Interleaved Boost Converter with ZVT-ZCT for the Main Switches and ZCS for the Auxiliary Switch

Abstract

A soft-switching interleaved topology is presented herein and applied to the boost converter. The basic operating principle is that the main power switches are turned on at zero voltage and turned off at zero current via the same auxiliary resonant circuit whose switch is turned on from zero current. Furthermore, as compared to the traditional boost converter, the proposed topology has three additional auxiliary diodes, two additional auxiliary capacitors, one additional auxiliary inductor, and one additional auxiliary switch. On the other hand, since the interleaved control is adopted herein, the difference in current between the two phases exists. Hence, the cascaded control is utilized to regulate the output voltage to the desired voltage via the first phase, whereas the current-sharing control, based on half of the input current as the current reference for the second phase, is employed so as to make the load current extracted from the two phases as evenly as possible. In this paper, the effectiveness of the proposed topology and control strategy is demonstrated by some experimental results.

1. Introduction

Generally, the traditional switching power supply operates under hard switching. However, due to the parasitic components, large electromagnetic interference and high switching loss will happen the instant the switch is turned on/off. Accordingly, the soft switching concept is presented [1,2,3,4,5]. Based on an auxiliary inductor connected in series with the switch, this inductor will oscillate with the parasitic capacitor during the turn-off period, and, as soon as the voltage across the parasitic capacitor resonates to zero, the switch will be turned on. This behavior is called zero-voltage switching (ZVS) at turn-on. Moreover, as soon as the current in the auxiliary inductor resonates to zero, the switch will be turned off. This behavior is called zero-current switching (ZCS) at turn-off. However, although the switching loss is reduced based on ZVS or ZCS or both, high resonant voltage stress or high resonant current stress is generated so as to select proper components, thereby increasing the corresponding circuit cost. In addition, since the turn-on and turn-off intervals are determined by the resonant period, the variable-frequency control is chosen so as to stabilize the output voltage, thereby making the filter design difficult.

As seen in the half-resonant drawbacks, the active clamp [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], the zero-voltage transition (ZVT) [21,22,23,24,25,26,27] and the zero-current transition (ZCT) [28,29,30] are presented. As the voltage clamp is applied to the non-isolated power supply, the parasitic inductance of the line and the leakage inductance of the transformer are used as the auxiliary inductance, which will oscillate with the auxiliary capacitance. Via this way, the switch can reach soft switching during the resonant period. As the auxiliary switch is turned off, the current in the auxiliary inductance flows through the input terminals, thereby making the body diode of the main switch turn on, and hence the main switch has soft switching and the energy stored in the auxiliary inductance is transferred to the input terminals. By doing so, the overall efficiency is increased. As the active clamp technique is applied to the non-isolated power converter [31], one auxiliary inductance, one auxiliary capacitance, and one auxiliary switch are used to form a resonant loop, and, during the resonant period, the soft switching of the main switch and auxiliary switch can be achieved. Via this way, the voltage stress on the main switch is reduced in addition to the switching loss. However, the switching frequency is varied according to output load and input voltage, and an auxiliary inductance is inserted in the power path. Consequently, although the soft switching of the main switch can be achieved, the low-pass filter is designed difficultly, and the conduction loss is severe as this converter operates under the half or rated load.

As the ZVT or ZCT technique is applied to the power supply, one auxiliary resonant circuit is connected in parallel with the main switch. Before the main switch is turned on or off, the auxiliary switch is turned on and hence the resonance occurs, forcing the voltage on the main switch or the current in the main switch to be zero. Since the resonance circuit does not locate in the main power path, the conduction loss is reduced and hence the overall efficiency is increased. The literatures [32,33,34] employ ZVT and ZCT simultaneously, so that the switching loss can be reduced and hence the overall efficiency can be enhanced.

On the one hand, in order to upgrade the output current as well as to improve the efficiency, the multiphase converter, along with interleave control, is widely used. The fact that the AC components of the inductor currents for multiple phases are cancelled to some extent makes the output current ripple reduce as well as the frequency of the output current ripple increase. By doing so, the required filter design will be easier and the corresponding size will be smaller. In general, the total loss created from multiple phases will be smaller than that created from a single phase. Accordingly, the multiphase converter with soft switching is presented. The literatures [33,34,35,36] adopt multiple phases with the corresponding number of auxiliary resonance circuits, leading to increasing the number of components to increase conduction loss as well as cost. In the literature [35], the two-phase converter uses the same auxiliary resonant circuit. However, only the ZVS is used, such that the efficiency improvement is limited. In the literature [36], the two-phase converter uses one snubber circuit so as to make the main switches achieve soft switching. However, the resonant inductor locates in the power path, thereby making conduction loss increased.

