Cycloconverter with natural (line) commutation A step-down cycloconverter receives a sinusoidal input of frequency f. When natural (line) commutation is used, what restriction applies to the output frequency that can be synthesized?

Introduction / Context:
Cycloconverters directly convert AC at one frequency to AC at a lower frequency without an intermediate DC link. With natural (line) commutation, the thyristors turn off at current zero crossings of the supply. This operating principle constrains the possible output frequency to specific fractions of the input frequency, which is fundamental to understanding where cycloconverters are used (e.g., low-speed, high-power drives).

Given Data / Assumptions:

• Input frequency = f (sinusoidal AC source).
• Natural (line) commutation using thyristors.
• Step-down cycloconverter intended to produce a lower output frequency.
• Idealized wave synthesis using phase-controlled segments of the input.

Concept / Approach:

With line commutation, turn-off occurs only at natural current zero. Therefore, gating patterns must be synchronized to the input cycles. To build a lower-frequency output, the converter stitches together segments from successive input half-cycles following a repetitive pattern. Such repetitive patterns inherently repeat over an integer number of input cycles, which forces the output period to be an integer multiple of the input period. Hence, the output frequency is a sub-multiple of the input frequency, typically much lower (often f/3, f/5, etc.).

Step-by-Step Solution:

Verification / Alternative check:

Practical cycloconverter outputs are limited to fout ≲ f/3 to maintain acceptable waveform quality and commutation margins. This reinforces the sub-multiple relation and the low-frequency nature of line-commutated cycloconverters.

Why Other Options Are Wrong:

• Any frequency (option b): impossible with line-commutated thyristors since turn-off is tied to source zero-crossings.
• Even-only or odd-only sub-multiples (options c and d): there is no such parity restriction; both f/3, f/4, etc., are feasible in principle.

Common Pitfalls:

Confusing line-commutated cycloconverters with PWM inverters (which can synthesize a wide range of frequencies) and overlooking that commutation method dictates frequency constraints.

Final Answer:

It must be a sub-multiple of the input frequency.