### I. Introduction

### II. CM EMI Behavioral Model

### 1. EMI Noise Source and CM Propagation Paths in GaN HEMT Synchronous Buck Converters

_{L}-C

_{L}and R

_{N}-C

_{N}branches. C

_{P}denotes the parasitic capacitance between the source of the GaN HEMT device and the heat sink of the half bridge. Owing to high-frequency switching of the HEMT device, significant dv/dt and di/dt are generated in the phase-leg node M, which is coupled to the ground through C

_{P}, leading to the generation of CM conducted noise. Here, because the packages used for the HEMTs are identical and the heat sink, as a whole, is fixed under the device, we can ignore the asymmetry of the conduction path and assume that the parasitic capacitances C

_{P}of the device to the ground are identical. C

_{bus1}and C

_{bus2}represent the parasitic capacitances between the alignments of positive and negative DC power on the PCB and the earth ground. Generally, these capacitances can be considered identical because they are composed of the same material and have the same alignment lengths.

_{Pload}to the earth ground on the output side should be considered when analyzing the CM conduction path.

_{1}is turned on, synchronous device Q

_{2}is turned off, and the power supply charges inductor L

_{out}, which converts electrical energy into magnetic energy and stores it in the magnetic core. The switching speed of GaN HEMTs is generally of the order of tens of nanoseconds, during which time the potential at point M increases rapidly to the input voltage. Therefore, in the on state, the voltage V

_{DS}across the drain-source terminal of control device Q

_{1}is the noise source. Similarly, when the converter is operated in the off state, control device Q

_{1}is turned off, synchronous device Q

_{2}is turned on, and the magnetic energy stored in inductor L

_{out}is discharged as electrical energy to form a continuous loop through synchronous device Q

_{2}. Therefore, in the off state, the drain current I

_{D}of synchronous device Q

_{2}is the noise source. because of the parasitic parameters in the CM EMI propagation paths, the voltage source V

_{DS}and current source I

_{D}produce the CM noise that flows through C

_{P}and C

_{bus}to the earth and returns through the R

_{L}-C

_{L}and R

_{N}-C

_{N}branches.

_{out}on the high-frequency signals, most of the switching noise is isolated in the phase-leg node M. Therefore, the contribution of the output side to the CM EMI in the buck converter is considered minimal, and the EMI-related problems caused by Q

_{1}and Q

_{2}are mainly considered and analyzed herein. Moreover, the drain-source voltage V

_{DS}across Q

_{1}and drain current I

_{D}through Q

_{2}can be considered to contain all CM EMI noise source information pertaining to the converter system. Based on the above analysis, the CM EMI loops in the GaN HEMT synchronous buck converter are as follows: V

_{DS}of Q

_{1}, I

_{D}of Q

_{2}, R

_{L}-C

_{L}, R

_{N}-C

_{N}, and parasitic capacitance branches C

_{bus}and C

_{P}.

### 2. Equivalent Circuit of EMI Noise Source and CM Propagation Paths

_{L}and C

_{N}illustrated in Fig. 1 is 0.1 μF, while the capacitance of C

_{in}is high at several hundred microfarads to obtain a good filtering function for the input voltage. At a given frequency, the impedance of C

_{in}is considerably smaller than those of C

_{L}and C

_{N}. Therefore, the positive and negative terminals L/N can be simplified as one node in the two-terminal model of the buck converter, as illustrated in Fig. 2.

_{1}is turned on, and the lower GaN HEMT Q

_{2}is turned off, a high dv/dt voltage slew rate is produced on the drain-source voltage V

_{DS}of GaN HEMT Q

_{1}. Conversely, a high di/dt current slew rate is generated on the drain current I

_{D}of GaN HEMT Q

_{2}. Therefore, during the switching transient process, the upper GaN HEMT is modeled as the voltage source V

_{DS}and impedance Z

_{S}in series, according to Thevenin’s theorem, and the lower GaN HEMT is modeled as the current source I

_{D}and impedance Z

_{D}in parallel, according to Norton’s theorem.

