Single-phase fully controlled bridge converter supplied by v_s(t) = Vm sin(ωt) What are the expressions for the average and RMS output voltages (continuous current, no overlap)?

Introduction / Context:
The fully controlled single-phase bridge (four SCRs) allows control of the average DC output voltage by adjusting the firing angle α. Under continuous current and neglecting source inductance (no overlap), the RMS output voltage equals the source RMS voltage because the squared waveform energy over one period is unchanged by phase control, while the average value depends on α.

Given Data / Assumptions:

• Input: v_s(t) = Vm sin(ωt).
• Fully controlled bridge, continuous load current.
• No overlap and ideal devices (no drops).
• Output voltage segments are sinusoidal portions selected by gating (shifted by α).

Concept / Approach:

For continuous current, the bridge transfers the instantaneous source voltage (with polarity control) to the load from ωt = α to ωt = α + π each cycle. The average over one period is proportional to cos α. The RMS value, being energy-based, remains equal to the source RMS without overlap since the waveform is a full sine segment over π radians each half-cycle.

Step-by-Step Solution:

Verification / Alternative check:

As α increases from 0° to 90°, V_avg decreases from 2Vm/π to 0, while V_rms remains Vm/√2, matching standard converter results for continuous-current operation without overlap.

Why Other Options Are Wrong:

Options with Vm/π or Vm scaling are dimensionally or conceptually incorrect. Swapping cos α between average and RMS is wrong since RMS is independent of α in this idealized case.

Common Pitfalls:

Confusing average with RMS; forgetting that overlap and device drops would reduce RMS slightly; misinterpreting Vm as RMS instead of peak.

Final Answer:

V_avg = (2Vm/π) * cos α and V_rms = Vm/√2