Subject : Power Electronics
Unit : AC to AC Voltage Converter
Analysis of the Cycloconverter Output Waveform
Analysis of the cyclo converter output waveform:
Fig: Output voltage waveform for mphase converter with firing angle α
 An mphase converter circuit is assumed in which each phase conducts for ((2.π)/m) electrical radians in one cycle of supply (input) voltage.
 For example, in a threephase, halfwave (threepulse) converter (m = 3), each phase conducts for ((2.π)/3 = 120^{0}) radians in a cycle of 2π radians. Similarly, in a threephase, fullwave (sixpulse) converter (m = 6), the conduction period of the periodic waveform is ((2.π)/3 =π/3 = 60^{0}) radians in one cycle.
 With the time origin, PP^{`} taken at the peak value of the supply voltage, the instantaneous phase voltage is given by , where E_{ph} = supply voltage per phase (rms). The conduction period is from ( π/m) to (π/m), if the firing angle is α = 0^{0}. For the firing angle α, the conduction period is from (( π/m) α) to ((π/m) α). The total conduction period is ((2π)/m).

The average value of the output voltage is
 When the firing delay angle is α = 0^{0}_{, }E_{dc} has the maximum value of
 If the delay angle in the cycloconverter is slowly varied as given earlier, the output phase voltage at any point of the low frequency cycle may be calculated as the average voltage for the appropriate delay angle. This ignores the rapid fluctuations superimposed on the average low frequency waveform. Assuming continuous conduction, the average voltage is E_{dc} = E_{d0} . cosα
 If E_{0r} is the fundamental component of the output voltage (rms) per phase for the cycloconverter, then the peak output voltage for firing angle of 0^{0} is
 However, the firing angle of the positive group α_{p} cannot be reduced to zero, for this value corresponds to a firing angle of (α_{n} = 180^{0}) in the negative group. The firing delay angles of the two (positive and negative) converters are related by (α_{p} α_{n} = 180^{0}).
 Practically, inverter firing cannot be delayed by, because sufficient margin must be allowed for commutation overlap and thyristor turnoff time, as given in module 2. Consequently, the delay angle of the positive group cannot be reduced below a certain finite value,α_{min}. Therefore the maximum output voltage per phase is
Where, r = cosα_{min} , and is called the ‘voltage reduction factor’.
 Thus, the expression for the fundamental component of the phase voltage (rms) delivered by the cycloconverter is,