Center-tapped single-phase full-wave controlled rectifier If the voltage across each half of the transformer secondary is v_s(t) = Vm sin(ωt), what is the peak inverse voltage (PIV) across each thyristor?

Introduction / Context:
Peak inverse voltage (PIV) is the maximum reverse voltage a device must withstand when it is off. In center-tapped full-wave rectifiers (using two controlled devices on each half of the secondary), knowing the PIV is essential for selecting properly rated SCRs or diodes.

Given Data / Assumptions:

• Center-tapped transformer secondary, each half produces Vm sin(ωt) (Vm is the peak of half-winding).
• Only one SCR conducts at a time (ideal operation, no overlap).
• Negligible leakage and device drops for PIV estimation.

Concept / Approach:

When one SCR is forward-biased and conducts, the other is reverse-biased. The non-conducting device sees its own half-winding voltage (Vm sin(ωt)) plus the instantaneous load potential referred through the conducting half which effectively places approximately the opposite half-winding peak across it. The worst case occurs near the peak of the opposite half cycle, leading to a reverse stress of approximately 2 Vm.

Step-by-Step Solution:

Verification / Alternative check:

Textbook results for center-tapped full-wave rectifiers list PIV of each device as twice the maximum half-secondary peak. Bridge rectifiers (without center tap) reduce individual device PIV requirements compared to center-tap circuits.

Why Other Options Are Wrong:

Vm underestimates the stress; 0.5 Vm and 0.25 Vm are far too low for the off device in this topology.

Common Pitfalls:

Confusing bridge and center-tap PIV values; forgetting that the off device sees the sum of two half-winding peaks under worst case.

Final Answer:

2 Vm