## 2 Operating Principle and Modes  
This section describes the working principle and all possible operational modes of the proposed converter in some detail. The developed circuit shown in Figure 2 is composed of six high-frequency diodes (\(D_{1}\) to \(D_{6}\)) and six transistors (\(T_{r1}\) to \(T_{r6}\)). This circuit is a modified form of the circuit presented in [23], where the voltage step-down capabilities are enhanced by adding two more switching transistors (\(T_{r1}\) and \(T_{r3}\)). These transistors are used to convert the constant sinusoidal voltage of the input to its controllable absolute form through PWM control. In any of the operating intervals of the developed circuit, one transistor and one diode operate at high frequency along with the low frequency (input or output frequency) operation of two transistors and diodes. So, there is always the conduction of three diodes and transistors [11; 20]. There is also the use of one inductor (\(L\)) and two capacitors (one for input (\(C_{in}\)) and the other for output (\(C_{out}\)) to tackle the power quality issues. The series connection of diode and transistor forms pairs \(D_{1}\)-\(T_{r1}\), \(D_{3}\)-\(T_{r3}\), \(D_{5}\)-\(T_{r5}\) and \(D_{6}\)-\(T_{r6}\). This makes sure the elimination of shoot-through owing to the parallel connection of input and output capacitors, shorting of input or output capacitors. As an example, the connection of diodes \(D_{1}\) and \(D_{3}\) avoids the possibility of the direct parallel connection of input and output capacitors. The use of an intermediate inductor avoids the shorting of the input source or capacitor during the situation in which all transistors remain on. This situation may be possible due to the defects in the manufacturing process of the transistors or incorrect control inputs. This problem is normally faced when two transistors must turn on and off in a complementary way. There may be a possibility that turning off transistor may turn off later than turning on transistor. Similarly, the series connection of \(D_{5}\)-\(T_{r5}\) and \(D_{6}\)-\(T_{r6}\) prevents the shorting of the output capacitor. The details of the operation in dual polarity voltage step-down and step-up modes are explained here with the help of mathematical equations and circuit loops. The control strategy shown in Figure 3a,b to turn on and off the transistors for non-inverting and inverting voltage buck operation, respectively, is almost the same as ex  
Figure 2: Proposed circuit. plained in [20]. Here all the generated control signals follow the variation in the polarity of the input voltage. For this purpose, the input voltage polarity sensing circuit generates high (5 V) and low (0 V) outputs indicating positive and negative input values, respectively. As an example of voltage step-down operation for both polarities of the output voltage (inverting and non-inverting outputs), the PWM control signals \(c_{1}\) and \(c_{3}\) shown in Figure 2(a),b are responsible for power conversion with voltage buck capabilities during the positive and negative input. So, the variation in the instantaneous output voltage is obtained by the high-frequency PWM switching of the transistors \(T_{r1}\) and \(T_{r3}\) during positive and negative input values, respectively. Here the role of the front-end circuit is to convert the constant sinusoidal input voltage into its regulated absolute form. The control of non-inverting and inverting output buck operation is determined from the low-frequency switching operation of the transistors employed in the second stage circuit. For this purpose, the remaining four control signals \(c_{2}\), \(c_{6}\) and \(c_{4}\), \(c_{5}\) shown in Figure 2(a) have logic high and low values throughout the intervals in which input is positive and negative, respectively. It should be noted that control signals \(c_{4}\) and \(c_{5}\) are generated in the complementary form of \(c_{2}\) and \(c_{6}\). The same control scheme can effectively be employed for an inverting buck operation of the output voltage.