## 3 Validation through Comparative Analysis  
The effectiveness of the proposed circuit can be proven by computing the peak value of the switching currents of the semiconductor devices as it is used to compute their average and rms value. The maximum break-over voltage and the value of the conversion losses, especially conduction losses, are the main parameters for the comparative analysis. The number of active transistors used is a key factor that determines the overall size and cost of the switching converter. For the on-off operation of a switching transistor, the control signal is applied at its control terminal with respect to its reference terminal. However, in high switching AC-AC converters, the reference terminal of the used transistors is always not at the same potential level. Thus, the switching operation of a transistor cannot be successful without employing a gate control circuit. Therefore, the number of gate control circuits is almost equal to the number of switching transistors. The realization of a gate control circuit requires large space due to the use of a large number of passive components and semiconductor devices. Therefore, mostly the cost and size of a gate control circuit exceed the required space and size of a transistor. The use of a large number of switching transistors always remains a big challenge for the design engineer. The proposed topology may be one of the possible choices for the design as its implementation only needs four switching transistors, as in [23], ensuring a reduction in two switching transistors. The voltage rating of the semiconductor devices is determined by the value of the maximum break-over voltage that develops across them during their off-state condition. In this regard, the maximum break-over voltage of the employed transistors and diodes (switching devices) is equal to the peak value of the input voltage. \[V_{p(sd)}=V_{s(p)} \tag{12}\]  
In a similar approach, the peak value of the switching devices depends on the instantaneous value of the inductor current. This value in voltage buck operation is equal to the instantaneous output current. The value of the peak ripple current is ignorable as the selected switching frequency is very high. The peak value of the switching devices' current may be approximated by the peak load current. \[I_{p(sd)}=I_{o(p)} \tag{13}\]  
With the connection of the output capacitor, the load current can be treated in sinusoidal form as  
\[i_{o}(\omega t)=I_{o(p)}\sin(\omega t) \tag{14}\]  
The maximum conduction period of a diode or a transistor in the proposed converter or converter in [23] cannot exceed the half period of the input voltage. The conduction losses of a transistor with its internal resistance \(R_{Q}\) or a diode with given forward voltage \(V_{D}\) and forward resistance \(R_{D}\) in the above-stated period can be computed by considering the sinusoidal characteristics of switching current as  
\[P_{cond(diode)}=\frac{V_{D}I_{o(p)}}{\pi}+\frac{I_{o(p)}^{2}}{4}R_{D} \tag{15}\]  
\[P_{cond(transistor)}=\frac{I_{o(p)}^{2}}{4}R_{Q} \tag{16}\]In the proposed circuit, during the one period of the output voltage for the value of voltage gain (\(k_{o}\)) of 0.5, there is the conduction of three transistors and three diodes in the half period equivalent form. The total conduction losses of these devices are calculated as  
\[P_{cond}=\frac{3V_{D}I_{o(p)}}{\pi}+\frac{3I_{o(p)}^{2}}{4}\big{(}R_{Q}+R_{D} \big{)} \tag{17}\]  
However, with the above-stated condition, the converter's output in [23] needs the conduction of four transistors and four diodes. Correspondingly, their overall conduction losses can be obtained as  
\[P_{cond}=\frac{4V_{D}I_{o(p)}}{\pi}+I_{o(p)}^{2}\big{(}R_{Q}+R_{D}\big{)} \tag{18}\]  
Switching losses of the operating diodes at low and high frequencies are ignorable as they have low switching frequencies and low values of their reverse recovery times, respectively [12].