On the other hand, there are differences in component features and line impedance between the two phases. Consequently, the current-sharing control will be needed. As for current sharing, there are two types of current-sharing control methods. One is passive; the other is active. The former employs capacitors or differential-mode transformers or both to do current sharing [37,38,39,40], whereas the latter contains current regulators and current sensors to balance currents [41,42,43,44,45].

Based on what has been discussed above, a two-phase converter with one resonant inductor, two resonant capacitors, two resonant diodes, one auxiliary diode, one auxiliary switch, and two main switches are proposed. This converter can achieve ZVT and ZCT for the main switches and ZCS for the auxiliary switch, so as to further increase the overall efficiency. In addition, the proposed current-sharing control is adopted herein so that the output voltage is regulated by the first phase and the current sharing between the two phases is controlled by the second phase.

2. Two-Phase Converter with Proposed Soft Switching

In Figure 1, the proposed inductor resonant circuit applied to the two-phase interleaved converter is built up by only one resonant L_r, two resonant capacitors C_r1 and C_r2, two resonant diodes D_r1 and D_r2, one auxiliary switch S_a, and one auxiliary diode D_a.

3. Basic Operating Principles

Prior to the circuit analysis, there are some assumptions as below: (i) all the main switches and diodes are viewed as ideal; (ii) no parasitic resistances exist in the inductor and capacitors; (iii) the ideal input inductor can be considered as current source such that L₁, L₂, and V_in can be removed.; (iv) the ideal output capacitor can be regarded as a voltage source such that C_o and R_o can be removed. Based on the above, the circuit in Figure 2 is an equivalent circuit for Figure 1. In Figure 3, there are twenty-two operating states. Since this converter is controlled by interleave, the behavior of the first eleven states is the same as that of the last eleven states. Therefore, only the first eleven states are described.

State 1: $\left[t_0\le t\le t_1\right]$. As shown in Figure 4, the main switches S₁ and S₂ are turned off but the auxiliary switch S_a is turned on, whereas the freewheeling diodes D₁ and D₂ as well as the resonant diodes D_r1 and D_r2 are turned on. During this state, the resonant inductor L_r is magnetized, and hence the resonant inductor current i_Lr is linearly increased. In addition, the energy required by the load is provided by the current I_L, which is equal to the current I_L1 plus the current I_L2. As soon as i_Lr is equal to I_L, D₁ and D₂ are turned off, and hence this state comes to the end. During this interval, the corresponding state equation can be expressed as follows:

$$i_{Lr}(t)=\frac{V_o}{L_r}(t-t_0)+i_{Lr}(t_0)$$

(1)

As t = t₁, i_Lr(t₁) = I_L, and hence the corresponding time elapsed is as follows:

$$(t_1-t_0)=\frac{[I_L-i_{Lr}(t_0)]L_r}{V_o}$$

(2)

State 2: $\left[t_1\le t\le t_2\right]$. As shown in Figure 5, the main switches S₁ and S₂ are still turned off but the auxiliary switch S_a is still turned on, whereas the freewheeling diodes D₁ and D₂ are turned off but the resonant diodes D_r1 and D_r2 are still turned on. During this state, the parasitic capacitors of S₁ and S₂, called C_S1 and C_S2, resonate with the resonant inductor L_r, thereby making the resonant inductor current i_Lr keep increasing. In addition, the output capacitor C_o provides energy to the load. The moment C_S1 and C_S2 are discharged to zero, the parasitic diodes of the main switches S₁ and S₂, called D_S1 and D_S2, are turned on, and hence this state comes to the end. During this interval, the corresponding state equation can be represented as follows:

$$\{\begin{array}{l}{i}_{Lr}(t)=I_L+\frac{v_S(t_1)}{Z_2}\sin {\omega }_2(t-t_1)-[I_L-i_{Lr}(t_1)]\cos {\omega }_2(t-t_1)\\ \\ v_S(t)=Z_2[I_L-i_{Lr}(t_1)]\sin {\omega }_2(t-t_1)+v_S(t_1)\cos {\omega }_2(t-t_1)\end{array}$$

