Thyristor (SCR) characteristics and commutation
A thyristor turns on when a gate pulse is applied while it is forward-biased; it turns off only when the anode current falls below the holding current. Natural commutation relies on the AC source reversing polarity. Forced commutation uses an auxiliary circuit to reverse-bias the thyristor. The firing angle α delays turn-on from the natural conduction point.
Check yourself: What mechanism returns the thyristor current to zero in this circuit?
Controlled rectifiers
For a single-phase fully-controlled bridge with a highly inductive load (constant load current), the average output voltage is V_dc = (2V_m/π) cos α. With a resistive load, conduction may become discontinuous for large α. Three-phase bridges have lower ripple and higher power capability; the average voltage formula changes to V_dc = (3V_m,LL/π) cos α for a six-pulse bridge.
Check yourself: Is the load sufficiently inductive to assume continuous and constant current?
DC–DC converters (choppers)
A buck (step-down) converter in continuous conduction mode (CCM) gives V_out = DV_s, where D is the duty ratio. A boost (step-up) converter gives V_out = V_s/(1 − D). A buck-boost converter gives V_out = −DV_s/(1 − D). These relations follow from volt-second balance on the inductor over one switching period.
Check yourself: Is the inductor current continuous throughout the switching cycle?
Voltage-source inverters
A single-phase full-bridge inverter produces a square-wave or quasi-square-wave AC output from a DC source. The fundamental-frequency RMS component of a square wave of amplitude V_dc is (2√2/π)V_dc. Pulse-width modulation (PWM) shapes the switching pattern to control the output voltage magnitude and reduce lower-order harmonics.
Check yourself: Have you identified which pair of switches conducts during each half-cycle?
AC voltage controllers
A single-phase AC voltage controller uses back-to-back thyristors or a triac to regulate RMS voltage by delaying the firing angle. For a resistive load, the RMS output voltage involves the integral of v² from α to π. Power factor decreases as α increases because the displacement and distortion factors both worsen.
Check yourself: Does your integral account for conduction in both half-cycles?