**3. Experimental Results**

This section provides the results of an experimental system. All presented analyses and measurements concern a buck-converter topology, with a C2-class high speed insulated-gate bipolar transistor (IGBT), and a hardware interface for signal and ground to the R-Series Multifunction RIO (FPGA PXI-7854R). The control signal output (RanM or DetM) is provided, at the hardware level, by the NI SCB-68A shielded connector block. Combined with the shielded cables, the SCB-68A provides rugged, very low-noise signal termination to the transistor gate drive. Figure 13 illustrates the scheme of the measuring testbed.

**Figure 13.** Schematic diagram of measuring testbed.

According to the schematic diagram illustrated in Figure 13, the buck-converter topology is powered by a regulated laboratory power supply. Additionally, the FPGA control board power is controlled by the PXIe 8135 to prevent additional couplings through the power source. A Leybold sliding resistor 320 Ω, 1.5 A was connected as load for the buck converter output. The EMI measurement was performed with the 50 Ω/50 μH Line Impedance Stabilization Network (LISN). The important parameters of the buck-converter and the testbed are summarized in Table 1.


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

Figure 14 shows the measurements for all cases (DetM and RanM) presented in Section 2. The results have been obtained using the TDMI X6 EMI receiver, which provides a 3D spectrogram for Quasi Peak (QP) detector, which is required by EMC standards in CISPR A frequency band.

The Figure 14a refers to the measurement for DetM with *Nm* = *NAV* = 500 and *δN* = 0. The first harmonic magnitude (occurring at 80 kHz) is the most significant in the whole frequency spectrum. The magnitude of this harmonic is equal to 93.76 dBμV. The Figure 14b refers to measurement for RanM with *NAV* = 667, *δN* = 668 and *SCTL* = 1. As expected, the maximal harmonic magnitude is not connected with the *fsw* = 80 kHz. Despite this, the frequency varied within the assumed range (Figure 5), and the spectrum level is lowered to value 74.24 dBμV. The Figure 14c presents the measurement results for RanM with *NAV* = 500, *δN* = 330 and *SCTL* = 1. As expected, the maximal harmonic magnitude is lowered and its frequency is more connected with the *fsw* = 80 kHz. The maximum amplitude of the disturbances is equal in this case to 73.43 dBμV, and despite the smaller range of *fsw*, variation is lower than in the case of RanM from Figure 14b. Therefore, we can conclude that increasing the *δN* range does not always lead to a lowering of the spectrum level. The Figure 14d refers to the measurement for RanM with *NAV* = 50, *δN* = 34 and *RSCTL* ∈< 7 : 13 >. The maximal harmonic magnitude is connected with the *fsw* = 80 kHz, and a little EMI noise reduction is provided, whether compared with Figure 14b,c. The Figure 14e refers to the measurement for RanM2 for parameters: *NAV*<sup>1</sup> = 750 with *δN*<sup>1</sup> = 500, *NAV*<sup>2</sup> = 416 with *δN*<sup>2</sup> = 167, and *SCTL*. As expected, two extremes are visible in the spectrum. The Figure 14f shows the result of measurement for RanM2 with *RSCTL* (concept of additional randomization). The parameters of modulator are: *RSCTL* ∈< 7 : 13 >, *NAV*<sup>1</sup> = 75, *δN*<sup>1</sup> = 50, *NAV*<sup>2</sup> = 42 and *δN*<sup>2</sup> = 17. The EMI noise is spread with a better shape between all RanM proposed. Unfortunately, the spread of *fsw* value is the largest of the analysed cases (Figure 11). Based on the measurement, it is difficult in this case to determine the main/dominant frequency of disturbances.

**Figure 14.** The electromagnetic interference (EMI) spectrum for DetM with *N* = 500 (**a**), RanM with *NAV* = 667, *δN* = 668 (**b**), RanM with *NAV* = 500, *δN* = 330 (**c**), RanM with *RSCTL* for *NAV* = 50, *δN* = 34 and *RSCTL* ∈< 7 : 13 > (**d**), RanM2 with *NAV*<sup>1</sup> = 750, *δN*<sup>1</sup> = 500, *NAV*<sup>2</sup> = 416, *δN*<sup>2</sup> = 167 (**e**), RanM2 *RSCTL* ∈< 7 : 13 >, *NAV*<sup>1</sup> = 75, *δN*<sup>1</sup> = 50, *NAV*<sup>2</sup> = 42 and *δN*<sup>2</sup> = 17 (**f**).

