Pulsed radar systems operate by transmitting short, high-power bursts (pulses) of electromagnetic energy and then listening for the echoes that return from targets during the quiescent (silent) period between transmissions. The time delay between the transmission of a pulse and the reception of its echo provides the range to the target, while the direction of the antenna indicates the target's angular position.

The process begins in the radar transmitter. High-power microwave pulses are generated by specialized electronic devices. Historically, magnetrons were common for their high peak power and simplicity, while klystrons offered higher coherence for Doppler processing. Modern systems increasingly use solid-state power amplifiers (SSPAs) for their reliability, efficiency, and flexibility. A modulator is a key component that controls the timing and duration of these high-power pulses. It essentially acts as a high-speed switch, turning the transmitter on for very brief periods. The output of the transmitter, a stream of RF pulses, is then fed to the antenna.

The Pulse Repetition Frequency (PRF) is defined as the number of pulses transmitted by the radar per second. It is a fundamental parameter that directly influences the radar's maximum unambiguous range and its ability to measure Doppler shifts. PRF=PRT1 where PRT is the Pulse Repetition Time, which is the total time from the start of one pulse to the start of the next pulse. The PRT includes both the pulse width and the listening time. A higher PRF means more pulses are transmitted per unit time, potentially allowing for more updates on target position or better Doppler resolution, but it also reduces the listening time between pulses, thereby limiting the maximum unambiguous range.

The pulse width (τ) (often denoted as Tp or τp ) is the temporal duration of a single transmitted radar pulse. It is a critical design parameter that affects several key radar performance metrics: ● Minimum Detectable Range: During the transmission of a pulse, the receiver is typically 'blanked' or desensitized to prevent it from being overwhelmed by the powerful outgoing signal. This means that targets too close to the radar, whose echoes return before the end of the transmitted pulse, cannot be detected. The minimum detectable range is approximately Rmin =2cτ. ● Range Resolution: A shorter pulse width provides better range resolution, allowing the radar to distinguish between targets that are closer together in range. ● Average Power: For a given peak power, a longer pulse width means more energy is transmitted over time, leading to higher average power and thus generally a longer detection range.

The Duty Cycle (D) of a pulsed radar is a dimensionless quantity that represents the fraction of time the radar transmitter is actively emitting energy. It is a crucial parameter for power calculations and thermal management. Duty Cycle (D) = Pulse Repetition TimePulse Width =PRTτ Using the relationship PRT=1/PRF, the duty cycle can also be expressed as: Duty Cycle (D) = τ×PRF The relationship between the average transmitted power (Pavg ) and the peak transmitted power (Ppeak ) is directly determined by the duty cycle: Pavg =Ppeak ×D=Ppeak ×τ×PRF This means that while the radar might transmit very high peak power during its brief pulses, its average power consumption and thermal dissipation are significantly lower, which is beneficial for radar design and operation.

The unambiguous range (Runamb ) is the maximum distance from which an echo can be received by the radar before the next pulse is transmitted. If an echo from a very distant target arrives after the transmission of the subsequent pulse, the radar will incorrectly associate it with the later pulse, leading to an ambiguous range measurement. This phenomenon is known as 'second-time around echoes' or 'range folding.' To avoid range ambiguity, the round-trip time for an echo from the most distant target of interest must be less than or equal to the Pulse Repetition Time (PRT). The round-trip time to a target at range R is τdelay =c2R. For unambiguous range, we require τdelay ≤PRT. Thus, c2Runamb =PRT. Rearranging for Runamb: Runamb =2c×PRT. Since PRT=1/PRF, we can also write: Runamb =2×PRFc. To detect targets at greater distances without ambiguity, the PRF must be reduced. However, reducing PRF can lead to issues with Doppler measurement (blind speeds) and a lower data rate. Radar designers must carefully choose the PRF to balance unambiguous range, data rate, and Doppler performance.

Range Resolution (ΔR) is a measure of a radar's ability to distinguish between two closely spaced targets that lie along the same radial line (i.e., at different ranges but roughly the same bearing from the radar). For a radar to resolve two targets, their reflected echoes must be separable in time. The minimum separation in range at which two targets can be resolved is determined primarily by the pulse width (τ). If two targets are closer than a certain distance, their echoes will overlap and appear as a single, elongated echo. For two targets to be resolved, the leading edge of the echo from the more distant target must arrive at the receiver after the trailing edge of the echo from the closer target. This requires a time separation of at least τ. The distance corresponding to this time separation is: ΔR=2c×Δt where Δt is the minimum time difference required for resolution, which is τ. Therefore, the range resolution is given by: ΔR=2c×τ. A shorter pulse width (τ) directly leads to better (smaller) range resolution, allowing the radar to discriminate between targets that are closer together in range. This is why radars requiring very fine range detail (e.g., for high-resolution imaging) use extremely short pulses.