In radar engineering, the duty cycle of a pulsed transmitter is defined as the fraction of time the RF is ON during one pulse-repetition interval. If PRF is the pulse repetition frequency (in Hz) and pulse width is τ seconds, what is the correct expression for duty cycle?

Introduction / Context:
In pulsed radar, the transmitter emits short bursts of RF energy separated by silent intervals. The duty cycle quantifies how “busy” the transmitter is within each repetition period and directly affects average power, thermal loading, and system range versus resolution trade-offs.

Given Data / Assumptions:

• Pulsed operation with rectangular pulses for simplicity.
• PRF is the pulse repetition frequency in Hz (pulses per second).
• Pulse width τ is the duration of each pulse in seconds.
• Repetition period T = 1 / PRF.

Concept / Approach:

Duty cycle is the fraction of time the transmitter is ON in one PRF period. It is dimensionless and equals ON-time divided by total period. With ON-time = τ and period T = 1/PRF, duty cycle D = τ / T = τ * PRF.

Step-by-Step Solution:

Verification / Alternative check:

Average power P_avg equals peak power P_peak multiplied by duty cycle. If τ doubles at constant PRF, P_avg doubles, matching practical radar transmitter behavior.

Why Other Options Are Wrong:

• PRF / pulse width: Yields units of 1/s^2; not dimensionless.
• Pulsed width / PRF: Equals τ / (1/PRF) only if inverted; this gives duty *period, not a fraction.
• (Pulse width) + PRF: Adds incompatible quantities.
• 1 / (PRF * pulse width): The reciprocal of the correct expression.

Common Pitfalls:

Confusing PRF (Hz) with PRI (s); mixing average and peak powers; forgetting that duty cycle must be dimensionless and typically far less than 1 in radar.

Final Answer:

Duty cycle = PRF * (pulse width)