#### **4. Discussion and Analysis of Results**

According to Figure 14a, the maximum harmonic magnitude in the spectrum (observed at 80 kHz) for DetM is about 93.76 dBμV. Furthermore, Figure 14d shows the maximum harmonic magnitude in the spectrum (observed at 80 kHz) for RanM with *RSCTL*, which is about 72.15 dBμV. Therefore, RanM with *RSCTL* provides 21.61 dBμV for QP detector, with lower EMI levels than DetM. Applying the concept of additional randomization with *RSCTL* and sectional distribution of *Nm*, RanM2 obtained the best results—Figure 14f. The results are about 22.90 dBμV for the QP detector, being lower than DetM. According to the literature, the evaluated harmonic reduction could also be provided by the Harmonic Spread Factor (HSF) [16,17]. The HSF is an accurate evaluation index of any waveform for testing its harmonic spreading effects, and is defined as follows in Equations (8) and (9).

$$HSF = \sqrt{\frac{1}{N} \sum\_{j=1}^{N} (H\_j - H\_o)^2} \tag{8}$$

$$H\_0 = \frac{1}{N} \sum\_{j=1}^{N} (H\_j) \tag{9}$$

where: *Hj* is the amplitude of the *j*th harmonics and *Ho* is the average value of all *N* harmonics.

The ideally spread spectrum must be near zero, i.e., white noise, presenting an HSF equal to zero. In this manuscript, the HSF analysis provides in absolute value, the harmonic reduction into CISPR A frequency band, for QP detector measurement and additionally for AV detector. Figure 15 shows the results of HSF calculation.

It is possible to observe that there are almost no differences between all HSF provided by RanM and RanM2 (for both QP and AV detectors). Of course, there is a significant difference between RanM2 and DetM. RanM2 based on the concept of additional randomization with *SCTL* presents the best HSF. However, whether compared with RanM2 based on the concept of additional randomization with *RSCTL* the difference is only 0.3% for QP and 0.1% for AV. In terms of EMI noise reduction, the difference between RanM2 with *SCTL* and with *RSCTL* is not too big for both detectors (less than 4 dB). Despite this, the frequency distribution was different in each case.

Additionally, hardware resources were also analysed. The hardware resources on an FPGA are indicated by the number of slices. The DetM code after the compilation process presents total slices of 3.0% from all available slices in the VIRTEX-5 LX110 FPGA. On the other hand, among all RM codes, the concept of additional randomization, RanM2 with *RSCTL* presents greater use of the number of slices, with 5.5%.

**Figure 15.** Harmonic Spread Factor (HSF) calculations: (**a**) detector Quasi Peak (QP) and (**b**) detector Average (AV).

#### **5. Conclusions**

This manuscript demonstrates how to design RanM, and DetM oriented for FPGA implementation with the LabVIEW engineering software. Since there are some FPGA software limitations (fixed-point operation, and a lack of basic arithmetic functions), it may be challenging to complete the RanM and the DetM implementation. Therefore in the article, we have highlighted how to do some calculations required for PWM modulator implementation in FPGA. We have also shown that the realization of RanM in FPGA should consider the distribution of randomized time and frequency parameters of the PWM signal. One should pay the primary attention to the range of switching frequency *fsw* changes and the average value of this frequency.

The presented algorithms have been implemented in FPGA - R-Series Multifunction RIO (PXI-7854R), with VIRTEX-5 LX110. The most extensive version of the algorithm (RanM2 with *RSCTL*) used only 5.5% of FPGA resources. Presented algorithms are weary simple, and they can be easily expanded. Likewise, implementing the modulator to a control system inside the same FPGA is also possible. Therefore, the proposed solutions can be used in all DC/DC converters applications. However, one may obtain the most significant benefits in automotive and lighting applications where

there are direct limits on interference emission in the CISPR A band, and proposed control methods help fulfill these requirements.

Proposed modulators were tested experimentally. All measurements were carried out according to EMC standards in the frequency domain for CISPR A frequency band. The EMI emission (for design RanM) was significantly reduced compared to the DetM. We have achieved a reduction of the maximum EMI level value by over 20 dB. One should also remember, according to [8], that although pseudo-random modulations reduce the maximum level of interference, they do not change its aggregate power. Considering experimental research and implementation in FPGA, we assess that offered solutions have reached level 7 of Technology readiness levels (TRLs).

The differences between the EMI emission for different RanM were not significant. However, presented modulators differed in *fsw* distribution. The minimum value of *fsw* affects the operating conditions of the filters and and maximum amplitude of output current ripple. The maximum value of *fsw* frequency will be significant with the restrictions of the transistors. Keeping the average value of this frequency unchanged, we will not change the overall losses, and converter efficiency will be consistent. Therefore, by using the proposed methods (with appropriate parameters), one can achieve energy neutrality for the converter. In the future research, we are planning to investigate which shape of the frequency distribution is preferred in respect of EMI level emissions and other operation of the converter.

**Author Contributions:** Conceptualization, H.L., P.L., R.S. D.N. and W.S.; methodology, H.L., P.L. and R.S.; validation, formal analysis, visualization H.L. and P.L.; software, investigation, H.L.; writing–original draft preparation, H.L., P.L. and W.S.; writing–review and editing, H.L., P.L. and R.S.; supervision, project administration, funding acquisition, R.S. 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 grant agreement No 812391 – SCENT.

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

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


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