2.1 Mode 1(T0~T1) : Resonant Stage

Fig. 2 shows waveforms of ZCT-PWM boost converter^[14]. Fig. 3 shows equivalent circuit diagrams of each mode. Before Mode 1 starts, the $C_{r}$ is charged with $-V_{Cr}^{peak}$. The first mode of ZCT-PWM begins when S1 turns on. Resonance of the resonant branch starts and the negative voltage charged in $C_{r}$ is discharged. The current of $L_{r}$ is increased. When the resonant current becomes larger than the input current $I_{i}$, the reverse body diodes of $S$ is conducted.

Fig. 2. Waveforms of ZCT-PWM Boost Converter[14]

Fig. 3. Equivalent circuits of each mode

Then, main switch satisfies ZCS condition. The ZCS condition is maintained until T1, when the resonance current becomes smaller than $I_{i}$ again. This is called zero current transition (ZCT). Negative voltage of $C_{r}$ is discharged and becomes zero during $t_{d 1}$. At this time, the resonant current is the maximum. The $t_{d1}$ is quarter of resonance period ($T_{r}=2\pi\sqrt{L_{r}C_{r}}$). Maximum resonant current value can be represented by this equation.

The voltage across the entire resonant tank is zero in this mode.

2.2 Mode 2(T1~T2) : Resonant Stage

Mode 2 starts with $S_{1}$-off and current flows through $D$ and $D_{1}$. The resonant current value of $T_{1}$ ($i_{L_r}(T_{1})$) is always $I_{i}$ in steady state operation. If $i_{L_r}(T_{1})>I_{i}$ , a mode shown in Fig. 4-(a) is added between Mode 2 and Mode 3. This mode reduces the energy stored in the resonant branch. If $i_{L_r}(T_{1})<I_{i}$ , a mode shown Fig. 4-(b) is added between Mode 2 and Mode 3. This mode increases the energy stored in the resonant branch. When these processes are repeated, $i_{L_{r}}(T_{1})$ is always $I_{i}$ in the steady state operation regardless of the load condition. If $V_{C_{r}}^{peak}\le V_{o}$, resonant capacitor’s peak voltage is

$t_{d2}$ is the delay between the turn-off of gate signal of $S$ and $S_{1}$. With $\alpha =2\pi T_{d2}/T_{r}$, resonant inductor’s maximum current is

If $V_{C_{r}}^{peak}\le V_{o}$ is satisfied, ZCT condition is satisfied regardless of input voltage or load current fluctuation. $V_{Cr}^{peak}$ cannot exceed $V_{o}$, since $D_{1}$would conduct during $T_{4}$-$T_{0}$ if $V_{Cr}^{peak}$ exceed $V_{o}$. The voltage across the entire resonant tank voltage is zero in this mode.

Fig. 4. Equivalent circuits of additional mode (a) $i_{L_{r}}(T_{1})>I_{i}$ (b) $i_{L_{r}}(T_{1})<I_{i}$

2.3 Mode 3(T2~T3) : Conventional Boost Stage

After $i_{L_r}=0$ on $T_{2}$, it operates as the power transfer mode of the conventional boost converter. At this mode, the resonance branch doesn’t belong to the main power path. The current through the entire resonant is zero in this mode.

2.4 Mode 4(T3~T4) : Resonant Stage

Mode 4 is for the inductor voltage second balance of $L_{r}$ and the capacitor ampere second balance of $C_{r}$. The current through main switch reaches maximum in this mode. The voltage across the entire resonant tank is zero in this mode.

2.5 Mode 5(T4~T5) : Conventional Boost Stage

Mode 5 starts when the resonance current is 0. This mode operates as the power transfer mode of the conventional boost converter. In this mode, resonant branch doesn’t belong to the main power path and the current through the entire resonant tank is zero.

In steady state operation, energy transfer between resonant branch and main power path is zero, because the voltage or current of the entire resonant tank is zero for each mode. The circulating energy is very small since the resonant stage is very short compared to the QRC. Additionally, there is no voltage ringing phenomenon at turn-off of main switch because the current of the semiconductor device doesn’t change rapidly. Therefore, the voltage stress on the power transistor and the rectifier diode is small. On the other hand, the conduction loss of ZCT-PWM converter is similar to conventional PWM converter because peak current and rms current of ZCT-PWM converter similar to conventional PWM converter.

3.1 Resonant Branch Design

We use Eqs.(1), (2), and (3) to design $L_{r}$ and $C_{r}$ of the resonant branch. In order to use the above equations, $V_{C_{r}}\le V_{o}$ must be satisfied. In the ideal case, the constant input current is used in the above equations, but in practical case, the input side has a small current ripple even if the boost inductor is large. The current at the turn-off of the main switch ($I_{S,\:off}$) is used as $I_{i}$ in practice because the reason for using resonant branch is to solve the problem that occurs when the main switch (IGBT) turns-off. Fig. 5-(a) is a conventional boost converter circuit diagram that uses PSIM software to measure $I_{S,\:off}$. Fig. 5-(b) shows the waveform of the current through main switch $S$ ($i_{S}$) and the gate signal of $S$. Table 1 is the specification of the design. Specification is the same as the target ZCT-PWM converter except the resonant branch.