(3)

where

$${\omega }_2=\sqrt{\frac{1}{L_r{C}_S}},Z_2=\sqrt{\frac{L_r}{C_S}},C_S=C_{S1}+C_{S2}\mathrm{and}{v}_{S1}=v_{S2}=v_S$$

(4)

And hence, the corresponding time elapsed is as follows:

$$(t_2-t_1)=\frac{\pi }{2{\omega }_2}$$

(5)

State 3: $\left[t_2\le t\le t_3\right]$. As shown in Figure 6, the main switches S₁ and S₂ are still turned off but the auxiliary switch S_a is still turned on, whereas the freewheeling diodes D₁ and D₂ are still turned off but the resonant diodes D_r1 and D_r2 are still turned on. During this state, the parasitic diodes of the main switches S₁ and S₂, called D_S1 and D_S2, are turned on, and hence the voltages across S₁ and S₂, called v_s1 and v_s2, are zero. In addition, the output capacitor C_o still provides energy to the load. The instant the auxiliary switch S_a is turned off, S₁ has zero-voltage-transition (ZVT) turn-on and hence this state comes to the end. During this interval, the corresponding state equation can be signified as follows:

$$i_{Lr}(t)=I_L+\frac{V_o}{Z_2}$$

(6)

State 4: $\left[t_3\le t\le t_4\right]$. As shown in Figure 7, the main switch S₁ is turned on but the main switch S₂ is still turned off and the auxiliary switch S_a is turned off, whereas the freewheeling diodes D₁ and D₂ are still turned off but the resonant diodes D_r1 and D_r2 are still turned on. During this state, the current i_S1 begins to increase, and the auxiliary diode D_a is turned on due to S_a being turned off, thereby making the voltage across the resonant inductor L_r change its polarity such that L_r is demagnetized. Once i_S1 = I_L1 and i_Lr = I_L2, the resonant diode D_r1 is turned off, and hence this state comes to the end. During this interval, the corresponding state equation can be represented as follows:

$$i_{Lr}(t)=\frac{-V_o}{L_r}(t-t_3)+I_L+\frac{V_o}{Z_2}$$

(7)

As t = t₄, the corresponding time elapsed is as follows:

$$(t_4-t_3)=\frac{[I_L+\frac{V_o}{Z_2}-i_{Lr}(t_4)]L_r}{V_o}$$

(8)

State 5: $\left[t_4\le t\le t_5\right]$. As shown in Figure 8, the main switch S₁ is still turned on but the main switch S₂ is still turned off and the auxiliary switch S_a is still turned off, whereas the freewheeling diodes D₁ and D₂ are still turned off and the resonant diode D_r1 is turned off but the resonant diode D_r2 is still turned on. During this state, the inductor current I_L2 charges the parasitic capacitor of the main switch S₂, called C_S2, and also charges the resonant capacitor C_r1 in the opposite direction. At the same time, the resonant inductor L_r still keeps demagnetized, and as the resonant current i_Lr is deceased to zero, the voltage across C_S2, called v_S2, is increased to the output voltage V_o and the voltage across C_r1, called v_Cr1, is decreased to −V_o. The moment the auxiliary diode D_a is turned off, the freewheeling diode D₂ is turned on, and hence this state comes to the end. During this interval, the corresponding state equation can be signified as follows:

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{L2}+\frac{v_A(t_4)-V_o}{Z_5}\sin {\omega }_5(t-t_4)-[I_{L2}-i_{Lr}(t_4)]\cos {\omega }_5(t-t_4)\\ \\ v_A(t)=V_o+Z_5[I_{L2}-i_{Lr}(t_4)]\sin {\omega }_5(t-t_4)+[v_A(t_4)-V_o]\cos {\omega }_5(t-t_4)\end{array}$$

(9)

where v_A is the voltage across C_A, and

$$C_A=C_{r1}+C_{S2},{\omega }_5=\sqrt{\frac{1}{L_r{C}_A}}\mathrm{and}{Z}_5=\sqrt{\frac{L_r}{C_A}}$$

(10)

Hence, the corresponding time elapsed is as follows:

$$(t_5-t_4)=\frac{\pi }{2{\omega }_5}$$

(11)

State 6: $\left[t_5\le t\le t_6\right]$. As shown in Figure 9, the main switch S₁ is still turned on but the main switch S₂ is still turned off and the auxiliary switch S_a is still turned off, whereas the freewheeling diode D₁ is still turned off but the freewheeling diode D₂ is turned on but the resonant diode D_r1 is still turned off and the resonant diode D_r2 is turned off. During this state, the operating behavior of this converter is the same as that of the traditional boost converter. The instant D_r2 and S_a are both turned on, this state comes to the end. At the same time, since S_a is connected in series with the resonant inductor L_r, the current flowing through S_a, called i_Sa, is slowly increased from zero, making S_a turned on with zero current switching (ZCS).

