Simple Structure of Soft Switching for Boost Converter

Abstract

A soft switching boost converter, with a small number of components and constant frequency control, is proposed herein by using the quasi-resonance method and the zero-voltage-transition method, realizing (1) the zero-voltage switching during the switch-on transient of the main switch, (2) the zero-current switching during the switch-off transient of the main switch, (3) the zero-current switching during the switch-on transient of the auxiliary switch, and (4) the zero-current switching during the switch-off transient of the auxiliary switch. Accordingly, the corresponding efficiency can be improved. The feasibility and effectiveness of the proposed structure are validated by the field programmable gate array (FPGA).

1. Introduction

As generally recognized, the switching power supply, which can operate at high frequency, has the advantages of small size, light weight, high efficiency, large voltage input range, etc. Switching power electronic converters can be roughly classified into the following three types: (a) traditional pulse-width modulation (PWM) power electronic converters; (b) resonant power electronic converters; (c) soft switching power electronic converter.

1.1. Traditional PWM Power Electronic Converter

As far as the traditional PWM power electronic converter is concerned, the PWM control technology is employed to control the on and off time of the power switch to realize the purpose of output voltage boosting or bucking. By increasing the switching frequency, the size of the inductor and capacitor can be reduced. In addition, when the power switch is operated in the on or off region, theoretically the power loss of the power switch is almost zero. However, due to the parasitic components in the circuit, when the power switch is switched, the voltage on the switch or the current in the switch is not zero momentarily, resulting in additional switching loss. This switching method is called hard switching. Therefore, in order to miniaturize the magnetic components and electrolytic capacitors, the switching frequency required for the converter should go up. However, when the switching frequency increases, the switching loss of the power switch during switch on and switch off will also increase. In addition to causing energy loss, it will also increase the heat sink required by the power switch, increasing the volume. Furthermore, when the switch is switched, the parasitic components of the circuit are prone to generate voltage surges or current surges or both, and this not only increases the stresses of the circuit components but also is a source of electromagnetic interference (EMI), which will interfere with the normal action of the control circuit.

1.2. Resonant Power Electronic Converter

Based on the foregoing, we can see that since the switching of the traditional PWM power electronic converter belongs to hard switching, serious switching losses are caused, and the efficiency cannot be improved. Resonant power electronic converters are the traditional PWM power electronic converters with inductor and switch connected in series or capacitor and switch connected in parallel to form a resonant circuit, so that the current or voltage on the power switch becomes a sine wave, reducing the overlap area of the current and voltage waveforms during the switching transient. Hence, reducing power loss leads to increasing the efficiency of the converter. This type of power electronic converter can be divided into: (1) traditional resonant converter (RC) [1,2,3]; (2) resonant-switch converter [4,5,6].

1.2.1. Traditional Resonant Converter (RC)

Traditional resonant converters are also called load-resonant converters. This converter includes an inductance-capacitance (LC) resonant tank. The resonant tank is in series or parallel with the load terminal, and the resonant components participate in the whole process of converter energy conversion. Using the resonant voltage or current generated by the resonance tank achieves zero-voltage switching (ZVS) or zero-current switching (ZCS). The power required by the load can be adjusted by the resonant tank circuit.

1.2.2. Resonant-Switch Converter

Resonant-switch power electronic converters only utilize resonant components to create resonance when the switch is switched to provide the voltage or current required for zero switching of the switch. The resonant energy only partially participates in the energy conversion process of the converter. Such a converter is called a quasi-resonant converter (QRC) and can be divided into zero-current-switching quasi-resonant converter (ZCS-QRC) and zero-voltage-switching quasi-resonant converter (ZVS-QRC).

1.3. Soft Switching Power Electronic Converter

The soft switching power converter uses auxiliary switches and resonant components to act, so that the main power switch resonates only at the moment of switching. Because resonance only occurs the moment the main power switch is switched, no resonance occurs during the rest of the time and hence constant frequency control can be realized. Soft switching power electronic converters can be classified into the following three types: (1) ZCS/ZVS PWM power converter; (2) zero-voltage transition (ZVT)/zero-current transition (ZCT) power converter; (3) ZCZVT power converter. Their characteristics are as follows.

