## 3 Performance-Wise Comparison with Existing Topologies  
The attractive features of the suggested topology may also be validated by comparing its characteristics with the existing converter as in [24] employed to have similar outputs. The transformer-less implementation is one of the major achievements of the proposed topology. This not only reduces the overall size and cost but also reduces the conversion losses as core losses are more significant than the losses caused by the semiconductor  
Figure 10: Output step-up frequency control with respect to input frequency: (**a**) two times; (**b**) three times. devices. The center tap transformer that is an integral part of the multi-converter reported in [24], is employed for multiple outputs. The flow of unidirectional and low-frequency current is a big issue in this type of transformer compared to a two-winding transformer. These currents normally cause the core saturation issue. The absence of an intermediate inductor in [24] may cause the shoot-through issue and switching devices may damage due to the flow of excessive current during these intervals. The performance of the AC-AC converters may be evaluated in terms of a maximum breakover voltage (\(V_{br}\)) for the switching devices, switching or chopping voltage (\(V_{ch}\)) and currents (\(I_{ch}\)), power factor (\(PF\)), harmonic factor (\(HF\)), switching (\(P_{S}\)), and conduction losses (\(P_{C}\)) as performance index parameters. The maximum breakover voltage that can be developed across the switching devices in the proposed architecture is limited only to the peak value of input voltage (\(V_{m}\)). The architecture of the converter [24] is implemented with a center tap transformer having two secondary windings. At any time instance, if switching devices of one secondary winding are conducting then switching elements of the other secondary winding remain in non-conducting. The maximum breakover voltage of the switching devices in this architecture is the sum of the peak voltage of the two secondary (output) windings. The same is true for the switching or chopping voltage. Therefore, the maximum breakover and switching voltage of the converter architecture in [24] is double that of the developed architecture, i.e.,  
\[V_{br(proposed)}\ =\ V_{m} \tag{16}\]  
\[V_{br([24])}\ =\ V_{m}\ =\ 2V_{br(proposed)} \tag{17}\]  
\[V_{ch(proposed)}\ =\ V_{in} \tag{18}\]  
\[V_{ch([24])}\ =\ 2V_{in}\ =\ 2V_{ch(proposed)} \tag{19}\]  
The power conversion losses of the suggested architecture include only the switching (\(P_{S}\)) and conduction (\(P_{C}\)) losses of operating transistors and diodes. The switching losses of the fast recovery diode can be ignored due to the low value of the reverse current and reverse recovery time. These losses for one transistor and diode are computed as. \[P_{S(transistor)}\ =\ \frac{1}{6}V_{ch}I_{S}f_{ch}(t_{r}+t_{t}) \tag{20}\]  
\[P_{C(transistor)}\ =\ I_{S}^{2}R_{T(on)} \tag{21}\]  
\[P_{C(diode)}\ =\ V_{D(on)}I_{S}+I_{S}^{2}R_{D(on)} \tag{22}\]  
Here, \(I_{S}\) is the steady-state current conducted by the switching devices, \(f_{ch}\) is switching or chopping frequency, and \(t_{r}\) and \(t_{f}\) are the rise and fall times of the switching transistors. \(R_{T(on)}\) is the internal resistance of the transistor during its on-state. In the same way, \(R_{D(on)}\) and \(V_{D(on)}\) are the on-state resistance and voltage of the forward-biased diode respectively. The harmonic coefficients of the input current are computed to determine the power quality of the input current by computing the harmonic and power factor. They are computed with the total RMS value of the input current (\(I_{in}\)), input RMS current at the fundamental component (\(Iin_{(1)}\)), and its displacement angle (\(\theta_{1}\)). Mathematically, they are computed as  
\[H.F\ =\ \frac{\sqrt{I_{in}^{2}-I_{in(1)}^{2}}}{I_{in(1)}} \tag{23}\]  
\[P.F\ =\ \frac{I_{in(1)}}{I_{in}}\cos(\theta_{1}) \tag{24}\]  
Now above-defined performance indices are numerically computed with the 160 V peak value of the input voltage.