) [25]:

_{0}) and the ABCD parameters of the two-port network, which is determined by the calibration setup (the BCI probe, the multiple-turn wire, and the parasitic components). The calibration procedure presented in Section 2.3 allows skipping the determination of the ABCD parameters (e.g., by probe modeling and accounting for all parasitic effects).

#### 2.2. Sensitivity Analysis for Justification of the Two-Turn Loop Setup

_{x}is to the measured S

_{11}, keeping other parameters (k

_{1}, k

_{2,}and k

_{3}) fixed. Under the assumption that S

_{11}is a real number (i.e., resistive load), the sensitivity coefficient ${S}_{{S}_{11}}^{{Z}_{x}}$ is obtained by differentiating (4):

_{turns}.

_{11}), and the reference impedance of the VNA (Z

_{0}):

_{11}= 1), the sensitivity coefficient is singular and reaches infinity, indicating that the single-probe setup can provide high accuracy in measuring high impedances. On the contrary, the short circuit condition (S

_{11}= −1) is the worst case, exhibiting the minimum sensitivity as:

_{turns}of the loop wire or choosing probes with a small N

_{probe}. For the latter, commercial BCI probes are already designed with a small number N

_{probe}(usually one to three) to maximize coupling efficiency in BCI testing. In this respect, the category of BCI probes is best suited for the proposed impedance-measured method compared to other inductive probes, like current-monitor probes, which usually involve many primary turns. Anyway, after a specific BCI probe is selected (this choice is based on the working band), this number N

_{probe}is fixed and out of the control of the test operator.

_{turns}of the loop wire, there is a trade-off between many factors. On the one hand, increasing this number is helpful in improving the worst-case sensitivity (12). On the other hand, this choice can introduce two critical issues. First, when this setup is employed to measure the impedance of an active device like an operating power converter (this application will be presented in the next section), if $k={N}_{probe}/{N}_{turns}<1$, then an interference-noise current I

_{n}generated by such a converter and flowing in the secondary would result in an increased noise current I

_{n}/k injected in the VNA port connected to the primary, which could cause measurement errors and even possible instrument damage. Second, the use of too many hand-made wire turns would increase the uncertainty of the geometrical arrangement, which reduces the repeatability of the test setup.

#### 2.3. Calibration Procedure and Validation of the Proposed Method

_{1}, k

_{2,}and k

_{3}) needed in (4), in order to be able to correctly measure the impedance of the circuit under test with no need for an explicit probe model [25]. This allows users to avoid the determination of an accurate model of the BCI probe as a two-port network to be used for computing A, B, C, and D. Additionally, the calibration procedure can be repeated with any BCI probe with no need for a specific setup.

_{11}parameters of three known resistors (nominal values 1.1 Ω, 50 Ω and 1 kΩ), whose actual impedances (see Figure 3b) are determined with an impedance analyzer by reflectometric measure. The VNA is configured to measure 1601 points from 10 kHz up to 30 MHz, with 100 Hz resolution bandwidth and 8 dBm transmitted power. The same configurations have been used both for the calibration discussed in this section and for the tests reported in the following sections.

_{1.1Ω}, Z

_{50Ω}, and Z

_{1kΩ}are actual impedances of three resistors measured by an impedance analyzer, and S

_{1.1Ω}, S

_{50Ω}, and S

_{1kΩ}are the measured S

_{11}parameters in the calibration setup (see Figure 3a).

_{1}, k

_{2}, and k

_{3}obtained from the calibration procedure are plotted in Figure 4a, and are consistent with the ideal theoretical expectations (10) in the in-band region (1–5 MHz). Specifically, since the turn ratio k is equal to 1 in our setup, the coefficients become k

_{1}= k

_{2}= −Z

_{0}= −50 Ω and k

_{3}= −1. Outside that narrow in-band region, the coefficients exhibit a non-trivial frequency response, which is determined by all the possible complex phenomena (e.g., lossy and dispersive ferrite core, inductive and capacitive parasitic effects) associated with the specific BCI probe model.

_{1}, k

_{2,}and k

_{3}, and by an impedance analyzer. The minor discrepancies of the 3.3 µF capacitor around its self-resonance frequency are expected due to the low sensitivity at low impedance, confirming the conclusions of sensitivity analysis. The deviations of the 100 µH inductor are likely due to the different shape of the impedance analyzer fixture (involving a small ground plane below the component under test) and the proposed method (without ground plane), which has an impact on capacitive parasitic effects.