1.3.1. ZCS/ZVS PWM Power Converter

Adding an auxiliary switch to the quasi-resonant circuit and using the auxiliary switch to control when the resonance works make the resonance pause for a period of time adjustable, and this improves the shortcomings of fixed on or off time of quasi-resonant power converters [7,8,9,10]. That is, the resonance time can be controlled by the auxiliary switch without changing the switching frequency so that constant frequency control can be realized. However, the components should endure high voltage or current stress due to resonance, thereby causing serious conduction loss.

1.3.2. ZVT/ZCT Power Converter

Placing the resonance element on the non-main energy transmission path reduces conduction loss [11,12,13]. Prior to the main switch being switched on, the auxiliary switch is switched on to form a resonant circuit, which generates transient resonance, so that the voltage on or current in the main switch resonates to zero and then this switch is switched. When the auxiliary switch is not switched, the converter does not resonate and will not cause high voltage or high current stress. Therefore, the conduction loss can be reduced. In addition, constant frequency control can be used, and hence the filter design is easy. However, ZVT converter can only achieve zero-voltage switching, whereas ZCT converter can only achieve zero-current switching.

1.3.3. ZCZVT Power Converter

As the main switch is switched to the pre-transient state of the switch on and the post-transient state of the switch off, respectively, the auxiliary switch will be turned on first to form a resonant circuit, so that the voltage on and current in the main switch resonate to zero, achieving zero-voltage switching and zero-current switching [14,15,16,17]. Therefore, the main switch has both functions of ZVT and ZCT. Over one switching cycle, a total of two transient resonances occurs, and these two transient resonances only occupy a small proportion of the entire switching cycle. As the auxiliary switch does not operate, the ZCZVT power converter acts like a traditional PWM power electronic converter. That is, this soft switching method can reduce component stress and conduction loss, and such a converter can be controlled by a constant frequency. Although this converter can reach ZVT and ZCT, the auxiliary switch over one switching cycle should produce two transient resonances, so the circuit design is complicated and there are many components, resulting in cost increase.

In order to realize the zero-voltage or zero-current switching of the main switch, the above-mentioned individual structures can be adopted, depending on the situation. However, the general soft switching power electronic converter requires additional complex auxiliary circuits, which increases the number of components [7]. Moreover, most of the auxiliary switches of soft switching power electronic converters are floating, and this increases the complexity of the circuit design [14]. In summary, although the general soft switching power electronic converter can increase the switching frequency, reduce electromagnetic interference (EMI), and reduce the component stress of the switch, the addition of too many components can tend to lead to higher cost, larger volume and inability to effectively improve efficiency.

Based on the mention above, this paper presents a soft switching boost converter, with a small number of components and constant frequency control by using the QR method and the ZVT method, to achieve the zero-voltage switching during the switch-on transient of the main switch and the zero-current switching during the switch-off transient of the main switch as well as to achieve the zero-current switching during the switch-on transient of the auxiliary switch and the zero-current switching during the switch-off transient of the auxiliary switch.

2. Proposed Circuit

Figure 1 displays the proposed soft switching boost converter, which is constructed by one traditional boost converter along with one auxiliary switch module. The former is constructed by one input inductor L_in, one main switch S₁ along with one body diode D₁, one output diode D_o, and one output capacitor C_o. The latter is established by one auxiliary switch S₂ along with one body diode D₂, one resonant diode D_r, one resonant inductor L_r, one resonant capacitor C_r. The output load is represented by one resistor R_L.

3. Basic Operating Principles

The behavior of the proposed converter with soft switching will be described as follows. Prior to this, the symbols and assumptions relevant to this circuit shown in Figure 1 will be given: (i) V_in is the DC input voltage; (ii) i_Lr is the current flowing through L_r; (iii) v_Cr is the voltage imposed on C_r; and (iv) all the components are ideal except that the switches have individual body diodes. There are nine states in the converter operating, as shown in Figure 2. In the following description, ω_r and Z_r are called resonant radian frequency and characteristic impedance, respectively, and are equal to

$${\omega }_r=\frac{1}{\sqrt{L_r{C}_r}}\mathrm{and}{Z}_r=\sqrt{\frac{L_r}{C_r}}$$

(1)

3.1. State 0

As displayed in Figure 2 ($t\le t_0$) and Figure 3a, both of S₁ and S₂ are in the off state. Before S₂ is switched on, the current I_in will flow through D_o. In this time interval, the voltage imposed on C_r is the voltage V_o. Once S₂ is switched on, the operation proceeds to state 1. Two state equations for state 0 is

$$\{\begin{array}{l}{i}_{Lr}(t)=0\\ v_{Cr}(t)=V_o\end{array}$$

(2)