State 7: $\left[t_6\le t\le t_7\right]$. As shown in Figure 10, the main switch S₁ is still turned on but the main switch S₂ is still turned off but the auxiliary switch S_a is turned on, whereas the freewheeling diode D₁ is still turned off but the freewheeling diode D₂ is still turned on but the resonant diode D_r1 is still turned off but the resonant diode D_r2 is turned on. During this state, since S_a and D_r2 are turned on, the resonant inductor L_r is to be magnetized. Once i_Lr = I_L2, this state comes to the end. During this interval, the corresponding state equation can be expressed as follows:

$$i_{Lr}(t)=\frac{V_o}{L_r}(t-t_6)+i_{Lr}(t_6)$$

(12)

As t = t₆, i_Lr(t₆) = 0, whereas as t = t₇, i_Lr(t₇) = I_L2. Accordingly, the corresponding time elapsed is

$$(t_7-t_6)=\frac{I_{L2}{L}_r}{V_o}$$

(13)

State 8: $\left[t_7\le t\le t_8\right]$. As shown in Figure 11, the main switch S₁ is still turned on but the main switch S₂ is still turned off but the auxiliary switch S_a is still turned on, whereas the freewheeling diodes D₁ and D₂ are turned off and the resonant diode D_r1 is still turned off but the resonant diode D_r2 is still turned on. During this state, the resonant capacitor C_r1 and the parasitic capacitor C_S2 of the main switch S₂ resonate with the resonant inductor L_r. Therefore, C_S2 is discharged, C_r1 is discharged in the opposite direction, and the resonant inductor remains demagnetized. In addition, the output capacitor C_o provides energy to the load. As soon as the current in S₁ is decreased to zero, S₁ is turned off with zero current transition (ZCT) and hence this state comes to the end. During this interval, the corresponding state equation can be represented as follows:

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{L2}+\frac{v_A(t_7)}{Z_8}\sin {\omega }_8(t-t_7)-[I_{L2}-i_{Lr}(t_7)]\cos {\omega }_8(t-t_7)\\ \\ v_A(t)=Z_8[I_{L2}-i_{Lr}(t_7)]\sin {\omega }_8(t-t_7)+v_A(t_7)\cos {\omega }_8(t-t_7)\end{array}$$

(14)

where

$${\omega }_8=\sqrt{\frac{1}{L_r{C}_A}}\mathrm{and}{Z}_8=\sqrt{\frac{L_r}{C_A}}$$

(15)

Accordingly, the corresponding time elapsed is as follows:

$$(t_8-t_7)=\frac{1}{{\omega }_8}{\sin }^{-1}\left(\frac{\left[i_{Lr}(t_8)-I_{L2}\right]Z_8}{V_o}\right)$$

(16)

State 9: $\left[t_8\le t\le t_9\right]$. As shown in Figure 12, the main switch S₁ is turned off and the main switch S₂ is still turned off and the auxiliary switch S_a is turned off but the auxiliary diode D_a is turned on, whereas the freewheeling diodes D₁ and D₂ are still turned off and the resonant diode D_r1 is still turned off but the resonant diode D_r2 is still turned on. During this state, the resonant capacitor C_r1 is still discharged in the opposite direction, and the input inductor currents I_L1 and I_L2 charge the capacitors C_S1 and C_S2 of the main switches S₁ and S₂, respectively. As soon as C_S2 is charged to V_o, this state comes to the end. During this interval, the corresponding state equation can be expressed as follows:

$$\{\begin{array}{l}{i}_{Lr}(t)=-\frac{V_1}{Z_9}\sin {\omega }_9(t-t_8)-I_1\cos {\omega }_9(t-t_8)+I_1-I_{Lr}(t_8)\\ \\ v_{S1}(t)=-\frac{C}{C_{S1}}\left[V_1\cos {\omega }_9(t-t_8)-I_1{Z}_9\sin {\omega }_9(t-t_8)-V_1\right]\\ \\ +\frac{I_{L1}}{C_r+C_{S1}}(t-t_8)\\ \\ v_{Cr}(t)=\frac{C}{C_r}\left[V_1\cos {\omega }_9(t-t_8)-I_1{Z}_9\sin {\omega }_9(t-t_8)-V_1\right]\\ \\ +\frac{I_{L1}}{C_r+C_{S1}}(t-t_8)+V_{Cr}(t_8)\end{array}$$

