## 1 Introduction
The harmonic factor of the output voltage for one-third and one-fourth frequency requirement is reduced to approximately 55% by regulating the amplitude of some selected output half cycles as described in [19; 20]. The circuit diagram of these converters is illustrated in Figure 2a,b. The circuit describes in [19] needs eight diodes and four thyristors. However, the realization of a converter in [20] uses five Triacs or ten thyristors. These converters cannot be implemented without using a bulky low-frequency multi-winding transformer. The use of this transformer is absent in the converter described in [21]. This setup is shown in Figure 2c wherein the voltage adjustment of the output half cycles is governed through the high-frequency PWM control. Figure 2: Various frequency converters with voltage adjustment control: (**a**) multi-winding transformer-based approach; (**b**) center tape transformer-based approach; (**c**) transformerless approach. The output half-cycle voltage control approach cannot improve power quality for some output frequencies. For example, there is no way to lower the harmonic factor of the output voltage for the frequency requirement of one-half of the input frequency. The improvement in the harmonic factor of output voltage for other output frequency requirements introduces the low-frequency harmonics in the input current. That degrades the input power quality indexes severely by increasing the input current harmonic factor and lowering the input power factor. So, the input side gets more harmonic pollution than the power quality improvement of the output voltage. In existing converters, the concerns related to the power quality of the output voltage are addressed, but this concern for input current is not yet explored in the literature. The added harmonic pollution in the input current needs more investigation. So, in this research article, these power quality concerns of output voltage and input current are numerically addressed in detail. The harmonic investigation of the input current and output voltage recognizes that decrement in the HF of output voltage severely increases the HF of the input current. This conclusion suggests that for low-frequency applications, the improvement in the input power quality indexes is ensured by eliminating the variation of the output half cycles. In this regard, our already proposed high-frequency controller in [22] can also be effectively be employed for low output frequency operation. The only modification in this circuit is that one input voltage polarity sensing circuit has to be included to align the control inputs with the source voltage to detect its variation. Its output may be used by any signal generator to synchronize its generated signal with the polarity of the input voltage. All operational modes of the circuit of Figure 3a are comprehensively described in [22]. The use of the rectifier's bridge enables the input alternating voltage to convert into its absolute form by non-inverting and inverting all input positive and negative half-cycles, respectively. The role of the inverter's bridge is to arrange the absolute value pulses into the required frequency AC form. The control signal that enables to obtain the load frequency to one-third compared to input may be seen in Figure 3b. In summary, the following are the main issues or research gaps in the circuit topologies that improve the power quality-related concerns of the output voltage obtained via the magnitude control of the selected half cycles. 1. It is not possible to improve the harmonic profile of the output voltage for the output frequency that is one-half of the input. 2. Improvement in the harmonic profile of the output voltage adds unwanted harmonic components in the input current, and this issue is not yet investigated according to the authors' best knowledge or information. Figure 3: Output frequency control: (a) recommended circuit; (b) control inputs. 3.