### III. CM EMI Behavioral Modeling Procedure

_{LISN}is in parallel without or with a shunt impedance Z

_{SHUNT}.

_{LISN}, and the drain-source voltage V

_{DS}of the upper HEMT and drain current I

_{D}of the lower HEMT are modeled as CM EMI noise sources. According to Thevenin’s and Norton’s theorems, these two noise sources can be equated to a voltage source V

_{DS}in series with an impedance Z

_{S}and a current source I

_{D}in parallel with an impedance Z

_{D}, respectively, to obtain the equivalent circuit of the approximate model, as illustrated in Fig. 3(b). In this manner, the characteristics of the CM noise source are contained in V

_{DS}and I

_{D}, and the parasitic characteristics of the noise conduction path are contained in Z

_{S}and Z

_{D}.

_{DS}of the upper GaN HEMT on the CM current in the loop, which corresponds to the “on” operating state of the buck converter, as illustrated in Fig. 4(a). Then, the voltage source V

_{DS}is short-circuited to consider the drain current I

_{D}of the lower GaN HEMT with respect to the CM current, which corresponds to the “off” operating state of the buck converter, as illustrated in Fig. 4(b).

_{DS}and the CM current

_{CM}in terms of V

_{DS}, I

_{D}, Z

_{D}, Z

_{S}, and

_{D}and Z

_{S}, more equations should be developed for attenuated cases by adding the shunt impedances Z

_{SHUNT1}and Z

_{SHUNT2}between L/N and G. Thus, the CM loads of the model in the attenuated cases can be written as

_{CM1}and I

_{CM2}, in the following equations.

_{CM1}and its corresponding equivalent circuit are obtained by applying the superposition theorem, and they are given in Eq. (4) and presented in Fig. 6.

_{CM2}, can be obtained by replacing Z

_{SHUNT1}with Z

_{SHUNT2}.

_{DS}, and I

_{D}in Eqs. (4) and (5) correspond to the drain-source voltage V

_{DS}of the upper GaN HEMT and drain current I

_{D}of the lower GaN HEMT, respectively. Because the drain-source voltage V

_{DS}of the upper GaN HEMT and drain current I

_{D}of the lower GaN HEMT are mainly determined by the duty cycle of the control signal, the switching frequency, input voltage level, parasitic capacitance of the device itself, parasitic inductance introduced by the package, parasitic inductance of the PCB alignment, and variation of the CM load impedance have little effect on them. Therefore, we can assume that V

_{DS}and I

_{D}are constant in the nominal and attenuated cases.

_{D}and Z

_{S}of the CM EMI noise source shown in Fig. 3 can be determined using Eqs. (6) and (7), respectively.

_{D}and Z

_{S}are functions of I

_{CM1}, I

_{CM2}, V

_{DS}, I

_{D},

_{CM1}and I

_{CM2}can be measured directly using the experimental setup. Moreover, the model parameters V

_{DS}and I

_{D}can be measured experimentally.

### IV. Extraction of CM EMI Behavioral Model Parameters

### 1. Experimental Setup

*f*is 500 kHz, and the drive signal duty cycle of the converter D is 0.5. The input capacitor consists of two 150-μF electrolytic capacitors, one 3-μF film capacitor, and four 100-nF multilayer ceramic capacitors in parallel. Two GaN HEMTs (INN650D140A; Innoscience, Zhuhai, China) are used in the synchronous buck converter. A photograph of the corresponding GaN HEMT synchronous buck converter setup is presented in Fig. 8. The digital controller (DSP TMS320F28335; Texas Instruments, Dallas, TX, USA) provides pulse-width-modulated driving signals for the driver IC (STDRIVEG600; STMicroelectronics, Geneva, Switzerland) of the GaN HEMTs. The LISN used in the experiment (NSLK 8127; Rohde & Schwarz, Munchen, Germany) can operate between 9 kHz and 30 MHz. The CM currents I

_{CM1}and I

_{CM2}can be measured directly in the frequency range 10 Hz–7 GHz by using an equivalent series resistance (ESR) EMI test receiver (Rohde & Schwarz). The drain-to-source voltage V

_{DS}and current source I

_{D}of the GaN HEMTs are measured using a digital oscilloscope (DPO 5034B; Tektronix, Beaverton, OR, USA) with a bandwidth of 350 MHz, sampling rate of 5 GS/s, and four channels.