(17)

where

$$\begin{array}{l}C=\frac{C_r{C}_{S1}}{C_r+C_{S1}},{\omega }_9=\sqrt{\frac{1}{L_{r}C}}=\sqrt{\frac{C_r+C_{S1}}{L_r{C}_r{C}_{S1}}}\\ \\ Z_9=\sqrt{\frac{L_r}{C}}=\sqrt{\frac{L_r(C_{S1}+C_r)}{C_r{C}_{S1}}}\\ \\ V_1=V_o+V_{Cr}(t_8),I_1=I_{Lr}\frac{C}{C_{S1}}+I_{L2}+I_{Lr}(t_8)\end{array}$$

(18)

State 10: $\left[t_9\le t\le t_{10}\right]$. As shown in Figure 13, the main switch S₁ is still turned off and the main switch S₂ is still turned off and the auxiliary switch S_a is still turned off but the auxiliary diode D_a is still turned on, whereas the freewheeling didoes D₁ is still turned off but the freewheeling diode D₂ is turned on but the resonant diode D_r1 is still turned off but the resonant diode D_r2 is still turned on. During this state, the voltage across the parasitic capacitor C_S2 of the main switch S₂ is the input voltage V_o, making D₂ turned on, the auxiliary capacitor C_r1 is still discharged in the opposite direction, and the parasitic capacitor C_S1 of the main switch S₁ is still charged. Since D₂, D_r2, and D_a are turned on, the voltage across the resonant inductor L_r is zero. The moment C_S1 reaches V_o, the diode D₁ is turned on, and hence this state comes to the end. During this interval, the corresponding state equation can be signified as follows:

$$\{\begin{array}{l}{v}_{S1}(t)=\frac{I_{L1}}{C_{S1}+C_{r1}}t+v_{S1}(t_9)\\ \\ v_{Cr1}(t)=\frac{I_{L1}}{C_{S1}+C_{r1}}t+v_{S1}(t_9)-V_o\end{array}$$

(19)

State 11: $\left[t_{10}\le t\le t_{11}\right]$. As shown in Figure 14, the main switch S₁ is turned still off and the main switch S₂ is still turned off and the auxiliary switch S_a is still turned off but the auxiliary diode D_a is turned on, whereas the freewheeling didoes D₁ is turned on and the freewheeling diode D₂ is still turned on and the resonant diode D_r1 is turned on and the resonant diode D_r2 is still turned on. The instant the auxiliary switch S_a is turned on, this state comes to the end. During this interval, the corresponding state equation can be represented as follows:

$$i_{Lr}(t)=i_{Lr}(t_{10})$$

(20)

As the time interval between t₀ and t₁₁ is finished, the time interval between t₁₁ and t₂₁ begins. In other words, the converter enters into the operating states of the second phase. The corresponding operating states are the same as those of the first phase. Eventually, as the time interval between t₁₁ and t₂₁ is finished, the time comes back to the instant t₀ and the next cycle is repeated.

4. Proposed Control Strategy

Figure 15 shows the proposed control strategy block diagram. First, the output voltage is sensed by a voltage divider with a gain of k. The sensed voltage is sent to the first analog-to-digital converter (ADC1) to obtain the sensed output voltage $V_o^{\prime }$. After this, the error coming from V_ref minus $V_o^{\prime }$ is passed to the controller G_c1(z) so as to generate a control force. The sensed current after ADC2 is subtracted from this control effort. Therefore, a resulting error is created and sent to the controller G_c3(z) so as to yield one pulse-width modulated (PWM) signal after the first PWM generator. This signal will control the main switch of the first phase. On the other hand, the sensed current of the second phase after ADC3, called $I_{L2}^{\prime }$, is subtracted from half of the sum of $I_{L1}^{\prime }$ and $I_{L2}^{\prime }$, and the corresponding error is sent to the controller G_c2(z) to obtain the other PWM signal after the second PWM generator. This PWM signal is shifted by 180 degrees and then used to drive the main switch of the second phase.