3.2. State 1

As displayed in Figure 2 $(t_0\le t\le t_1)$ and Figure 4a, S₁ is still in the off state, but S₂ is switched on with the current going up from zero and D_r conducted. Hence, S₂ has ZCS switch on. During the initial switch-on transient of S₂, the diode D_o is still in the on state, the current i_Lr is linearly increased. Before i_Lr increases to the current I_in, the voltage v_Cr is kept constant at V_o. As soon as i_Lr increases to I_in, the diode D_o is turned off, proceeding to state 2. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_0)=0\\ v_{Cr}(t_0)=V_o\end{array}$$

(3)

Based on Figure 4b, one state equation can be obtained to be

$$i_{Lr}(t)=i_{Lr}(t_o)+\frac{1}{L_r}{\displaystyle {\int }_{t0}^t{V}_{o}dt}=i_{Lr}(t_o)+\frac{V_o}{L_r}(t-t_0)$$

(4)

Substituting (3) into (4) yields

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

(5)

Since i_Lr(t₁) = I_in, we can obtain the corresponding time elapsed from (5) as

$$(t_1-t_0)=\frac{I_{in}{L}_r}{V_o}$$

(6)

3.3. State 2

As displayed in Figure 2 $(t_1\le t\le t_2)$ and Figure 5a, S₁ is still in the off state but S₂ is still in the on state. Since S₂ keeps conducting, L_r keeps resonating with C_r. In this time interval, the energy stored in C_r is passed to L_r, thereby making v_Cr decreased. The moment v_Cr decreases to zero, the operation goes to state 3. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_1)=I_{in}\\ v_{C}r(t_1)=V_o\end{array}$$

(7)

Based on Figure 5b, two state equations can be obtained to be

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-i_{Cr}(t)=I_{in}-C_r\frac{d{v}_{Cr}(t)}{dt}\\ v_{Cr}(t)=v_{Lr}(t)=L_r\frac{d{i}_{Lr}(t)}{dt}\end{array}$$

(8)

By applying the Laplace transform to (8), we can obtain

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{I_{in}}{s}-C_r\left[s{V}_{Cr}(s)-v_{Cr}(t_1)\right]=\frac{I_{in}}{s}-s{C}_r{V}_{Cr}(s)+C_r{v}_{Cr}(t_1)\\ V_{Cr}(s)=s{L}_r{I}_{Lr}(s)-i_{Lr}(t_1)L_r\end{array}$$

(9)

Therefore, we can obtain the solution of (9) as

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{\frac{I_{in}}{s{C}_r{L}_r}}{s^2+{\omega }_r{}^2}+\frac{s{i}_{Lr}(t_1)}{s^2+{\omega }_r{}^2}+\frac{\frac{v_{Cr}(t_1)}{L_r}}{s^2+{\omega }_r{}^2}\\ V_{Cr}\left(s\right)=\frac{\frac{I_{in}}{C_r}}{s^2+{\omega }_r{}^2}+\frac{s{v}_{Cr}(t_1)}{s^2+{\omega }_r{}^2}-\frac{\frac{i_{Lr}(t_1)}{C_r}}{s^2+{\omega }_r{}^2}\end{array}$$

(10)

By applying the inverse Laplace transform to (10), we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_1)+i_{Lr}(t_1)\cos {\omega }_r(t-t_1)+\frac{v_{Cr}(t_1)}{Z_r}\sin {\omega }_r(t-t_1)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_1)+v_{Cr}(t_1)\cos {\omega }_r(t-t_1)-i_{Lr}(t_1)Z_r\sin {\omega }_r(t-t_1)\end{array}$$

(11)

Substituting (7) into (11) yields

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}+\frac{V_o}{Z_r}\sin {\omega }_r(t-t_1)\\ v_{Cr}(t)=V_o\cos {\omega }_r(t-t_1)\end{array}$$

(12)

Since $i_{Lr}(t_2)=I_{in}+\frac{V_o}{Z_r}$, we can obtain the corresponding time elapsed from (12) as

$$(t_2-t_1)={\sin }^{-1}\frac{1}{{\omega }_r}$$

(13)

