Bridge single-phase cycloconverter conduction sequence

A single-phase bridge cycloconverter converts AC at frequency $f_i$ directly to AC at a lower frequency $f_o = f_i/n$, using two full-bridge thyristor converters connected back to back: the positive (P) converter supplies the positive half of the output and the negative (N) converter the negative half.

Circuit

        P-converter          N-converter
     +--P1---P3--+        +--N1---N3--+
 vs  |           |  load  |           |
 ~ --+           +--[R]---+           +-- ~
     |           |        |           |
     +--P4---P2--+        +--N4---N2--+

• P-converter: P1, P2 (conduct when supply positive) and P3, P4 (conduct when supply negative); output current flows A to B through the load (+ve).
• N-converter: N1, N2 and N3, N4 connected in reverse, so load current flows B to A (−ve).
• Only one converter is enabled at a time (circulating-current-free mode).

Operation for $f_o = f_i/2$ (example, $\alpha = 0$, R load)

For the first output half cycle (two input half cycles), the P-converter acts as a full-wave rectifier, so both input half cycles appear positive on the load. For the next two input half cycles the N-converter works, and both appear negative.

 vs   /\    /\    /\    /\
     /  \  /  \  /  \  /  \
 ---/----\/----\/----\/----\-
              (each hump is
               one half cycle)
 vo   /\  /\
     /  \/  \
 ---/--------\--------/-----
              \  /\  /
               \/  \/
     |<--P--->|<--N--->|
       To = 2 Ti

So the output period is twice the input period, i.e. $f_o = f_i/2$ (25 Hz from 50 Hz). With firing angle $\alpha$, each hump starts at $\alpha$, reducing the rms output.

Conduction sequence ($f_o = f_i/2$)

For $f_o = f_i/3$, each converter works for three input half cycles (P1P2, P3P4, P1P2, then N3N4, N1N2, N3N4 style alternation), giving 3 humps per output half cycle.

RMS output (R load)

$$V_o = V_s\sqrt{\frac{1}{\pi}\left(\pi - \alpha + \frac{\sin 2\alpha}{2}\right)}$$

Uses: low-speed, high-power AC drives (cement mills, ship propulsion), induction heating supplies.