The basic operating behavior is described as follows. Since 0.5(I_L1 + I_L2) is used as the current reference for I_L2, the difference between 0.5(I_L1 + I_L2) and I_L2 is 0.5(I_L1 − I_L2) and this value will be sent to the feedback controller such that I_L1 is almost equal to I_L2. On the other hand, I_o1 = (1 − D)I_L1 and I_o2 = (1 − D)I_L2, where D is a duty cycle. Since I_L1 = I_L2 and I_o1 = I_o2 = 0.5I_o, the current sharing will be achieved.

5. Design of the Key Components

The system specifications of the proposed interleaved boost converter with soft switching can be seen in

Table 1. System specifications of the proposed converter.

System Parameters	Specifications
Operating mode	CCM
Input voltage (Vin)	$24\mathrm{V}\pm 10\%$
Output voltage (Vo)	42 V
Rated output current (Io,rated)	6 A
Minimum output current (Io,min)	0.3 A
Switching frequency (fs)	25 kHz

, whereas the components used in this converter can be seen in

Table 2. Components used in the proposed converter.

Components	Specifications
Input Inductor for the first phase (L1)	720 μH
Input Inductor for the second phase (L2)	720 μH
Output capacitor (Co)	680 μF
Resonant inductor (Lr)	6 μH
Resonant capacitor for the first phase (Cr1)	220 μF
Resonant capacitor for the second phase (Cr2)	220 μF

. The design of the key components is based on Table 1.

5.1. Design of L₁ and L₂

The used converter operates in the continuous conduction mode (CCM) all over the input voltage range and the output current range. The worst case for the design of L₁ is under the minimum input voltage and the minimum output current. It is assumed that as the auxiliary switch is turned on, the voltage across each input inductor is not affected by the resonant inductor. Hence, Figure 16 displays the current in L₁ under the discontinuous conduction mode (BCM), whose direct current (DC) value is I_LB1.

Therefore, based on the following equation, the minimum value of the input inductor, called L_1,min, can be figured out as below:

$$L_{1,\mathit{min}}=\frac{V_{in,\mathit{min}}{D}_{\mathit{max}}{T}_s}{2\times 0.5I_{o,\mathit{min}}}=\frac{V_{in,\mathit{min}}{D}_{\mathit{max}}{T}_s}{I_{o,\mathit{min}}}=699.84\mathsf{\mu }\mathrm{H}$$

(21)

Eventually, the value of L₁ is set at 720 μH, which is also for the value of L₂.

5.2. Design of C_o

It is assumed that the voltage ripple is smaller than 0.2% of the output voltage. Since this converter takes a two-phase interleaved structure, the frequency of the output voltage ripple is 50 kHz. Therefore, based on the following equation, the minimum value of the output capacitor, C_o,min, is as follows:

$$C_{o,\mathit{min}}=\frac{0.5I_{o,rated}{D}_{\mathit{max}}\times 0.5T_s}{0.2\%V_o}=\frac{125I_{o,rated}{D}_{\mathit{max}}{T}_s}{V_o}=346.43\mathsf{\mu }\mathrm{F}$$

(22)

Finally, the value of C_o is set at 680 μH.

5.3. Design of L_r, C_r1 and C_r2

For one PWM cycle, before the main switches S₁ and S₂ are turned off, the auxiliary switch S_a has been turned on so that the main switches S₁ and S₂ will have zero-current transition at turn-off. Since the input voltage locates between 21.6 and 26.4 V, the turn-on time of the main switches locates between 15 and 20 μs. It is assumed that the turn-on time of the auxiliary switch S_a is set to 0.1 times of the turn-on time of the main switches, equal to 1.5 and 2 μs. Hence, the turn-on time of S_a is chosen to be 2 μs, which is the sum of the time intervals of [t₆, t₇] and [t₇, t₈]. The resonant current at t₈, called i_Lr(t₈), makes the current flowing through the main switch S₁ zero, causing S₁ to be turned on with ZCT. Since i_Lr(t₈) = I_L1 + I_L2 and t₈ − t₆= 2 μs, based on (13) and (16), the following equation can be obtained as below:

$$(t_8-t_7)+(t_7-t_6)=\frac{1}{{\omega }_8}{\sin }^{-1}\left(\frac{I_{L1}{Z}_8}{V_o}\right)+\frac{I_{L2}{L}_r}{V_o}=2\mathsf{\mu }\mathrm{s}$$

(23)

In addition, it is assumed that the resonant period is set at four times of the turn-on time of S_a.

$$f_r=\frac{1}{2\pi \sqrt{L_r{C}_{r1}}}=125\mathrm{kHz}$$

(24)

From (23) and (24), the value of L_r can be worked out to be 6.7 μH, and the value of C_r1 can be figured out to be 230 μF. Eventually, the value of L_r is set at 6 μH and the value of C_r1 is set at 220 μF, which is also for the value of C_r2.

