# Time–Frequency Analysis of Experimental Measurements for the Determination of EMI Noise Generators in Power Converters

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- To measure the voltage and current signals characteristic of semiconductors by selecting the appropriate measuring instruments (voltage and current probes, oscilloscope and spectrum analyser) and establish a methodology for carrying out these experimental measurements with sufficient fidelity or resolution to be able to combine low switching frequencies with the observation of high-frequency phenomena responsible for the generation of EMI;
- (2)
- Obtain the spectrum from the complete experimental signals instead of obtaining the spectrum as the sum of individual time signal effects (switching slope, reverse recovery current, ringing, etc.). This can be considered one of the main gaps because, although there are authors who mention the existence of oscillations that give rise to peaks in the spectrum, these considerations are made only theoretically [26] or without clearly explaining how the signal is decomposed [27].
- (3)
- Analyse whether spectral analysis techniques other than the commonly used FFT are able to establish a one-to-one relationship between the characteristic time events of the switching signals and their corresponding spectra. Although techniques such as the short-time Fourier transform (STFT) or the continuous wavelet transform (CWT) are widely known by researchers in the field of signal processing, their application to the world of power electronics is more limited, and only a few examples can be found in the literature, as will be mentioned in Section 2.2.

## 2. Overview of the Time–Frequency Characteristics of Switching Signals and Spectrum Analysis Techniques

#### 2.1. Time–Frequency Characteristics of Switching Signals

#### 2.2. Spectrum Analysis Techniques

## 3. Materials and Methods for Switching Waveforms Measurement

## 4. Experimental Measurements and Spectrum Analysis Results

#### 4.1. PCB and Measurement System Characteristics, and Time Measurement Results

- Case in which a false turn-on appears reflected in an overvoltage at $\Delta V~160\mathrm{V}$ and an overcurrent $\Delta I=-27.5\mathrm{A}$ and $\Delta I\prime =8.4\mathrm{A}$.
- Switching case with gate resistor ${R}_{g}=15\mathsf{\Omega}$, resulting in a higher overshoot in voltage and current $\Delta I=0.3\mathrm{A}$ and $\Delta {I}^{\prime}=-3.2\mathrm{A}$ (due to reverse recovery current).
- Switching case with gate resistor ${R}_{g}=82\mathsf{\Omega}$, resulting in a current overshoot, $\Delta I=0.7\mathrm{A}$ and $\Delta {I}^{\prime}=-1.3\mathrm{A}$ (due to reverse recovery current).

#### 4.2. Spectrum Analysis Results

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of a switching system, noise sources and propagation paths for common mode (CM) and differential mode (DM), and EMI measurement.

**Figure 3.**Spectrum and envelope of a basic trapezoidal switching wave and effect of changing parameters such as switching frequency, $dv/dt$ or $di/dt$. In red, appearance of peaks on the envelope due to ringing effects.

**Figure 4.**Test bench for measurement of switching waveforms: (

**a**) block diagram of a half-bridge and positioning of measuring probes; (

**b**) PCB detail with location of current shunt and voltage probes.

**Figure 5.**Detail of coaxial shunt: (

**a**) with shortened pads (top) to reduce inductance, and original (bottom) with long 1” pads; (

**b**) frequency response of reactance of current shunt resistor up to 30 MHz for original sensor (brown line) and shortened pads sensor (blue line).

**Figure 6.**Results of experimental measurements for 3 different cases: (

**a**) false turn-on; (

**b**) switching with gate resistor ${R}_{g}=15\mathsf{\Omega}$; (

**c**) switching with gate resistor ${R}_{g}=82\mathsf{\Omega}$.

**Figure 7.**Time resolution vs. frequency resolution in STFT calculation for different length Hamming windows: (

**a**) $N=512$; (

**b**) $N=2048$; (

**c**) $N=8192$.

**Figure 8.**STFT analysis comparison for several windows and window lengths: (

**a**) flat top window $N=512$; (

**b**) flat top window $N=2048$; (

**c**) rectangular window $N=512$; (

**d**) rectangular window $N=2048$; (

**e**) Hamming window $N=512$; (

**f**) Hamming window $N=2048$.

**Figure 9.**Wavelet analysis comparison using different wavelet types, number of octaves (${N}_{o}$) and number of voices (${N}_{v}$): (

**a**) Morse wavelet ${N}_{o}=13$, ${N}_{v}=6$; (

**b**) Morse wavelet ${N}_{o}=13$, ${N}_{v}=40$; (

**c**) Morlet wavelet ${N}_{o}=13$, ${N}_{v}=6$; (

**d**) Morlet wavelet ${N}_{o}=13$, ${N}_{v}=40$; (

**e**) bump wavelet ${N}_{o}=11$, ${N}_{v}=6$; (

**f**) bump wavelet ${N}_{o}=11$, ${N}_{v}=40$.

**Figure 10.**Event detection and discrimination using STFT and wavelet: (

**a**) time signal I_s; (

**b**) time–frequency–magnitude representation of the STFT; (

**c**) frequency–magnitude representation of the STFT; (

**d**) detail of the wavelet transform in the interval 0–2 μs using Morse wavelet; (

**e**) detail of the wavelet transform in the interval 6–8 μs using Morse wavelet.

Type | Advantages | Drawbacks | |
---|---|---|---|

Voltage probe | Differential | Galvanic isolation | Low bandwidth Connection leads |

Voltage divider | Very high bandwidth | Loading requirements Not for ${V}_{ds}$ measurement | |

Passive | High bandwidth Suitable for bridge low side measurement Connection leads | Nongalvanic isolation | |

Current probe | Rogowski coil | Galvanic isolation Size | Low bandwidth (tenths of MHz) Low accuracy |

Current transformer | Galvanic isolation | Low bandwidth (up to ~100 MHz) Added loop inductance Larger size | |

Coaxial shunt | High bandwidth (up to GHz) High accuracy AC-DC Size | Non galvanic isolation Added loop inductance Heating |

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**MDPI and ACS Style**

Oyarzun, J.; Aizpuru, I.; Baraia-Etxaburu, I.
Time–Frequency Analysis of Experimental Measurements for the Determination of EMI Noise Generators in Power Converters. *Electronics* **2022**, *11*, 3898.
https://doi.org/10.3390/electronics11233898

**AMA Style**

Oyarzun J, Aizpuru I, Baraia-Etxaburu I.
Time–Frequency Analysis of Experimental Measurements for the Determination of EMI Noise Generators in Power Converters. *Electronics*. 2022; 11(23):3898.
https://doi.org/10.3390/electronics11233898

**Chicago/Turabian Style**

Oyarzun, Javier, Iosu Aizpuru, and Igor Baraia-Etxaburu.
2022. "Time–Frequency Analysis of Experimental Measurements for the Determination of EMI Noise Generators in Power Converters" *Electronics* 11, no. 23: 3898.
https://doi.org/10.3390/electronics11233898