3.4. State 3

As displayed in Figure 2 $(t_2\le t\le t_3)$ and Figure 6a, S₁ is still in the off state, but S₂ is still in the on state. In this time interval, L_r still resonates with C_r. Once i_Lr drops to zero, S₁ is switched on but S₂ is switched off with ZCS, the operation proceeds to state 4. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_2)=I_{in}+\frac{V_o}{Z_r}\\ v_{Cr}(t_2)=0\end{array}$$

(14)

Based on Figure 6b, two state equations can be obtained to be

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-i_{Cr}(t)=I_{in}-C_r\frac{d{v}_{Cr}(t)}{dt}\\ v_{Cr}(t)=v_{Lr}(t)=L_r\frac{d{i}_{Lr}(t)}{dt}\end{array}$$

(15)

By applying the Laplace transform to (15), we can obtain

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{I_{in}}{s}-C_r\left[s{V}_{Cr}(s)-v_{Cr}(t_2)\right]=\frac{I_{in}}{s}-s{C}_r{V}_{Cr}(s)+C_r{v}_{Cr}(t_2)\\ V_{Cr}(s)=s{L}_r{I}_{Lr}(s)-i_{Lr}(t_2)L_r\end{array}$$

(16)

Therefore, we can obtain the solution of (16) as

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{\frac{I_{in}}{s{C}_r{L}_r}}{s^2+{\omega }_r{}^2}+\frac{s{i}_{Lr}(t_2)}{s^2+{\omega }_r{}^2}+\frac{\frac{v_{Cr}(t_2)}{L_r}}{s^2+{\omega }_r{}^2}\\ V_{Cr}\left(s\right)=\frac{\frac{I_{in}}{C_r}}{s^2+{\omega }_r{}^2}+\frac{s{v}_{Cr}(t_2)}{s^2+{\omega }_r{}^2}-\frac{\frac{i_{Lr}(t_2)}{C_r}}{s^2+{\omega }_r{}^2}\end{array}$$

(17)

By applying the inverse Laplace transform to (17), we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_2)+i_{Lr}(t_2)\cos {\omega }_r(t-t_2)+\frac{v_{Cr}(t_2)}{Z_r}\sin {\omega }_r(t-t_2)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_2)+v_{Cr}(t_2)\cos {\omega }_r(t-t_2)-i_{Lr}(t_2)Z_r\sin {\omega }_r(t-t_2)\end{array}$$

(18)

Substituting (14) into (18) yields

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}+\frac{V_o}{Z_r}\cos {\omega }_r(t-t_2)\\ v_{Cr}(t)=-\frac{V_o}{Z_r}\sin {\omega }_r(t-t_2)\end{array}$$

(19)

Since $i_{Lr}(t_3)=0$, we can obtain the corresponding time elapsed from (19) as

$$(t_3-t_2)={\cos }^{-1}\frac{(-I_{in}\frac{Z_r}{V_o})}{{\omega }_r}$$

(20)

3.5. State 4

As displayed in Figure 2 $(t_3\le t\le t_4)$ and Figure 7a, S₁ is switched on, but S₂ is switched off. Since the voltage on S₁ is clamped at zero in state 3, S₁ is switched on with ZVS. In this time interval, i_Lr is negative with a peak value of I_in − V_o/Z_r. Once i_Lr is zero again, the operation moves to state 5. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_3)=0\\ v_{Cr}(t_3)=-\frac{V_o}{Z_r}\sin {\omega }_r(t_3-t_2)\end{array}$$

(21)

Based on Figure 7b, two state equations can be obtained to be

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-i_{Cr}(t)=I_{in}-C_r\frac{d{v}_{Cr}(t)}{dt}\\ v_{Cr}(t)=v_{Lr}(t)=L_r\frac{d{i}_{Lr}(t)}{dt}\end{array}$$

(22)

By applying the Laplace transform to (22), we can obtain

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{I_{in}}{s}-C_r\left[s{V}_{Cr}(s)-v_{Cr}(t_3)\right]=\frac{I_{in}}{s}-s{C}_r{V}_{Cr}(s)+C_r{v}_{Cr}(t_3)\\ V_{Cr}(s)=s{L}_r{I}_{Lr}(s)-i_{Lr}(t_3)L_r\end{array}$$

(23)

