Virtual Laboratory - Principles of the Pulse Radar

1. Objectives

After completing this virtual laboratory, the student will be able to:

Explain the fundamental principle of pulse radar operation: transmitting short electromagnetic pulses and measuring the round-trip time delay of the echo.
Calculate target range from the echo delay using R = c·Δt / 2.
Relate the pulse repetition frequency (PRF) to the maximum unambiguous range and explain range folding (ambiguities).
Relate pulse width to minimum detectable range and to range resolution.
Interpret a radar A-scope display and a plan-view pulse-propagation diagram.
Compute duty cycle, peak/average power, and Doppler shift for a pulsed radar.
Apply the basic radar equation to estimate received echo power.

2. Theory

2.1 Basic Principle

A pulse radar determines the distance to a target by transmitting a short burst (pulse) of electromagnetic energy and measuring the time Δt that elapses until the echo reflected by the target returns to the receiver. Because the wave travels to the target and back, the total path length is 2R:

R = c·Δt / 2 R = target range (m), c = 3×10⁸ m/s, Δt = round-trip echo delay (s)

The radar cannot transmit and receive on the same antenna at the same instant, so a duplexer (T/R switch) connects the antenna alternately to the transmitter and the receiver.

2.2 Block Diagram

The essential blocks of a basic pulse radar are:

Timer (synchronizer) – triggers the transmitter at the pulse repetition frequency and starts the range sweep.
Transmitter – generates high-power RF pulses of width τ.
Duplexer – switches the antenna between transmitter and receiver.
Antenna – radiates the pulses and collects the echoes (directional, often scanning).
Receiver – amplifies and demodulates the weak echo (superheterodyne, with matched filter).
Display (A-scope / PPI) – shows echo amplitude versus time (range).

Figure 1. Basic pulse radar block diagram. Solid blue lines: transmit and timing paths; dashed orange lines: echo path.

2.3 Timing Quantities

Quantity	Symbol	Relation	Meaning
Pulse width	τ	—	Duration of each transmitted pulse
Pulse repetition frequency	PRF	PRF = 1/T_p	Number of pulses transmitted per second
Pulse repetition interval	T_p	T_p = 1/PRF	Time between successive pulses
Duty cycle	D	D = τ·PRF = τ/T_p	Fraction of time the transmitter is on
Average power	P_av	P_av = P_peak·D	Mean transmitted power
Minimum range	R_min	R_min = c·τ/2	Closest range whose echo returns after the pulse ends
Range resolution	ΔR	ΔR = c·τ/2	Minimum separation to distinguish two targets
Max unambiguous range	R_u	R_u = c/(2·PRF)	Longest range measurable without echo folding

Range ambiguity (folding): if the target is farther than R_u, its echo arrives after the next pulse has already been transmitted. The radar then assigns the echo a folded (shorter) range R_folded = R mod R_u. To measure long ranges unambiguously, a low PRF is required.

Doppler dilemma: a high PRF gives a large unambiguous Doppler (velocity) measurement but a small unambiguous range, and vice versa. This trade-off is fundamental to pulsed radar design.

2.4 The Radar Equation (peak-power form)

P_r = P_t G² λ² σ / [ (4π)³ R⁴ L ] P_r = received echo power, P_t = peak transmitted power, G = antenna gain, λ = wavelength, σ = radar cross section (RCS) of the target, R = range, L = system losses

The echo power falls with the fourth power of range – the reason radar requires high peak power and sensitive receivers.

2.5 Doppler Shift

f_d = 2 v_r / λ f_d = Doppler shift (Hz), v_r = radial velocity (m/s), λ = c/f_c

A moving target shifts the carrier frequency of the echo; measuring f_d yields the target’s radial velocity (approaching targets give a positive shift).

2.6 A-Scope Display

The A-scope plots received signal amplitude versus time (equivalently, range) for one pulse repetition interval. The transmitted pulse appears at t = 0 and the echo appears at t = 2R/c. The sweep time corresponds to the maximum displayed range; echoes beyond R_u appear folded back into the display.

