A single-phase to single-phase cycloconverter is shown in Fig. (1) supplying an inductive load comprising a resistance of 5 Ω and an inductance of 40 mH from a 230 V, 50 Hz single-phase supply. It is required to provide an output frequency which is 1/3 of the input frequency. If the converters are operated in the Circulating Current Free mode (the two bridges are acting alternately; only one bridge carries load current at any given time; there is no current circulating between the two bridges, the temporarily idle converter must be blocked), such that 0 ≤ α ≤ π and firing delay angle α_f = 120°. Neglecting the harmonic content of the load voltage, the AC/DC converter is an ideal converter. Determine:

(a) rms value of the output voltage; (20 marks)
(b) rms value of the load current; (10 marks)
(c) input VA power rating; (10 marks)
(d) input power factor; (10 marks)
(e) Fundamental Component a₁, b₁; (10 marks)
(f) average value of the load voltage; (10 marks)
(g) sketch approximately to scale, the waveforms of v₁(t), v₂(t), and v₀(t); (15 marks)