Therefore, we can obtain the solution of (23) as

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{\frac{I_{in}}{s{C}_r{L}_r}}{s^2+{\omega }_r{}^2}+\frac{s{i}_{Lr}(t_3)}{s^2+{\omega }_r{}^2}+\frac{\frac{v_{Cr}(t_3)}{L_r}}{s^2+{\omega }_r{}^2}\\ V_{Cr}(s)=\frac{\frac{I_{in}}{C_r}}{s^2+{\omega }_r{}^2}+\frac{s{v}_{Cr}(t_3)}{s^2+{\omega }_r{}^2}-\frac{\frac{i_{Lr}(t_3)}{C_r}}{s^2+{\omega }_r{}^2}\end{array}$$

(24)

By applying the inverse Laplace transform to (24), we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_3)+i_{Lr}(t_3)\cos {\omega }_r(t-t_3)+\frac{v_{Cr}(t_3)}{Z_r}\sin {\omega }_r(t-t_3)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_3)+v_{Cr}(t_3)\cos {\omega }_r(t-t_3)-i_{Lr}(t_3)Z_r\sin {\omega }_r(t-t_3)\end{array}$$

(25)

Substituting (21) into (25) yields

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_3)+\frac{v_{Cr}(t_3)}{Z_r}\sin {\omega }_r(t-t_3)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_3)+v_{Cr}(t_3)\cos {\omega }_r(t-t_3)\end{array}$$

(26)

Since $i_{Lr}(t_4)=0$ and $v_{Cr}(t_4)=-V_o$, we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t_4)=I_{in}-I_{in}\cos {\omega }_r(t_4-t_3)+\frac{v_{Cr}(t_3)}{Z_r}\sin {\omega }_r(t_4-t_3)=0\\ v_{Cr}(t_4)=I_{in}{Z}_r\sin {\omega }_r(t_4-t_3)+v_{Cr}(t_3)\cos {\omega }_r(t_4-t_3)=-V_o\end{array}$$

(27)

Therefore, we can obtain the corresponding time elapsed from (27) as

$$(t_4-t_3)={\sin }^{-1}\frac{\left(\frac{-V_o-v_{Cr}(t_3)}{I_{in}{Z}_r+\frac{v_{Cr}^2(t_3)}{Z_r{I}_{in}}}\right)}{{\omega }_r}$$

(28)

3.6. State 5

As displayed in Figure 2 $(t_4\le t\le t_5)$ and Figure 8a, S₁ is still in the on state, but S₂ is still in the off state. In this time interval, v_Cr resonates to V_o and then keeps constant at V_o. The current I_in flows into L_r, causing i_Lr to be linearly increased. As soon as i_Lr rises to I_in, the operation moves to state 6. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_4)=0\\ v_{Cr}(t_4)=-V_o\end{array}$$

(29)

Based on Figure 8b, one state equation can be obtained to be

$$i_{Lr}(t)=i_{Lr}(t_4)+\frac{1}{L_r}{\displaystyle {\int }_{t_4}^t{V}_{o}dt=i_{Lr}(t_4)+\frac{V_o}{L_r}(t-t_4)}$$

(30)

Substituting (29) into (30) yields

$$i_{Lr}(t)=\frac{V_o}{L_r}(t-t_4)$$

(31)

Since $i_{Lr}(t_5)=I_{in}$, we can obtain the corresponding time elapsed from (31) as

$$(t_5-t_4)=\frac{I_{in}{L}_r}{V_o}$$

(32)

3.7. State 6

As displayed in Figure 2 $(t_5\le t\le t_6)$ and Figure 9a, S₁ is still in the on state, but S₂ is still in the off state. In this time interval, C_r resonates with L_r. The capacitor C_r transfers energy to L_r. That is, v_Cr begins to fall and i_Lr resonantly rises. Once v_Cr decreases to zero, the operation goes to state 7. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_5)=I_{in}\\ v_{Cr}(t_5)=V_o\end{array}$$

(33)

Based on Figure 9b, two state equations can be obtained to be

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-i_{Cr}(t)=I_{in}-C_r\frac{d{v}_{Cr}(t)}{dt}\\ v_{Cr}(t)=v_{Lr}(t)=L_r\frac{d{i}_{Lr}(t)}{dt}\end{array}$$

(34)

By applying the Laplace transform to (34), we can obtain

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{I_{in}}{s}-C_r\left[s{V}_{Cr}(s)-v_{Cr}(t_5)\right]=\frac{I_{in}}{s}-s{C}_r{V}_{Cr}(s)+C_r{v}_{Cr}(t_5)\\ V_{Cr}(s)=s{L}_r{I}_{Lr}(s)-i_{Lr}(t_5)L_r\end{array}$$

