⚡ Pulse Radar Virtual Laboratory

Undergraduate Electrical Engineering | RF & Microwave Systems

1. Theoretical Background

1.1 Basic Principle

A pulse radar transmits short bursts (pulses) of radio frequency energy and detects the echoes reflected from targets. By measuring the time delay between transmission and reception, the distance to the target can be determined.

1.2 Range Equation

The fundamental relationship in radar systems is the time delay measured to determine target range:

R = (c × Δt) / 2

R: Target range (meters)
c: Speed of light ≈ 3 × 10⁸ m/s
Δt: Round-trip time delay (seconds)

1.3 Radar Range Equation

The maximum detection range depends on system parameters:

R_max = [(P_t × G² × λ² × σ) / ((4π)³ × k × T₀ × B × F × (S/N)_min)]^1/4

Simplified Form: For quick calculations, we often use:

R_max ∝ (P_t × τ)^1/4

where τ is the pulse width.

1.4 Pulse Repetition Frequency (PRF)

The PRF determines how often pulses are transmitted:

PRF = 1 / T_p

where T_p is the pulse repetition period.

Maximum Unambiguous Range: If the echo returns after the next pulse is transmitted, range ambiguity occurs.

R_unambiguous = c / (2 × PRF)

1.5 Range Resolution

The ability to distinguish between two closely spaced targets:

ΔR = (c × τ) / 2

where τ is the pulse width. Shorter pulses provide better resolution but require higher peak power for the same detection range.

1.6 Duty Cycle

The ratio of pulse duration to pulse repetition period:

D = τ / T_p = τ × PRF

Average power: P_avg = P_peak × D

1.7 Doppler Effect (Supplementary)

While primarily a ranging system, pulse radar can detect velocity through pulse-to-pulse phase changes:

f_d = (2 × v_r) / λ

where v_r is the radial velocity and λ is the wavelength.

Block Diagram Description

A basic pulse radar consists of:

Transmitter: Generates high-power RF pulses (magnetron or klystron)
Duplexer: Switches antenna between transmitter and receiver
Antenna: Directional beam transmission and reception
Receiver: Low-noise amplification and down-conversion
Display: A-scope (amplitude vs. range) or PPI (plan position indicator)
Timing Unit: Controls PRF and synchronization

2. Interactive Radar Simulation

System Parameters

Target Range (km)

25 km

Pulse Width (μs)

1.0 μs

PRF (Hz)

1000 Hz

Peak Power (kW)

100 kW

Target RCS (m²)

10 m²

Frequency (GHz)

3.0 GHz

A-Scope Display (Amplitude vs Range)

Time Domain (Transmitted & Received Pulses)

Calculated Results

Two-Way Time Delay: 0.167 ms

Range Resolution: 150 m

Max Unambiguous Range: 150 km

Duty Cycle: 0.1%

Average Power: 100 W

Received Power (Pr): -85.2 dBm

Signal-to-Noise Ratio (SNR): 18.5 dB

Note: The simulation assumes standard atmospheric conditions (no attenuation) and a simplified radar equation model for educational purposes.

3. Experimental Procedure

Safety Notice: This is a virtual simulation. In actual laboratory settings with hardware radar systems, RF safety protocols must be followed to prevent exposure to high-power microwave radiation.

Objective

To understand the principles of pulse radar operation, measure target range, and analyze the effects of system parameters (PRF, pulse width, power) on radar performance.

System Familiarization

Launch the simulation and identify all control parameters. Observe the default settings:

Target Range: 25 km
Pulse Width: 1 μs
PRF: 1000 Hz
Peak Power: 100 kW

Observe both the A-scope display and the time-domain visualization.

Range Measurement

Vary the target range from 5 km to 80 km in steps of 5 km. For each setting:

Record the two-way time delay from the display
Calculate the range using: R = c × Δt / 2
Compare calculated range with set range
Record received power level

Analysis: Verify that the time delay increases linearly with range. Plot measured vs. actual range.

Range Resolution Analysis

Set the target range to 30 km. Vary the pulse width:

Minimum: 0.1 μs (ΔR = 15 m)
Maximum: 10 μs (ΔR = 1500 m)

Observe how the pulse width affects the pulse width on the A-scope display.