3. Procedure

Open the Simulation section below. Familiarize yourself with the controls: PRF, pulse width, target range, radial velocity, and peak power.
Set the default values (PRF = 1 kHz, τ = 1 µs, range = 60 km, v = 0). Press Start and observe:
- The expanding ring in the plan view represents the transmitted pulse; the returning ring represents the echo.
- The echo delay on the A-scope; verify that the measured range equals the true range.
Experiment 1 – Range measurement: vary the target range from 10 km to 100 km in steps of 15 km. Record the measured range and echo delay for each setting. Confirm that R = c·Δt/2.
Experiment 2 – Pulse width: set range = 30 km and vary τ from 0.5 µs to 5 µs. Observe the minimum-range limit R_min = cτ/2 and the effect on range resolution.
Experiment 3 – PRF and ambiguity: fix range = 120 km and increase the PRF until the echo folds. Record the PRF at which folding begins and compare with PRF = c/(2R).
Experiment 4 – Doppler: set a non-zero radial velocity and observe how the measured range changes with time and how the Doppler shift readout varies with carrier frequency.
Experiment 5 – Radar equation: vary the peak power and target RCS and record the received echo power; verify the R⁻⁴ dependence by doubling the range.
Pause the simulation, capture the required plots/screens, and complete the laboratory report following the guidelines below.

4. Simulation

The simulation shows a pulsed radar at the origin transmitting pulses at the selected PRF. The transmitted pulse propagates outward as an expanding ring; when it reaches the target, an echo ring returns to the radar. The A-scope below shows the received signal versus range for one pulse repetition interval, with a moving sweep line.

PRF 1000 Hz Pulse width τ 1.0 µs Initial target range 60 km Radial velocity 0 m/s Peak power 1 MW Carrier frequency 3.0 GHz Target RCS σ 10 m² Antenna gain G 30 dB

Plan View — Pulse Propagation (rings move at the speed of light)

Transmitted pulse Echo Target

A-Scope — Echo Amplitude vs Range (one pulse repetition interval)

Echo delay Δt

—

Measured range

—

True range

—

Max unamb. range R_u

—

Min range R_min

—

Duty cycle

—

Doppler shift f_d

—

Received P_r

—

5. Guidelines for Report Writing

Prepare your laboratory report as a single document (PDF or DOCX) containing the following sections:

Title page – laboratory title, course code, student name(s), ID, date, instructor.
Objectives – state the objectives of the experiment in your own words.
Theory – briefly summarize the pulse-radar principle, the range equation R = cΔt/2, the definitions of PRF, pulse width, duty cycle, minimum range, and maximum unambiguous range. Include one simplified block diagram (hand-drawn or computer-generated).
Procedure – describe, step by step, what you did in each experiment (including all parameter settings).
Results – present:
- Tables of measured range, echo delay, R_u, R_min, duty cycle, Doppler shift, and received power for every experiment.
- Annotated screenshots of the plan view and A-scope for at least three representative settings.
- Graphs: measured range vs true range (Experiment 1); measured power vs range on log-log axes verifying the R⁻⁴ law (Experiment 5).
Analysis and Discussion – answer:
- Why is the measured range equal to cΔt/2 and not cΔt?
- At what PRF does range folding occur for a 120 km target, and why?
- How do pulse width and PRF trade off against each other in radar design (the Doppler dilemma)?
- What happens to the echo power when the range doubles, and does the simulation agree with theory?
Conclusions – summarize the key findings in 4–6 sentences.
References – cite the lecture notes and at least one textbook (e.g., Skolnik, Introduction to Radar Systems).

Grading emphasis: correctness of calculations (40%), quality of plots and tables (25%), depth of discussion (25%), and presentation/formatting (10%). Reports must show sample calculations with units for at least two settings.