(35)

Therefore, we can obtain the solution of (35) as

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{\frac{I_{in}}{s{C}_r{L}_r}}{s^2+{\omega }_r{}^2}+\frac{s{i}_{Lr}(t_5)}{s^2+{\omega }_r{}^2}+\frac{\frac{v_{Cr}(t_5)}{L_r}}{s^2+{\omega }_r{}^2}\\ V_{Cr}\left(s\right)=\frac{\frac{I_{in}}{C_r}}{s^2+{\omega }_r{}^2}+\frac{s{v}_{Cr}(t_5)}{s^2+{\omega }_r{}^2}-\frac{\frac{i_{Lr}(t_5)}{C_r}}{s^2+{\omega }_r{}^2}\end{array}$$

(36)

By applying the inverse Laplace transform to (36), we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_5)+i_{Lr}(t_5)\cos {\omega }_r(t-t_5)+\frac{v_{Cr}(t_5)}{Z_r}\sin {\omega }_r(t-t_5)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_5)+v_{Cr}(t_5)\cos {\omega }_r(t-t_5)-i_{Lr}(t_5)Z_r\sin {\omega }_r(t-t_5)\end{array}$$

(37)

Substituting (33) to (37) yields

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}+\frac{V_o}{Z_r}\sin {\omega }_r(t-t_5)\\ v_{Cr}(t)=V_o\cos {\omega }_r(t-t_5)\end{array}$$

(38)

Since $i_{Lr}(t_6)=I_{in}+\frac{V_o}{Z_r}$, we can obtain the corresponding time elapsed from (38) as

$$(t_6-t_5)={\sin }^{-1}\frac{1}{{\omega }_r}$$

(39)

3.8. State 7

As displayed in Figure 2 $(t_6\le t\le t_7)$ and Figure 10a, S₁ is still in the on state, but S₂ is still in the off state. In this time interval, L_r still resonates with C_r. As i_Lr drops to zero, S₁ is switched off with ZCS. Once S₁ is switched off, the operation proceeds to state 8. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_6)=I_{in}+\frac{V_o}{Z_r}\\ v_{Cr}(t_6)=0\end{array}$$

(40)

Based on Figure 10b, two state equations can be obtained to be

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-i_{Cr}(t)=I_{in}-C_r\frac{d{v}_{Cr}(t)}{dt}\\ v_{Cr}(t)=v_{Lr}(t)=L_r\frac{d{i}_{Lr}(t)}{dt}\end{array}$$

(41)

By applying the Laplace transform to (41), we can obtain

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{I_{in}}{s}-C_r\left[s{V}_{Cr}(s)-v_{Cr}(t_6)\right]=\frac{I_{in}}{s}-s{C}_r{V}_{Cr}(s)+C_r{v}_{Cr}(t_6)\\ V_{Cr}(s)=s{L}_r{I}_{Lr}(s)-i_{Lr}(t_6)L_r\end{array}$$

(42)

Therefore, we can obtain the solution of (42) as

$$\{\begin{array}{l}{I}_{Lr}(s)=\frac{\frac{I_{in}}{s{C}_r{L}_r}}{s^2+{\omega }^2}+\frac{s{i}_{Lr}(t_6)}{s^2+{\omega }^2}+\frac{\frac{v_{Cr}(t_6)}{L_r}}{s^2+{\omega }^2}\\ V_{Cr}\left(s\right)=\frac{\frac{I_{in}}{C_r}}{s^2+{\omega }_r{}^2}+\frac{s{v}_{Cr}(t_6)}{s^2+{\omega }_r{}^2}-\frac{\frac{i_{Lr}(t_6)}{C_r}}{s^2+{\omega }_r{}^2}\end{array}$$

(43)

By applying the inverse Laplace transform to (43), we can obtain

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}-I_{in}\cos {\omega }_r(t-t_6)+i_{Lr}(t_6)\cos {\omega }_r(t-t_6)+\frac{v_{Cr}(t_6)}{Z_r}\sin {\omega }_r(t-t_6)\\ v_{Cr}(t)=I_{in}{Z}_r\sin {\omega }_r(t-t_6)+v_{Cr}(t_6)\cos {\omega }_r(t-t_6)-i_{Lr}(t_6)Z_r\sin {\omega }_r(t-t_6)\end{array}$$

