**3. Measurements of Aggregated EMI Generated by DC/DC Converters with Deterministic and Random Modulation**

In order to confirm the results of the simulation, standardized EMI measurements have been obtained from a laboratory setup fully compliant with EN 55011 based on a voltage probe. Two DC/DC buck-converters constitute the Equipment Under Test (EUT). Both converters are based on a C2-class high speed insulated-gate bipolar transistor (IGBT). The hardware interface for signal and ground are made by the R-Series Multifunction RIO (FPGA PXI-7854R), with VIRTEX-5 LX110. The control signal output (RanM and DetM) is provided at the hardware level by the shielded connector block NI SCB-68A. Figure 4 illustrates the scheme for the measuring testbed.

**Figure 4.** Schematic diagram of measuring testbed.

The schematic diagram presented in Figure 4 shows that both buck-converters are powered by the same regulated laboratory power supply by means of the cables of equal length. In addition, two FPGA control boards were used, and both were powered by controller PXIe 8135 to avoid additional couplings through the power source. A 1.5 A Leybold sliding resistor 320 Ω, was connected as the load on the

output of buck-converters (24 V) connected in parallel. In addition, equal length of cables has been applied. The most important parameters of the buck-converter topology have been summarized in Table 1.

**Table 1.** The main parameters of buck-converter topology.


The output voltage was measured by a differential voltage probe SI-9010A from Sapphire Instruments (with a 40 dB attenuation level). In both cases, for all presented experimental results, the *fsw* = 80 kHz and *d* = 0.5 remained unchanged. Figures 5 and 6 show the measurements obtained using a digital receiver type TDMIX6 EMI, which provides a 3D spectrogram for both Quasi Peak (QP) and Average (AV) detector and CISPR 16-1-1 compliant measurements. In order to increase readability of the figures, measurements have been taken up to 6*th* harmonic with IFBW = 200 Hz. The experimental results presented in Figure 5 have confirmed the presence of the frequency beat phenomenon observed in simulations. In a case of two converters low frequency envelopes resulting from frequency beat are superimposed on the interference harmonics.

The use of random modulation to disperse interference over the frequency range prevents the frequency beating phenomenon, which appears during aggregation of sinusoidal components of similar frequencies. Thus, in the case of RanM presented in Figure 6 the low frequency envelopes do not appear for aggregated interference introduced by two DC/DC converters connected in parallel Figure 6B.

Generally, the shapes of experimental results, presented in the form of 3D spectrograms, based on data from a laboratory setup, fit well with corresponding 3D spectrograms obtained by simulations. Both simulation and experimental results confirm the theoretical assumptions concerning aggregation of interference for deterministic and random modulation. The obtained results encouraged us to perform multiple measurements according to standard requirements.

**Figure 5.** Experimental 3D spectrograms of interference measured using AV detector, caused by one DC/DC converter with DetM (**A**), and two DC/DC converters with DetM (**B**).

**Figure 6.** Experimental 3D spectrograms of interference measured using AV detector, caused by one DC/DC converter with RanM (**A**), and two DC/DC converters with RanM (**B**).

#### **4. Statistical Analyses of Aggregated EMI Generated by Converters with Deterministic and Random Modulation Measured According to Standards**

In order to present measurement problems connected with the frequency beat phenomenon multiple measurements of the frequency linked with the highest emission were taken. The results of the measurements have been presented in the form of box-and-whisker plots, supplemented with individual values of measured EMI depicted as points. According to standard requirements [28], one final measurement taken during a measuring period equal to 1 s can be compared with the limit line for a presumption of conformity based on harmonized standards. The standards require measurements using QP as well as AV detector. Since the results obtained for both detectors did not differ significantly the presented analyses were based on AV detector measurements only. For each investigated case, 1000 final measurements during 1 s were taken [29].

Figure 7 shows distributions of the results obtained for single DC/DC converters with DetM (A) and RanM (B). The dispersion of the 1000 results in the case of DetM (A) is lower than 0.1 dB. The randomization of the switching frequency caused an increase of the dispersion up to 2 dB. Such distributions of the results confirm that a case of EMI generated by a single DC/DC converter is sufficient for EMI evaluation.

**Figure 7.** Box-and-whisker plots of 1000 average detector 1 s measurements for one DC/DC converter with: (**A**) deterministic modulation and (**B**) random modulation

The 2 dB dispersion remained unchanged in the case of aggregated interference introduced by two DC/DC converters with random modulation, Figure 8B. However, low frequency envelopes, linked with the frequency beat phenomenon and accompanying aggregation of EMI introduced by converters with deterministic modulation, caused a significant increase in the range of measured levels. The observed differences reached 25 dB (18 times), Figure 8A.

The observations based on the Figures 7 and 8 are confirmed by statistical parameters determined for empirical distributions presented in the figures. The values of variance and standard deviation of measurements in an arrangement consisting of two DC/DC converters are much greater than in other investigated cases (Table 2). The variance and standard deviation calculation, from the EMI measurement viewpoint, represent the dispersion of the measurements of the AV detector, indicating "how far" in general its values are from the expected value. In fact, such dispersion of the results makes evaluation of aggregated EMI, based on one final measurement, in arrangement consisting converters with deterministic modulation unreliable.

**Figure 8.** Box-and-whisker plots of 1000 average detector 1 s measurements for two DC/DC converters with: (**A**) deterministic modulation and (**B**) random modulation

**Table 2.** Statistical parameters of empirical distributions of 1000 final measurements using AV detector.


#### **5. Conclusions**

In the paper both simulation and experimental results concerning aggregated conducted electromagnetic interference generated by DC/DC converters with deterministic and random modulation have been presented. In the case of deterministic modulation the obtained results have shown that the amplitudes of aggregated interference are modulated with low frequency envelopes caused by the frequency beat phenomenon accompanying summation of sinusoidal components of close frequencies.

The investigation presented in this paper, despite consisting of two identical DC/DC converters, is corroborated by conducted electromagnetic interference in multiconverter systems, as recently investigated by [24], through a real 1 MW photovoltaic power plant. Furthermore, the statistical analyses of large series of final measurement data has confirmed assumptions that low-frequency envelopes might make the standardized EMI tests unreliable.

The research presented has revealed that in the case of random modulation a blurring of instantaneous values of switching frequency contributes to the decreasing of maximum EMI values as well as to the prevention of the frequency beat phenomenon.

**Author Contributions:** Conceptualization, H.L., R.S., P.L., D.N. and G.D.; methodology, H.L., P.L. and R.S.; validation, formal analysis, visualization H.L. and G.D.; software, investigation, H.L., D.N.; writing—original draft preparation, H.L., R.S., P.L. and G.D.; writing—review and editing, H.L., P.L. and R.S.; supervision, project administration, funding acquisition, R.S. and G.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This paper is part of a project that has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grants agreement No 812391—SCENT, 812753—ETOPIA and in part by the Government of Russian Federation under Grant 08-08.

**Conflicts of Interest:** The authors declare no conflict of interest.