### 2. Extraction of Model Parameters

_{SHUNT1}. Another series combination of a 330-Ω resistor and 0.1-μF capacitor is used as the shunt impedance Z

_{SHUNT2}. Additionally, the shunt impedances Z

_{SHUNT1}and Z

_{SHUNT2}are measured using the WK6500B SERIES impedance analyzer, and the measured impedance curves of Z

_{SHUNT1}and Z

_{SHUNT2}are depicted in Figs. 11 and 12, respectively.

_{DS}and I

_{D}, are measured using the digital oscilloscope. The time-and frequency-domain waveforms of V

_{DS}are presented in Fig. 13. The experimental measurements of the noise current source I

_{D}are presented in Fig. 14.

_{CM1}and I

_{CM2}are measured to calculate the model impedances Z

_{D}and Z

_{S}. Figs. 15 and 16 show the measured CM currents I

_{CM1}and I

_{CM2}, respectively, with the shunt impedance Z

_{SHUNT1}and Z

_{SHUNT2}added between L/N and G parallel to Z

_{LISN}. Notably, higher ringing in the time-domain waveforms of the CM current can be seen in Figs. 15(a) and 16(a); these waveforms are related to the turn-on and turn-off switching processes of the GaN HEMTs, respectively. Moreover, according to Figs. 15(a) and 16(a), the magnitude of ringing during the turn-on process of the upper GaN HEMT is higher than that during the turn-off process. In addition, according to Figs. 15 and 16, the magnitude of the I

_{CM2}spectrum is smaller than that of I

_{CM1}at frequencies lower than 1 MHz. This is because the higher resistance value of Z

_{SHUNT2}relative to that of Z

_{SHUNT1}has a dampening effect on the CM EMI noise.

### V. CM EMI Model Validation

_{D}and Z

_{S}in the CM EMI noise model were determined, as illustrated in Figs. 17 and 18, respectively. The drain-source voltage V

_{DS}and drain current I

_{D}of the GaN HEMTs were measured, as shown in Figs. 13 and 14, respectively. Eq. (3) was then used to calculate the resulting CM current through the GaN HEMT synchronous buck converter. Notably, the CM current was measured considering the shunt impedances, as illustrated in Fig. 20. A comparison between measured and predicted CM currents is presented in Fig. 21.

_{SHUNT1}and Z

_{SHUNT2}were affected by the parasitic parameters in the higher-frequency bands (greater than or equal to 10 MHz). This explained the appearance of a few spikes in the comparison results at frequencies higher than 5 MHz in Fig. 21. However, in general, the proposed CM EMI behavior model was accurate and reliable in predicting the CM EMI current.

### VI. CM EMI Prediction under Different Switching Frequencies

_{D}and Z

_{S}. The maximum deviation was approximately 5 dB in the 300–700 kHz and 1–4 MHz frequency ranges. Notably, the predicted magnitude of the CM current spectrum was higher than the measured magnitude at frequencies lower than 1 MHz owing to the effect of the LISN impedance in the 150 kHz–1 MHz frequency range.

In the process of predicting CM EMI noise, it is inevitable to ignore the contribution of the PCB layout basics, passive devices, active devices, and DSP controller to the EMI. However, the above factors do influence the experimental results.

The parasitic parameters of the two shunt impedances Z

_{SHUNT1}and Z_{SHUNT2}in the high-frequency band inevitably introduce some interference in the calculation of the model parameters.The accuracy of the measurement equipment in the high-frequency range and the interference due to environmental noise affect the experimental results to some extent.