(44)

Substituting (40) to (44) yields

$$\{\begin{array}{l}{i}_{Lr}(t)=I_{in}+\frac{V_o}{Z_r}\cos {\omega }_r(t-t_6)\\ v_{Cr}(t)=-\frac{V_o}{Z_r}\sin {\omega }_r(t-t_6)\end{array}$$

(45)

Since $i_{Lr}(t_5)=I_{in}$, we can obtain the corresponding time elapsed from (45) as

$$(t_7-t_6)={\cos }^{-1}\frac{(-I_{in}\frac{Z_r}{V_o})}{{\omega }_r}$$

(46)

3.9. State 8

As displayed in Figure 2 $(t_7\le t\le t_8)$ and Figure 11a, S₁ is switched off, and S₂ is still in the off state. During this state, the resonant behavior stops. i_Lr is kept constant at zero. C_r is charged by I_in, thereby making v_Cr increased. The moment v_Cr increases to V_o, the diode D_o is conducted, and the operation moves to state 0 with the next cycle repeated. The time elapsed is derived below.

The initial values of this state are

$$\{\begin{array}{l}{i}_{Lr}(t_7)=0\\ v_{Cr}(t_7)=-\frac{V_o}{Z_r}\sin {\omega }_r(t_7-t_6)\end{array}$$

(47)

Based on Figure 11b, one state equation can be obtained to be

$$v_{Cr}(t)=v_{Cr}(t_7)+\frac{1}{C_r}{\displaystyle {\int }_{t_7}^t{I}_{in}dt=}{v}_{Cr}(t_7)+\frac{I_{in}}{C_r}(t-t_7)$$

(48)

Substituting (47) to (48) yields

$$v_{Cr}(t)=-\frac{V_o}{Z_r}\sin {\omega }_r(t_7-t_6)+\frac{I_{in}}{C_r}(t-t_7)$$

(49)

Since $v_{Cr}(t_8)=V_o$, we can obtain the corresponding time elapsed from (49) as

$$(t_8-t_7)=\frac{C_r\left[V_o+\frac{V_o}{Z_r}\sin {\omega }_r(t_7-t_6)\right]}{I_{in}}$$

(50)

4. Design Considerations

Table 1. System and specifications (CCM: continuous conduction mode).

Operation Mode	CCM
Input Voltage (Vin)	24 V
Switching Frequency (fs)/Switching Period (Ts)	250 kHz/4 μs
Output Voltage (Vo)	48 V
Rated Output Current (Io,rated)	2.5 A
Minimum Output Current (Io,min)	0.25 A
Ideal Duty Cycle (D)	0.5
Main Switch (S1)	IRF540
Auxiliary Switch (S2)	IRF540
Output Diode (Do)	DSSK10
Resonant Diode (Dr)	DSSK40-015B

shows the system specifications. Based on Table 1, and Section 2, the input inductor L_in, the output capacitor C_o, the resonant capacitor C_r, and the resonant L_r will be figured out.

4.1. Design for L_in

As this converter works in the continuous conduction mode (CCM) above I_o,min, the following equation is used to find the minimum input inductor L_in,min [12], based on Table 1:

$$L_{in,\min }=\frac{V_{in}D{T}_s}{2I_{o,\min }}=\frac{24\times 0.5\times 4\mathsf{\mu }}{2\times 0.25}=96\mathsf{\mu }\mathrm{H}$$

(51)

Eventually, L_in is selected as 100 μH so as to make sure that such a converter works in CCM.

4.2. Design for C_o

By assuming that the output ripple voltage is lower than 0.1%, the following equation is used to find the minimum output capacitor C_o,min, based on Table 1:

$$C_{o,\min }=\frac{I_{o,rated}D{T}_s}{\Delta V_o}=\frac{5\times 0.5\times 4\mathsf{\mu }}{0.048}=208\mathsf{\mu }\mathrm{F}$$

(52)

Finally, C_o is selected as 220 μF.

4.3. Design for L_r

By assuming that there are two resonant cycles per one half of the PWM period and no resonant cycles per the other half of the PWM period, and the time elapsed for state 1 is the fifth of the resonant period, the value of L_r can be worked out as follows:

$$\begin{array}{l}(t_1-t_0)=\frac{I_{in,rated}{L}_r}{V_o}=\frac{I_{o,rated}{L}_r}{V_o(1-D)}=\frac{1}{250\times {10}^3\times 4}\times \frac{1}{5}=200\mathrm{ns}\\ \Rightarrow L_r=\frac{200\mathrm{n}\times V_o(1-D)}{I_{o,rated}}=\frac{200\mathrm{n}\times 48\times (1-0.5)}{2.5}=1.92\mathsf{\mu }\mathrm{H}\end{array}$$

(53)

Finally, L_r is selected as 2 μH.