## 3. Setups to Extract Equivalent Modal Circuits

#### 3.1. Measurement Setups to Extract the Equivalent Modal Circuits

_{MDS_DM}and Z

_{LISN_Cable_DM}stand for the DM impedances of the motor drive system and external circuit, respectively.

_{dm_tot}) can be used to calculate the impedance (Z

_{dm_tot}) seen at b-b’ by (14). In the second configuration in Figure 7c,d, the motor drive system is taken out, and the cable terminals of phases U, V, and W on the motor drive system side are connected to assess the external circuit (Z

_{dm_LC}), which is derived from the measured S

_{dm_LC}by (15). Eventually, the two impedances of the DM equivalent circuit (Z

_{LISN_Cable_DM}and Z

_{MDS_DM}) can be computed from (16) and (17) by circuit theory. Due to the symmetry assumption, the minor differences between measurements on each phase are assumed to be non-intentional deviations. Consequently, the results in the next section are based on the average values calculated from three measurements on each phase.

_{cm_tot}and Z

_{cm_LC}), and the equivalent impedances (Z

_{LISN_Cable_CM}and Z

_{MDS_CM}) are derived according to (18)–(21).

#### 3.2. Measurement Setup for Three-Phase EMI Filters

## 4. Measurement Results and IL Prediction

#### 4.1. Impedances of the Equivalent Modal Circuits of the Motor Drive System Setup

_{LISN_Cable_DM}and Z

_{LISN_Cable_CM}) are almost equal to 50 Ω and 50/3 Ω in the intermediate frequency range as expected. However, at higher frequencies, these impedances increase owning to cable effects, thus confirming the necessity to evaluate not only the source but also the load CM and DM actual impedance.

_{MDS_DM}of the motor drive system shows a significantly different behavior depending on the power being turned OFF and ON (see the black curve and other curves in Figure 10a). Thus, the online DM impedance cannot be represented by the one measured offline in this motor drive system setup. This conclusion is in line with other research works [17]. Except for a small portion below 70 kHz, where the switching frequency and its harmonics affect measurement accuracy, the impedance Z

_{MDS_DM}does not exhibit significant variations if the switching frequency is changed (sf = 5 kHz, 10 kHz, and 15 kHz). When power is ON, and the motor drive system is OFF (grey curve), it displays almost the same impedance as the other three operating conditions but with less noise at low frequency. This result suggests measuring the online DM impedance by simply turning ON the power while leaving the motor drive system OFF.

_{MDS_CM}, except for frequencies below 100 kHz, where the measured impedance is more affected by the switching frequency and its harmonics than in the DM case. However, no significant variations are observed if the CM impedance is measured online or offline. As a consequence, offline impedance measurement can be effectively used for the CM. These conclusions are consistent with those in [17,18].

#### 4.2. Definition of CM/DM IL of Three-Phase Filters

_{wo_DM}, V

_{wo_CM}across the load in the absence of the filter.

_{LISN_Cable_DM}and Z

_{MDS_DM}are the load and source impedances, respectively, in the DM test setup, and Z

_{LISN_Cable_CM}and Z

_{MDS_CM}are the same impedances in the CM setup.

_{1}and V

_{2}in (22), and V

_{1}in (23) involved in these expressions can be evaluated by combining the filter ABCD-parameter representation, relating voltages and currents at the filter ports, i.e.,

_{1}measured in the DM setup [(22), (25) set of equations on the left], and in the CM setup [(23), (25) set of equations on the right].

#### 4.3. Predictions of the DM and CM IL

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**(

**a**) Calibration setup and (

**b**) measurements of the magnitude and phase of the three resistors used for calibration (obtained by reflectometric measure with impedance analyzer).

