Parallel (Class B) inverter – relation of turn-off time to L and C For a parallel inverter employing an L–C commutation circuit, how is the required thyristor turn-off time tq related to the commutation components L and C?

Introduction / Context:
In Class B (parallel) commutation, a charged capacitor and inductor form an oscillatory loop that forces a reverse current through the conducting thyristor to turn it off. The commutation interval must exceed the device turn-off time tq. This links tq to the natural resonant period of the L–C network.

Given Data / Assumptions:

• Ideal L and C forming a lossless resonant path.
• Natural frequency ω0 = 1 / sqrt(L * C).
• Reverse current is provided roughly over a half-cycle of the L–C oscillation.

Concept / Approach:

Because the capacitor discharges and then recharges with reversed polarity through the inductor, the reverse bias on the thyristor lasts approximately for a half-sine of the L–C oscillation. The duration of a half-cycle is (π / ω0) = π * sqrt(L * C). To ensure reliable turn-off, this interval must be ≥ tq, hence the design criterion tq ≤ π * sqrt(L * C).

Step-by-Step Solution:

Verification / Alternative check:

Many design notes add a safety factor (e.g., 1.2–1.5) on top of the basic π * sqrt(L * C) interval to account for non-idealities and device parameter spread, confirming the proportionality.

Why Other Options Are Wrong:

• Linear LC expressions (options b–d) ignore the square-root relationship inherent to resonance.

Common Pitfalls:

Confusing full-cycle period 2π * sqrt(L * C) with the half-cycle interval that actually establishes reverse bias during commutation.

Final Answer:

tq = π * sqrt(L * C)