Simulation shows $I_{S,\:off}=3.62 A$ in conventional boost converter. MATLAB codes were used to obtain $L_{r}$ and $C_{r}$ that satisfy eqs. (2), (3) and $V_{C_{r}}^{peak}\le V_{o}$. 

Fig. 5. 300-W 100 V/200 V conventional boost converter (a) Circuit diagram using PSIM (b) $i_{S}$(red) and gate signal of main switch(blue)

Fig. 6 is a three-dimensional graph with $L_{r},\: C_{r},\: V_{C_{r},\:peak}$ as x,y,z axis. The range of each axis is $1\mu H\le L_{r}\le 100\mu H$, $1 n F\le C_{r}\le 100 n F$, $0\le V_{C_{r},\:peak}\le 200 V$. The reason for $T_{d2}=0.11*T_{r}$ is to make $I_{Lr}^{\max}$ 30 \% larger than $I_{i}$ in equation (3). It is better to design so that $V_{C_{r},\:peak}$ isn’t too large because parasitic inductance or capacitance may cause additional resonance. Also, the smaller the $T_{r}$, the shorter the resonant stage ($t_{d1}+t_{d2}$) and the advantages of ZCT-PWM can be maximized. Considering these conditions, one point in the graph ($6\mu H,\:10 n F,\:115 V$) is selected. $L_{r}$ used $6\mu H,\: 17 turns$ air core inductor to prevent saturation, and $C_{r}$ used $10 n F$ film capacitor.

Fig. 6. Resonant components design (a) MATLAB code for design (b) $L_{r}-C_{r}-V_{C_{r},\:peak}$ 3D graph

3.2 Simulation of 300-W ZCT-PWM Boost Converter

Fig. 7 shows a PSIM model of 300-W ZCT-PWM boost converter. The specifications of the converter are given in Table 2. Fig. 8 is a simulation waveforms. Simulation results show that when the main switch is switched off, the resonant current is larger than the boost inductor current and the reverse current flows through main switch. As a result, the ZCT condition is satisfied.

Fig. 7. PSIM model of 300-W ZCT-PWM boost converter

3.3 Gate Signal of Main Switch and Auxiliary Switch Using DSP

To operate ZCT-PWM boost converter, the 50\% duty, 100 kHz main switch gate signal and 100 kHz auxiliary switch gate signal which is turned on by $t_{d1}$ before turn-off of main switch and turned off $t_{d2}$ later than the turn-off of the main switch are required. The algorithm for the implementation of the auxiliary switch gate signal is Fig. 9. The ‘ePWM1’ provides the gate signal to the main switch, the ‘ePWM2’ provides the gate signal to the auxiliary switch. At the algorithm, ePWM1_CMPB = $(t_{S,\:on}-t_{d1})\times TBCLK$ and $t_{S,\:on}$ is the length of the time which the main switch is on state. If the TBCTR of ePWM1 equals ePWM1_CMPB, a synchronization signal is sent to the lower ePWM module(ePWM2). When the synchronization signal is arrived, TBCTR of ePWM2 is initialized to 0, and the output of ePWM2 becomes high. And if the TBCTR of ePWM2 equals to ePWM2_CMPA(=$(t_{d1}+t_{d2})\times TBCLK$), the output of ePWM2 becomes low. Using the resonant period $T_{r}$ of the resonant branch designed in this paper, $t_{d1}=385ns,\: t_{d2}=169ns$.

Fig. 8. Simulation results of 300-W ZCT-PWM boost converter

The output of the DSP is connected to the switch through the gate driver. The gate driver is configured using IXDD404, which is capable of 2-input/2-output. The boost converter's main switch is adjacent to the ground. Therefore, isolation transformer is not needed for the gate driver.

Fig. 9. ZCT-PWM gate signal

Fig. 10. Gate Signal Algorithm

Fig. 11 are the gate signal waveform obtained from actual experiments. The blue waveform is gate signal of main switch and the red waveform is gate signal of auxiliary switch. Fig. 11-(a) shows that experimental switching frequency is 100 kHz. Fig. 11-(b) shows that experimental $t_{d1}=390ns$ and Fig. 11-(c) shows that experimental $t_{d2}=160ns$. The difference between the design values and experimental values of $t_{d1}$ and $t_{d2}$ is negligible.

Fig. 11. Experimental waveforms of gate signal

3.4 Experimental Results

Applying the designed parameter examined through the simulation, 300-W ZCT-PWM boost converter was implemented. Fig. 12 is the entire experimental system : Converter, DSP board, SMPS, and Load resistor. SMPS was used to power DSP board and gate driver.

Fig. 13 is the experimental waveform that shows gate signal of main switch, auxiliary switch, boost inductor current, and resonant current. As designed, it can be seen that the resonant current is greater than the boost inductor current when the main switch is turned off. Therefore IGBT’s ZCT condition is satisfied.

Fig. 12. Entire experimental system

Fig. 13. Experimental waveform