Semiconverter with freewheeling diode (R–L–E load) A single-phase semiconverter supplies an R–L–E load and includes a freewheeling diode across the load. If the firing angle is α, the freewheeling diode conducts for how long?

Introduction / Context:
Semiconverters (half-controlled bridges) with a freewheeling diode are widely used in DC motor drives. The freewheel interval is critical for current continuity and ripple. This question asks for the freewheel conduction duration as a function of firing angle α.

Given Data / Assumptions:

• Single-phase semiconverter, R–L–E load.
• Freewheeling diode placed across the load.
• Continuous or quasi-continuous current; ideal devices and negligible overlap.

Concept / Approach:

During a positive half-cycle, the controlled SCR conducts from ωt = α to ωt = π. At ωt = π, the supply reverses polarity; the freewheeling diode takes over to keep current flowing, typically from ωt = π to ωt = 2π. The same pattern repeats each mains cycle. Thus, the freewheel interval per full cycle equals (π − α) (in radians) or (π − α)° when expressed in degrees.

Step-by-Step Solution:

Verification / Alternative check:

Waveforms in classic drive texts show the freewheel diode conduction increasing as α decreases, matching (π − α) dependence.

Why Other Options Are Wrong:

“α° in each half” and “α° in one full cycle” reverse the dependence; “(π + α)” is non-physical; “π° in each half-cycle” overestimates and ignores α.

Common Pitfalls:

Mixing half-cycle and full-cycle accounting; forgetting that the freewheel path dominates after mains zero-crossing.

Final Answer:

(π − α)° in each cycle