Half-wave rectifier with capacitor-input filter: If the input to the ideal diode rectifier is v(t) = Vm sin(ωt), what is the required Peak Inverse Voltage (PIV) rating of the diode?

Introduction / Context:
PIV (Peak Inverse Voltage) is the maximum reverse voltage that a rectifier diode must withstand. Choosing an adequate PIV is crucial for reliability, especially in capacitor-input filters where the reservoir capacitor holds a voltage between conduction intervals.

Given Data / Assumptions:

• Half-wave rectifier.
• Capacitor-input (reservoir) filter holds approximately V_m at the output between peaks.
• Ideal diode and negligible transformer resistance for peak estimation.

Concept / Approach:

At the instant just after the capacitor has charged to V_m, the input becomes negative. The diode is then reverse-biased by the instantaneous source voltage in series with the stored capacitor voltage. With the source at approximately −V_m and the capacitor still ~ +V_m, the diode sees a reverse voltage close to V_m + V_m = 2 V_m.

Step-by-Step Solution:

Verification / Alternative check:

Classic rectifier design tables list: Half-wave with capacitor-input → PIV ≈ 2 V_m; Full-wave bridge with capacitor-input → PIV ≈ V_m per diode, confirming the result.

Why Other Options Are Wrong:

• Vm: valid for some bridge configurations, not for half-wave with a reservoir capacitor.
• 3 Vm or 4 Vm: overly conservative for the idealised case; increases cost without benefit.
• Vm/2: far too low and unsafe.

Common Pitfalls:

• Ignoring the stored capacitor voltage when computing reverse stress.

Final Answer:

2 Vm.