Duty cycle statement check: In a pulse waveform, the duty factor is defined as the ratio T/d (period over pulse width). Is this statement correct?

Introduction / Context:The duty factor (also called duty cycle) is a basic descriptor of periodic pulse trains, widely used in sampling, switching power converters, digital logic timing, and pulse-width modulation. Knowing its correct definition avoids design and interpretation errors.

Given Data / Assumptions:

• A periodic pulse train with period T and on-time (pulse width) d.
• Duty factor commonly expressed as a fraction or percentage.
• Rise/fall times are not part of the ideal definition.

Concept / Approach:

By definition, duty factor D = (pulse width) / (period) = d / T. When expressed in percent, Duty % = 100 × (d/T). The inverse T/d is not the duty factor; it is simply the reciprocal and has different engineering meaning (average switching cycles per on-duration).

Step-by-Step Solution:

Verification / Alternative check:

Check extreme cases: If the signal is always on (d = T), D = 1 (100%). The reciprocal T/d would give 1 also here, but for small on-times (e.g., d = T/10), D = 0.1 (10%) while T/d = 10, clearly not a proper duty factor.

Why Other Options Are Wrong:

• True or conditional statements (symmetric pulses, aperiodic) do not change the definition.
• Dependence on rise time: ideal duty factor definition does not include edge slopes.

Common Pitfalls:

• Confusing duty cycle with its reciprocal, particularly when computing average values in PWM converters.
• Mixing up frequency f = 1/T with duty factor d/T.

Final Answer:

False