Question: What is the minimum separation required between two targets at 30 km and 35 km to resolve them separately?

PRF and Ambiguous Range

Set target range to 60 km. Vary PRF from 500 Hz to 5000 Hz:

Calculate unambiguous range: R_unamb = c/(2×PRF)
Identify when the target becomes ambiguous (echo appears at false range)
Record the critical PRF where aliasing occurs

Observation: At high PRF, note how second-time-around echoes appear.

Power Budget Analysis

Set target at 50 km, PRF = 1000 Hz. Vary peak power from 10 kW to 1000 kW:

Record received power (P_r) for each setting
Verify the relationship: P_r ∝ P_t and P_r ∝ 1/R⁴
Calculate system loss factor

Fix power at 100 kW and vary RCS from 0.1 m² to 100 m². Plot received power vs. RCS in dB scale.

Complete System Analysis

Design a radar system to detect a small aircraft (RCS = 2 m²) at 100 km range with SNR > 13 dB:

Determine required pulse width for 150 m resolution
Calculate minimum PRF to avoid ambiguity
Estimate required peak power
Verify your design using the simulation

Data Tables

Copy these tables into your lab notebook:

Table 1: Range vs Time Delay

Set Range (km)	Measured Δt (μs)	Calculated Range (km)	Error (%)	Received Power (dBm)
5
15
25
50
75

Table 2: Pulse Width vs Resolution

Pulse Width (μs)	Theoretical Resolution (m)	Observed Pulse Width (div)	Duty Cycle (%)
0.1
0.5
1.0
5.0
10.0

4. Report Writing Guidelines

Structure Requirements

Your laboratory report should follow this professional format (10-15 pages):

Title Page - Course name, experiment title, student name, date, instructor name
Abstract - Brief summary (150-200 words) of objectives, methods, and key findings
Introduction - Background on pulse radar applications and relevance
Theoretical Background - Derived radar equations used in analysis (not copied from manual)
Experimental Setup - Description of simulation parameters and configurations
Results & Discussion - Data tables, graphs, analysis, and error discussion
Conclusion - Summary of findings and engineering implications
References - IEEE format citations
Appendix - Raw data and supplementary calculations

Required Figures & Diagrams

Block diagram of pulse radar system (hand-drawn or CAD)
Plot of Range vs. Time Delay (theoretical and experimental overlay)
Graph of Received Power vs. Range (log-log scale showing 1/R⁴ dependence)
A-scope display sketches or screenshots for three different configurations
SNR vs. Range plot for different RCS values
Range resolution visualization showing pulse width effects

Key Analysis Questions

Address these questions in your discussion section:

Explain why the range calculation uses cΔt/2 rather than cΔt.
Discuss the trade-off between pulse width (resolution) and maximum detection range.
How does PRF selection affect the unambiguous range? Provide numerical examples from your data.
Calculate the processing gain achieved through pulse compression (if applicable to your simulation).
Analyze the power budget: What percentage of transmitted power is actually received?
Discuss real-world factors not included in this simulation (atmospheric attenuation, clutter, multipath).

Error Analysis Requirements

Include quantitative error analysis:

Calculate percentage error for all range measurements
Discuss sources of uncertainty in simulation parameters
Perform propagation of error for calculated quantities (e.g., if time measurement has ±1% error, what is the range error?)
Compare theoretical radar equation predictions with simulated values

Grading Rubric

Component	Weight	Criteria
Theoretical Background	20%	Correct equations, proper derivation, clear explanations
Data Presentation	25%	Complete tables, proper units, clear graphs with labels
Analysis & Discussion	30%	Insightful interpretation, answers to questions, error analysis
Technical Quality	15%	Professional formatting, correct terminology, IEEE references
Conclusion	10%	Summarizes findings, engineering significance, future improvements

Academic Integrity: While collaboration on understanding concepts is encouraged, all data analysis, plots, and written text must be your own work. Copying of graphs or tables from other students constitutes academic misconduct.

Submission: Submit your report as a single PDF file including all figures embedded. Name the file: RadarLab_LastName_FirstName_StudentID.pdf. Due date: One week after laboratory session.