Centre Tapped Transformer or Mid-point Cycloconverter

• The circuit diagram for mid-point cycloconverter is as shown in Figure A. In order to understand the circuit operation let us analyse the circuit for a purely resistive load.
• There are four SCRs S₁, S₂, S₃ and S₄. The SCRs 1, 2 and 3, 4 are connected in antiparallel as shown in Figure A. The load is connected between the centre tap of the secondary winding of the transformer and an inductance L.

Waveforms of Mid point Cycloconverter :

Figure B

• The load voltage waveforms for the midpoint configuration for an output frequency equal to one third of the input frequency are as shown in Figure B.

Operation of Centre Tapped Transformer Cycloconverter for [f_out
= 1/3 f_in]

1. First half cycle :

• Refer to Figure A. In the first positive half cycle of the ac input voltage, the secondary induced voltage is such that point “A” is positive with respect to centre tap “O” and “B” is negative with respect to “O”.
• Therefore the SCRs 1 and 4 are forward biased, out of which SCR1 is turned on at an angle “α“. 

Figure C

• The equivalent circuit is as shown in Figure C. The load voltage is positive and equal to V_AO. SCR₁ is turned off at the end of this half cycle ( ωt =  π ) due to natural commutation.

2. Second and third half cycles :

• In the second half cycle of input supply (π to 2π). V_AO is negative whereas V_BO is positive.
• Therefore SCRs 2 and 3 are forward biased out of which S₃, is turned on at instant (π + α).
• This will make the load voltage positive equal to  V_BO from (π + α) to 2π. SCR3 is turned off at 2π due to natural commutation. In the third half cycle of the ac supply (2π to 2π) the polarities of secondary voltage are identical to those in the first half cycle.
• Again SCR1 is turned on making the load voltage positive equal to V_AO as shown in Figure B.

Fourth, fifth and sixth half cycles :

• In these half cycles the SCRs 2, 4 and 2 respectively are turned on to make the load voltage negative as shown in Figure B.
• The firing angle of these SCRs is identical to that of SCRs 1 and 3. The triggering of SCRs 2 and 4 in fourth, fifth and sixth half cycles will produce negative three half cycles across the load.
• Then in the seventh half cycle of the input supply S₁ is turned on and the cycle repeats itself.

Half Cycle	1	2	3	4	5	6	7	8	9…..
Conducting SCR	S1	S3	S1	S2	S4	S2	S1	S3	S1…..

Output frequency (f_out) :

• As seen from Figure B, one cycle of output voltage waveform of the cycloconverter consists of three positive and three negative half cycles.
• Therefore the one cycle period of the output is three times more than that of the ac input. Therefore the output frequency f_out is one third of the ac supply frequency.

f_out = 1/3 f_in

• _{In general if the input frequency is to be divided by “N” (N is an integer) then “N” positive and “N” negative half cycles should be produced across the load by triggering the SCRs in a proper sequence.}
• _{The output voltage waveforms to divide the frequency by 2 and 4 are as shown in Figure D.}
• _{From the waveforms shown in Figure B and D it is clear that the waveform at the output of the cycloconverter is not sinusoidal in nature. In fact with reduction in the output frequency, it tends to be a square wave.}
• _{In order to produce a sinewave output the triggering of the individual SCR’s should be delayed by varying degrees so as to produce the waveform shown in Figure E.}

Output Voltage Control :

• _{The ac output voltage of the cycloconverter can be changed by varying the firing angle of the thyristors.}
• _{With the resistive load each SCR conducts for a duration of (} – ) and turns off naturally at the end of each half cycle.

Why is inductance L used ?

• By mistake if two SCRs from the two pairs are turned on simultaneously (e.g. S₁, and S₄ or S₂ and S₃) then the secondary winding of the transformer will be short circuited.
• The inductance L is introduced in the circuit to avoid this possible shortcircuit.

Should the output frequency be always a submultiple of input frequency ?

• Yes, the output frequency should be a submultiple of the input frequency f_in i.e. the ratio f_in / f_out = N should always be an integer ( 1,2,3 … ).
• If the output frequency is not the submultiple of the input frequency the incoming SCR will be turned on even before the outgoing SCR is turned off completely.
• This will result in zero output voltage. This condition continues for less than a half cycle period and occurs at every half cycle of the output frequency.
• Therefore for symmetrical output waveforms, the ratio of input to output frequency (N = f_in / f_out) should be an integer.
• Otherwise, the output wave is distorted due to periodic short circuits (output voltage zero).
• Due to the asymmetrical waveform the output transformer (if at all used) may get saturated.