*2.1. Topology Description*

The configurations of the proposed and conventional topologies are shown in Figure 1a,b, respectively. The proposed topology employs the voltage-doubler rectifier in the output side. The resonance capacitor (*Cr*) is placed before the bidirectional switch in the proposed topology. At the same time, it is integrated as part of the voltage-doubler rectifier in Figure 1b. In the proposed SRC topology, the capacitors *C*1 and *C*2 have much larger capacitance than *Cr* to keep the resonance frequency (*fr*) constant according to (1). The value of resonance inductance *Lr* equals either the value of the isolation transformer leakage inductance (*Llk*) or the sum of the transformer leakage inductance and the external inductance (*Lext*) if the leakage inductance is low. The cost and size of the converter can be reduced by utilizing only the transformer leakage. The average voltage of the resonant capacitor (*VCr*) equals zero due to the symmetry of the VDR during the switching period as will be explained later. Contrary to the topology [18], the average voltage across the resonant capacitors (*Cr*/2) equals half of the output voltage (i.e., *VOUT*/2). The bidirectional switch comprises the two MOSFETs *Q*1 and *Q*2. The conventional voltage-source full-bridge inverter is employed at the input side. The transistors of the input-side bridge are driven with complementary pulses of nearly 0.5 duty cycle, considering a small dead time between the control signals in the same leg. The input-side full-bridge inverter feeds the isolating transformer *TX* with a balanced rectangular voltage that features positive and negative magnitudes equal to the input voltage. The magnetizing inductance of the transformer (*Lm*) provides auxiliary circulating current that assists the soft switching of the primary-side transistors. The magnetizing current can recharge their parasitic output capacitance during the short dead times. The isolating transformer *TX* steps up the voltage fed by the input bridge inverter by the turns ratio *n*.

$$f\_r = \frac{1}{2\pi\sqrt{\mathcal{L}\_r\mathcal{C}\_r}}\tag{1}$$

where, *Lr* is the resonant inductance.

 **Figure 1.** Converter topology of (**a**) the proposed SRC based on the modified VDR with a bidirectional switch and (**b**) the SRC presented in [18].

#### *2.2. PWM Schemes for the Boost VDR*

The switches *Q*1 and *Q*2 form the bidirectional switch. They are used to short-circuit the transformer output winding; so, the resonant inductor can increase its energy serving as a boost inductor of the AC boost converter. The two switches are connected in the back-to-back configuration. The bidirectional switch allows its current to flow in both directions, while it can block both voltage polarities. Two PWM

schemes could be employed to generate the gating signal for the switches *Q*1 and *Q*2, as shown in Figure 2. First, only one of the switches is turned on at each half-cycle and forms a path for the current through the body diode of the other switch, as shown in Figure 2a. For example, during the positive voltage half-wave across the transformer secondary winding, the transistor *Q*1 is turned on, which results in the conduction of the body diode of the transistor *Q*2. In the other PWM scheme from Figure 2b, the switches are controlled with overlapped signals of equal duty cycle, which are shifted regarding the control signals of the input-side switches. Therefore, the body diodes are not used at all, and synchronous rectification is implemented to reduce the conduction losses. In both cases, the switching frequency of the switches *Q*1 and *Q*2 is the same as that of the primary-side switches. The voltage boosting mode occurs during two equal time intervals with the cumulative duty cycle *Db*, which are separated in time by half of the switching period *TSW*.

**Figure 2.** Possible PWM schemes for the bidirectional switch: (**a**) simple boost PWM and (**b**) phase-shifted PWM with overlapping signals.

The peak-to-peak ripple of the capacitor voltage is affected by the output power level (*POUT*), as given in (2). It is worth mentioning that the proposed topology can operate with the PWM technique from Figure 2b in a limited range of power and voltage. Abnormal operation occurs when the maximum capacitor voltage is larger than the voltage of the transformer secondary winding (i.e., Δ*VCr*/2 > *<sup>n</sup>*·*VIN*). As shown in Figure 3, when a positive voltage feeds the secondary winding of the transformer, the current begins to flow in the reverse direction after discharging the stored energy. This reverse current increases the conduction losses of the converter, which results in the deterioration of the system efficiency and reduction of the DC voltage gain.

$$
\Delta V\_{\text{Cr}} = \frac{P\_{\text{OUT}} T\_{\text{SW}}}{2n V\_{\text{IN}} \mathbb{C}\_r},
\tag{2}
$$

where *TSW* is the switching period, *n* is the transformer turns ratio, and *VIN* is the input voltage.

**Figure 3.** Abnormal operation of the proposed SRC with a boost VDR in the case of PWM scheme from Figure 2b when Δ*VCr*/2 > *nVIN*.

## **3. Steady-State Analysis and Comparison**

#### *3.1. Description of the Operating Principle*

The main voltage and current waveforms of the proposed topology and the state-plane trajectory of the state variables are given in Figures 4 and 5. The resonant current (*iLlk*(*t*)) is multiplied by the resonant impedance *Zr* defined in (3) to have the same units of the axes. The steady-state analysis was performed based on the following assumptions:

1. The output voltage (*VOUT*) is ripple-free due to the high value of the output capacitance (*CO*).

=

 (3)


**Figure 4.** Sketch of idealized voltage and current steady-state waveforms of the proposed converter.

**Figure 5.** The state-plane trajectory of the resonance tank of the proposed SRC.
