Radar timing – Compute the duty cycle from pulse width and PRF A pulsed radar transmits rectangular pulses of width 1 microsecond (1 μs) at a pulse repetition rate of 1000 pulses per second. What is the duty cycle (fraction of time the transmitter is on)?

Introduction:
Duty cycle in pulsed radar quantifies how much of each second the transmitter actually radiates energy. It is vital for estimating average power, thermal loading, and receiver protection timing. The concept ties directly to pulse width and pulse repetition frequency (PRF).

Given Data / Assumptions:

• Pulse width τ = 1 μs = 1 * 10^-6 s per pulse.
• PRF f_p = 1000 pulses per second.
• Rectangular pulses, negligible rise/fall for this calculation.

Concept / Approach:

Duty cycle D is the fraction of time the transmitter is on: D = τ * f_p. It is dimensionless and often expressed as a ratio or percentage. Average power equals peak power multiplied by D, so accurate D helps size power supplies and cooling systems.

Step-by-Step Solution:

Verification / Alternative check:

Compute on a per-second basis: total “on” time per second = 1000 pulses * 1 μs = 1000 μs = 1 ms; 1 ms / 1 s = 0.001—consistent.

Why Other Options Are Wrong:

0.01 and 0.1 imply 1% and 10%, which would require 10 μs or 100 μs pulses at 1 kHz. “1” would mean continuous wave (100% duty). 0.0001 corresponds to 0.01% (e.g., 0.1 μs at 1 kHz), not the given case.

Common Pitfalls:

Mixing μs and ms; forgetting that PRF is per second; confusing duty cycle with duty factor in decibels.

Final Answer:

0.001.