Duty cycle of a pulse train: A 20 kHz rectangular pulse waveform contains pulses that are 15 µs wide. What is the duty cycle of this waveform?

Introduction / Context:Duty cycle indicates the fraction of each period during which a pulse waveform is ON (high). It is crucial in pulse-width modulation (PWM), digital timing, and power control applications, where average power or voltage depends linearly on duty cycle for a fixed amplitude and baseline.

Given Data / Assumptions:

• Frequency f = 20 kHz → period T = 1 / f.
• Pulse width (ON time) t_on = 15 µs.
• Rectangular pulse train with a consistent period and width.

Concept / Approach:Duty cycle D is defined as D = t_on / T expressed as a percentage. Convert frequency to period in microseconds to match the given width, then compute the ratio and multiply by 100% to get the percentage value.

Step-by-Step Solution:

Verification / Alternative check:Reasonableness: A 15 µs pulse within a 50 µs period must correspond to less than half the period. 30% is consistent (since 25 µs would be 50% at 20 kHz, so 15 µs is noticeably smaller).

Why Other Options Are Wrong:

• 1%: Would correspond to t_on = 0.5 µs at 20 kHz, not 15 µs.
• 100%: Would require a continuous ON signal with zero OFF time (t_on = T).
• cannot be determined: Not true; both width and period are given explicitly.

Common Pitfalls:

• Failing to convert kHz to µs for an easy ratio.
• Confusing frequency with angular frequency (20 kHz vs. 2πf).

Final Answer:is 30%