Digital pulses and duty cycle: which formula correctly defines the duty cycle of a repetitive pulse train (express your answer in terms of pulse width and period)?

Introduction / Context:The duty cycle of a digital or pulse waveform is a core timing specification used in electronics, embedded systems, and communications. It tells us what fraction of each full period a signal remains in its active (usually logic HIGH) state. Understanding the correct formula is essential for power calculations, PWM motor control, LED dimming, and clock timing budgets.

Given Data / Assumptions:

• A repetitive pulse train with a well-defined period T.
• Pulse width (also called TON or HIGH time) is the time the pulse stays active within each period.
• Duty cycle is typically expressed as a percentage.

Concept / Approach:The duty cycle compares the active time of the signal to its total cycle time. If a signal is HIGH for half the period, its duty cycle is 50%. Expressing this as a formula, we divide the pulse width by the period and then multiply by 100% to convert to a percentage.

Step-by-Step Solution:Let pulse width = TON, period = T.Compute the fraction of the period that is HIGH: TON / T.Convert to percent: duty cycle = (TON / T) * 100%.Therefore, Duty cycle = (pulse width / period) * 100%.

Verification / Alternative check:If the pulse is HIGH for 2 ms and the period is 10 ms, then duty cycle = (2/10)*100% = 20%, matching intuitive expectations. If pulse width equals period, duty cycle is 100%; if pulse width is zero, it is 0%.

Why Other Options Are Wrong:

• Duty cycle = (rise time / period) * 100%: rise time measures edge speed, not the active fraction.
• Duty cycle = (fall time / pulse width) * 100%: mixes edge parameter with width; not a definition.
• Duty cycle = (period / pulse width) * 100%: the reciprocal; would exceed 100% for typical pulses.

Common Pitfalls:

• Confusing frequency with duty cycle; frequency changes period, but duty cycle remains a ratio.
• Mixing average value with duty cycle; average depends on amplitude as well as duty cycle.

Final Answer:Duty cycle = (pulse width / period) * 100%