Figure 1 shows the power circuit of a single-phase to single-phase cycloconverter employing a centre-tapped transformer. There are four thyristors, namely, $P_{1}, N_{1}, P_{2},$ and $N_{2}$ . Out of the four SCRs, SCRs $P_{1}$ and $P_{2}$ are responsible for generating positive halves forming the positive group.The other two SCRs $N_1$ and $N_2$ are responsible for producing the negative halves forming the negative group.This configuration is meant for generating 1/3 of the input frequency, i.e. this circuits generates a frequency of $16 \frac{2}{3} Hz$ at its output.

Depanding upon the polarities of the points P and Q of the transformer,SCRs are gated.

During the first positive half cycle,when point P is positive and Q is negative,SCR $P_1$ being in conducting mode is gated.The current flows through positive point P, SCR $P_1$,load and the negative point O. In the negative half cycle,when point Q is positive and point P is negative, SCR $P_1$ is automatically turned-off and SCR $P_2$ is triggered simultaneously.Path for the current flow in this condition will be from positive Q, SCR $P_2$,load and the negative point O.Direction of flow of current through the load remains the same as in the positive half cycle.In next cycle,again point P becomes positive and Q becomes negative,thus, SCR $P_2$ is automatically line commutated. SCR $P_1$ is gated simultaneously.The current path again becomes as in the previous case when SCR $P_1$ was conducting.Thus,it is seen that the direction of flow of current through the load remains same in all the three half cycle or in other words,the three positive half cycleare being obtained across the load to produce one combine half cycle as output.

Similarly,in the next negative half cycle of the a.c. input, when point Q is again positive and point P is negative ,SCR $P_1$ is automatically switched OFF.Now,instead of SCR $P_2$, SCR $N_1$ is gated.The path for the current flow will be from point Q,load,SCR $N_1$ and back to negative point P. Thus,The diection of flow of current through the load is reversed.

In the next positive half cycle,point P is positive and point Q is negative. SCR $N_1$ is automatically turned off.SCR $N_2$ which is in the conducting mode is simultaneously turned-on.The path for the current flow becomes from positive point P, load, SCR $N_2$ to negative point Q.Thus, the direction of flow of current through the load remains the same.For the next negative half cycle ofthe a.c. input when point Q is positive and point P is negative, SCR $N_2$ is automatically switched off and SCR $N_1$ is gated. The current flow through the load again remains in the same direction.Wecan thus analyse it as producing one negative half cycle at the output by combining three negative halves of the input.

In other words, it can be said that, three cycles of the input a.c. have been combined to produce one cycle at the output, i.e. three positive half cycles at the output by the SCRs $P_{1}$ and $P_{2}$ whereas, three negative half-cycle of the input a.c. are combined to produce one negative half cycle at the output by SCRs $N_{1}$ and $N_{2}$ . This clearly indicates that the input frequency 50 Hz is reduced to $1/ 3 rd$ $(16.2 / 3 \mathrm{Hz})$ at the output across the load. The input and output waves are shown in Fig.1.b. The output voltage magnitude can be changed by varying the firing angle of the SCRs.