**Figure 5.**(

**a**) Magnitude error (percentage) and (

**b**) phase error from the measure of discrete RLC components.

**Figure 6.**(

**a**) Diagram of the motor drive system, and (

**b**) a picture of the single-probe setup used to measure the motor drive system impedances.

**Figure 7.**Setups to determine the DM equivalent circuit: (

**a**,

**b**) in the presence and (

**c**,

**d**) in the absence of the motor drive system.

**Figure 8.**Setups to determine CM equivalent circuit: (

**a**,

**b**) in the presence and (

**c**,

**d**) in the absence of the motor drive system.

**Figure 9.**(

**a**) Setup for S-parameter measurement of a three-phase filter and (

**b**) filter arrangement inside a metallic enclosure equipped with SMA connectors.

**Figure 11.**Setups for computing the in-circuit IL. Left and right panels show the (

**a**,

**b**) DM and (

**c**,

**d**) CM setups without and with the filter, respectively.

**Figure 12.**One-stage filter: DM ILs between (

**a**) port 4–5, (

**b**) port 5–6 and (

**c**) port 4–6, and (

**d**) CM IL.

**Figure 13.**Two-stage filter: DM IL between (

**a**) port 4–5, (

**b**) port 5–6 and (

**c**) port 4–6, and (

**d**) CM IL.

Component | Maximum Magnitude Error [Ω] | Maximum Percentage Magnitude Error | Maximum Phase Error [°] |
---|---|---|---|

R 18 Ω | −2.08 Ω @ 30 MHz | −10.3% @ 30 MHz | −10.5° @ 30 MHz |

R 82 Ω | −2.66 Ω @ 11.4 kHz | −3.25% @ 11.4 kHz | 1.87° @ 10.5 kHz |

R 250 Ω | −24.6 Ω @ 11.8 kHz | −9.86% @ 11.8 kHz | 7.37° @ 10.5 kHz |

C 3.3 µF | −1.00 Ω @ 30.0 MHz | 20.8% @ 309 kHz | −16.4° @ 359 kHz |

L 100 µH | 720 Ω @ 17.0 MHz | 57.4% @ 25.9 kHz | −28.1° @ 43.8 kHz |

Component | Average Magnitude Error [Ω] | Average Percentage Magnitude Error | Magnitude Standard Deviation [Ω] | Average Phase Error [°] | Phase Error Standard Deviation [°] |
---|---|---|---|---|---|

R 18 Ω | −0.15 Ω | −0.77% | 0.40 Ω | −1.59° | 3.03° |

R 82 Ω | −0.01 Ω | −0.01% | 0.23 Ω | −0.05° | 0.18° |

R 250 Ω | −0.49 Ω | −0.20% | 2.40 Ω | −0.09° | 0.80° |

C 3.3 µF | −0.12 Ω | −3.41% | 0.26 Ω | −1.41° | 3.56° |

L 100 µH | 68.7 Ω | 21.4% | 212 Ω | −7.48° | 15.1° |

Component | Specifications |
---|---|

Variable frequency drive | Input: 3-phase, 380–480 V, 50 Hz Output: 0–460 V, 5 kVA, 2.2 kW, 0–599 Hz |

Induction motor | Nominal power: 0.75 kW, 2.1A, 50 Hz, 1430 rpm |

LISN | Schwarzbeck, NSLK8128, CISPR16-1-2, 9 kHz—30 MHz |

VNA | Keysight, E5061B, 5 Hz—1.5 GHz |

Bulk current injection probe | FCC, F-120-2, 10 kHz—230 MHz |

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**MDPI and ACS Style**

Wan, L.; Negri, S.; Spadacini, G.; Grassi, F.; Pignari, S.A.
Enhanced Impedance Measurement to Predict Electromagnetic Interference Attenuation Provided by EMI Filters in Systems with AC/DC Converters. *Appl. Sci.* **2022**, *12*, 12497.
https://doi.org/10.3390/app122312497

**AMA Style**

Wan L, Negri S, Spadacini G, Grassi F, Pignari SA.
Enhanced Impedance Measurement to Predict Electromagnetic Interference Attenuation Provided by EMI Filters in Systems with AC/DC Converters. *Applied Sciences*. 2022; 12(23):12497.
https://doi.org/10.3390/app122312497

**Chicago/Turabian Style**

Wan, Lu, Simone Negri, Giordano Spadacini, Flavia Grassi, and Sergio Amedeo Pignari.
2022. "Enhanced Impedance Measurement to Predict Electromagnetic Interference Attenuation Provided by EMI Filters in Systems with AC/DC Converters" *Applied Sciences* 12, no. 23: 12497.
https://doi.org/10.3390/app122312497