4.4. Design for C_r

In state 2, v_Cr(t₁) = V_o and i_Lr(t₁) = I_in. In order to make sure that the resonant behavior will happen, the following inequality should be obeyed:

$$\begin{array}{l}\frac{1}{2}{C}_r{V}_o^2\ge \frac{1}{2}{L}_r{I}_{{}_{in,rated}}^2\\ \Rightarrow C_{r,\min }=\frac{L_r{I}_{{}_{in,rated}}^2}{V_o^2}=\frac{L_r{I}_{{}_{o,rated}}^2}{V_o^2{(1-D)}^2}=\frac{2\mathsf{\mu }\times {2.5}^2}{{48}^2{(1-0.5)}^2}=21.7\mathrm{nF}\end{array}$$

(54)

Finally, C_r is selected as 22 nF.

5. Experimental Results

At rated load, Figure 12 displays the PWM signals v_g1 and v_g2 for S₁ and S₂; Figure 13 displays the PWM signal v_g1 for S₁, the voltage on S₁, named v_ds1, and the current in S₁, named i_ds1; Figure 14 shows the PWM signal v_g2 for S₂, the voltage on S₂, named v_ds2, and the current in S₂, named i_ds2; Figure 15 displays i_Lr and v_Cr. In Figure 12, we can see that the switch-on instant for S₂ is prior to that for S₁. In Figure 13, we can see that S₁ has ZVT switch on and ZCS switch off. In Figure 14, we can see that S₂ has ZCS switch on and ZCS switch off. In Figure 15, we can see that V_Cr and i_Lr have two resonant cycles per one half of PWM cycle and no resonant cycles per the other half of PWM cycle.

Moreover, Figure 16 displays how to measure the efficiency. First of all, the input current I_in is obtained by using one digital meter called Fluke 8050 A to measure the voltage across the current sensor. Afterwards, the input voltage V_in is attained by another digital meter. Hence, the input power is equal to the product of V_in and I_in. As for the output power, the output current I_o is obtained from the electronic load and the output voltage V_o is attained by the other digital meter. Therefore, the output power is equal to the product of V_o and I_o. Finally, the resulting efficiency can be attained. Figure 17 shows the relationship between efficiency and load. In Figure 17, we can see that the maximum difference in efficiency between soft switching and hard switching is about 2%. Figure 18 shows a photo of the experimental setup.

6. Comparisons

The circuit shown in [13] is chosen as a comparison. In

Table 2. Comparisons between [13] and the proposed circuits (ZVT: zero-voltage transition; ZCS: zero-current transition).

Comparisons	Resonant Component Count	Input Voltage (V)	Output Voltage (V)	Switching Frequency (Hz)	Output Power (W)	Main Switch ZVT Turn-on	Main Switch ZCS Turn-on	Maximum Efficiency (%)
[13]	6	200	400	30k	600	*		96.2
Proposed	4	24	48	250k	120	*	*	93.8

The sign * means that the converter possesses this soft switching type.

, the number of resonant components for the circuit shown in [13] is six, whereas the number of resonant components for the proposed circuit is four. The circuit shown in [13] has the ZVT turn on for the main switch, whereas the proposed circuit has the ZVT turn on and ZCS turn on for the main switch. The maximum value of the overall efficiency for the circuit shown in [13] is 96.2% with switching frequency of 30 kHz, whereas that for the proposed circuit is 93.8% with switching frequency of 250 kHz. It is noted that the lower the switching frequency, the higher the efficiency.

7. Conclusions

In this paper, by combining QR and ZVT, an auxiliary circuit, with a small number of components containing L_r, C_r and S₁, is added to the traditional boost converter, so as to realize the ZVT switch on and ZCS switch off of S₁ as well as the ZCS switch on and ZCS switch off of S₂. Accordingly, the difference in efficiency at light load between soft switching and hard switching is about 2%. In addition to improving the shortcomings of general resonant power electronic converters that require variable frequency control, this structure has the advantage of constant frequency control.