## 1 Introduction
The circuit described in [15] has a dual H-bridge, as shown in Figure 1a, to regulate the output frequency at a discrete level by employing a simpler control technique. One control input is generated by using Arduino UNO as a signal generator, ensuring the alignment of the signal to the input AC voltage. For this purpose, the output of the source voltage polarity sensing circuit is connected to an input port of the Arduino controller. A NOT gate is connected with the output port of the signal to obtain the inverted or complementary form of this signal. So, there are two signals whose control logic is complementary in nature. Each control input is converted to four signalswith the help of gate control circuits to govern the operating states of the eight switching transistors. The principal issue in this circuit is the use of large components and specially controlled solid electronic devices. Since it is not possible to govern the on and off behavior of a transistor directly with control input generated by the Arduino or some other signal controller. For this purpose, the use of gate control circuits is a fundamental requirement, and their numbers are proportional to the number of operating transistors. The cost, weight, and size of such circuit arrangement are normally much more than that of an operating transistor. The authors of the circuit reported in [16] (see Figure 1b) succeeded in reducing the use of two fast switching transistors and two diodes. Surely, the reduction of two transistors mitigates the need for two driving circuits. This would help to tackle the issue of space and weight. The research in [17] further simplifies the control effort by reducing the four more switching transistors, as shown in Figure 1c. This feature is achieved with an increase of two additional diodes. The total losses produced by the switching devices in [17] are low than in [16]. Although this topology simplifies the circuit in terms of devices and components, the use of a bulky source frequency transformer is a significant problem in terms of losses, weight, and cost. The circuits reported in [16; 17] can change the input frequency at the load terminal to a low value in discrete steps, that is one-half, one-third, or one-fourth of the input frequency. This variation in the output frequency is achieved with the help of the non  
Figure 1: Various frequency converters without voltage adjustment control: (**a**) dual bridge approach; (**b**) transformer-less approach; (**c**) transformer-based approach. inverted and inverted forms of the input voltage. The ultimate role of the frequency controller is to keep the number of positive half cycles for the first half period of the output voltage and the number of negative half cycles for the second half period of the output voltage. These positive and negative half-cycles in one output period are equal, and their numbers depend on the required output frequency. For example, there are two consecutive positive and two negative half-cycles for the requirement where the output frequency is one-half of the input. There is a series of three and four positive and negative half-cycles for the application that requires the frequency of one-third and one-fourth of the input frequency, respectively. This sort of output always exists in non-sinusoidal forms and contains unwanted components called harmonics. The harmonic coefficients of these output voltage waveforms are numerically computed in [18] to explore their power quality drawbacks. Then it is investigated that the harmonic factor of the output voltage is nearly 60%, 67%, and 70% for an output frequency of one-half, one-third, and one-fourth of input frequency, respectively. So, the output voltage quality decreases once their output frequency is reduced in discrete steps. This issue intends to tackle by adjusting the magnitude of some selected half cycles of output voltage.