Digital waveforms and duty cycle In a certain rectangular digital waveform, the total period T is equal to four times the pulse width t_on (that is, T = 4 * t_on). Based on this ratio, what is the duty cycle of the signal expressed as a percentage?

Introduction / Context:
Duty cycle is a fundamental parameter for rectangular and pulse waveforms used in digital electronics, PWM motor control, switching power supplies, LED dimming, and timing systems. It tells us what fraction of one full period a signal remains in its active or HIGH state and is commonly expressed as a percentage.

Given Data / Assumptions:

• Total period T equals four times the pulse width t_on (T = 4 * t_on).
• Duty cycle D% is defined with respect to the time the signal is HIGH during one complete period.
• The pulse is a clean rectangular waveform without additional substructure.

Concept / Approach:

By definition, duty cycle in percent is computed as (t_on / T) * 100. When period and on-time are related by a simple ratio, we substitute that ratio directly into the formula to get the percentage. This definition is widely used across oscilloscopes, function generators, and data sheets for digital circuits.

Step-by-Step Solution:

Verification / Alternative check:

Imagine one complete period split into four equal segments. If the signal is HIGH for only one segment and LOW for the remaining three, exactly one fourth of the time is HIGH, confirming a 25 percent duty cycle.

Why Other Options Are Wrong:

• 0%: would require the signal never be HIGH, which contradicts having a nonzero t_on.
• 50%: would need t_on = T / 2, not T / 4.
• 100%: would mean always HIGH, impossible if T = 4 * t_on with finite LOW time.
• 75%: corresponds to t_on = 3 * T / 4, not given here.

Common Pitfalls:

• Confusing pulse width with period or mixing milliseconds and microseconds. Always keep consistent units.
• Interpreting duty cycle as LOW time percentage instead of HIGH time percentage. Some systems define active time differently; read the context carefully.

Final Answer:

25%