## 2 Operating Principle of the Proposed Circuit
### Non-Inverting Voltage Buck Operation  
In this operation, the phase difference between the input and output voltage is maintained at zero means that the output voltage is positive and negative, respectively, for the positive and negative value of the input voltage. This operation is split to mode I, where  
Figure 3: Control signals producing the non-inverting and inverting outputs.  
input and output voltages are positive, but in operating mode II, input and output voltages are negative. In both cases, output and input voltage are in-phase, ensuring zero phase difference between them. The operation of each mode may be divided into two segments that are categorized with respect to turn-on and turn-off intervals of a high-frequency PWM control signal. The equivalent circuits in which the input source transfer its power to output for the operation of mode I and II are illustrated in Figure 4a-d, respectively. These figures illustrate the voltage step-down operation for positive and negative half cycles of the input voltage. During the operation of mode I, the active switching transistor \(Q_{1}\) maintains its on-state for the period in which the input voltage is positive. However, the switching transistor \(Q_{2}\) operates in conduction and non-conduction mode during PWM \(kT\) and \((1-k)T\), in which output inductor '\(L\)' store energy from input and release the energy towards the output. The diodes \(D_{5}\) to \(D_{8}\) remain reverse biased once transistors \(Q_{1}\) and \(Q_{2}\) are conducted to store the input power to output inductor '\(L\)', as may be viewed in Figure 4a. The diode \(D_{7}\) starts conducting to divert the flow of the inductor from transistor \(Q_{2}\) to \(D_{7}\) once \(Q_{2}\) turns off. This behavior of the operating devices ensures the continuous flow of the inductor current, as seen in Figure 4b. For the operation of mode II, where the input voltage is negative, and the required output voltage is also negative, the role of transistors \(Q_{1}\) and \(Q_{2}\) is exchanged with transistors \(Q_{3}\) and \(Q_{4}\) (see Figure 4c,d).  
Loop analysis theory may be used to find the equations of instantaneous inductor voltage for the operation of modes I and II.  
\[v_{L}(t)=v_{s}(t)-v_{o}(t) \tag{1}\]  
\[v_{L}(t)=-v_{o}(t) \tag{2}\]  
It is clear from Figure 4a,c that the inductor voltage is a difference between the input and output voltage. The input voltage is zero as a source is isolated, as seen in Figure 4b,d. The average value of the inductor voltage is always treated as zero as its energy absorbed  
Figure 4: Equivalent power transfer circuits for non-inverting voltage buck operation: (**a,b**) for mode I and (**c,d**) for mode II.  
in the on-period of the PWM signal is released to load during the off period of the PWM signal. This concept may be employed to find the voltage gain \(k_{v}\).  
\[\frac{1}{T}\int\limits_{0}^{T}v_{L}(t)dt=\frac{1}{T}\int\limits_{0}^{kT}[v_{s}( t)-v_{o}(t)]dt-\frac{1}{T}\int\limits_{0}^{(1-k)T}v_{o}(t)dt \tag{3}\]  
\[\frac{V_{o}}{V_{s}}=k=k_{v} \tag{4}\]  
The overall voltage gain is directly linked with the duty cycle control (\(k\)), which validates the voltage buck operation.