In addition, the turn-on time of S_a before the main switches S₁ and S₂ are turned on is set at 1 μs, which is half of the turn-on time of S_a before the main switches S₁ and S₂ are turned off.

6. Experimental Results

Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26 and Figure 27 are measured at the rated load. Figure 17 shows the gate driving signals for S₁, S₂ and S_a, called v_g1, v_g2 and v_ga. In addition, v_g1 and v_g2 are almost the same except that the difference in phase between them is 180 degrees, and S_a is turned on before S₁ and S₂ are turned on or off. Figure 18 shows the gate driving signal for S₁, called v_g1, the voltage across S₁, called v_S1, and the current flowing through S₁, called i_S1. Figure 19 is the zoom-in of Figure 18 as S₁ is turned on, whereas Figure 20 is the zoom-in of Figure 18 as S₁ is turned off. Figure 21 shows the gate driving signal for S₂, called v_g2, the voltage across S₂, called v_S2, and the current flowing through S₂, called i_S2. Figure 22 is the zoom-in of Figure 21 as S₂ is turned on, whereas Figure 23 is the zoom-in of Figure 21 as S₂ is turned off. Figure 24 displays the gate driving signal for S_a, called v_ga, the voltage across S_a, called v_Sa, and the current flowing through S_a, called i_Sa. Figure 25 is the zoom-in of Figure 24. In addition, Figure 26 shows the voltage across the resonant capacitor C_r1, called v_Cr1, the voltage across C_r2, called v_Cr2. Figure 27 displays the voltage across S₁, called v_S1, the current in L₁, called i_L1, and the current in L₂, called i_L2.

From Figure 19 and Figure 20, it can be seen that the main switch S₁ has ZVT turn-on and ZCT turn-off, whereas from Figure 22 and Figure 23, it can be seen that the main switch S₂ has ZVT turn-on and ZCT turn-off. From Figure 25, since the auxiliary switch S_a is connected in series with the resonant inductor L_r, thereby making i_Sa increase slowly and hence causing S_a to be turned on with ZCS. From Figure 26, via C_r1, C_r2, and L_r in the resonant loop along with C_S1 and C_S2 of the main switches S₁ and S₂, the soft switching of the main switches for individual phases can be realized. It is noted that due to the diode clamp, C_r1 and C_r2 can be reversely charged to −V_o. From Figure 27, it can be seen that the DC values of i_L1 and i_L2 are almost the same, and i_L2 is shifted from i_L1 by 180 degrees.

On the other hand, Figure 28 shows how to measure the efficiency. First of all, as displayed in Figure 28, the input current I_in is attained by measuring the voltage across the current-sensing resistor according to the digital meter named Fluke 8050 A. Next, the input voltage V_in is obtained also by the digital meter. Therefore, the input power is the product of V_in and I_in. Concerning the output power, the output current I_o is read from the electronic load and the output voltage V_o is attained also by the digital meter. Hence, the output power can be gotten. Eventually, the accompanying efficiency can be attained. Figure 29 displays the curves of efficiency versus load under the input voltage of 24 V. From Figure 29, it can be seen that the converter with the proposed soft switching circuit has higher efficiency than that of the converter without the proposed soft switching circuit. Particularly, the difference in efficiency between with and without the proposed soft switching can be up to about 9%, which occurs at minimum load.

7. Conclusions

A soft switching method is presented herein, which is applied to a two-phase interleaved boost converter. The concept of this method is that the auxiliary switch S_a is turned on before the main switches S₁ and S₂ are turned on/off. By doing so, the ZVT turn-on and ZCT-turn-off of S₁ and S₂ can be achieved, leading to improvement in the overall efficiency. Furthermore, two phases use the same resonant inductor such that the circuit size can be reduced. In addition, S_a is turned on with ZCS due to S_a and L_r being connected in series.