📡 Radar Principles Virtual Laboratory

Measure the Speed of a Fan Using Doppler Radar Techniques

Undergraduate Electrical Engineering | Microwave & Communication Systems

🎯 Learning Objectives

Upon successful completion of this virtual laboratory experiment, students will be able to:

Understand the Doppler Effect: Explain the physical principles behind frequency shift observed when radio waves reflect off moving objects.
Apply Radar Equations: Use the Doppler shift formula to calculate the velocity of a moving target from observed frequency changes.
Analyze CW Radar Systems: Describe the operation of continuous-wave Doppler radar and its application in speed measurement.
Relate RPM to Linear Velocity: Convert rotational speed (RPM) of a fan to linear tip velocity and understand the relationship between angular and linear motion.
Evaluate Measurement Accuracy: Identify sources of error in Doppler measurements and suggest methods to improve precision.
Design Experiments: Propose appropriate radar parameters (carrier frequency, sampling rate) for measuring different speed ranges.
Interpret Spectral Data: Analyze frequency spectra to distinguish between target returns and noise or clutter.

                Prerequisites: Basic electromagnetics, signal processing fundamentals, and introductory microwave engineering. Familiarity with MATLAB/Python for data analysis is recommended but not required.
            

📚 Theory

1. The Doppler Effect in Radar Systems

When a radar transmitter emits a continuous wave at frequency f_c toward a moving target, the reflected signal experiences a frequency shift known as the Doppler shift. This phenomenon occurs because the motion of the target either compresses or stretches the wavelength of the reflected wave, depending on whether the target is moving toward or away from the radar.

For a monostatic radar (where transmitter and receiver are colocated), the round-trip path introduces a factor of 2 in the Doppler shift equation:

Doppler Shift Formula:

f_d = (2 · v · f_c) / c = (2 · v) / λ

Where:
f_d = Doppler frequency shift (Hz)
v = Target velocity component along radar line-of-sight (m/s)
f_c = Carrier/transmitted frequency (Hz)
c = Speed of light ≈ 3 × 10⁸ m/s
λ = Wavelength of transmitted signal (m)

The sign of f_d indicates direction: positive for approaching targets (frequency increases) and negative for receding targets (frequency decreases).

2. Fan Blade Tip Velocity

A rotating fan presents a unique radar target. While the hub is stationary, the blade tips move at maximum linear velocity. For a fan rotating at N RPM with blade radius r:

Angular Velocity: ω = 2πN / 60 (rad/s)

Tip Linear Velocity: v_tip = ω · r = (2πN · r) / 60 (m/s)

Where:
N = Rotational speed (revolutions per minute)
r = Blade radius (meters)

3. Practical Considerations for Fan Measurement

Measuring fan speed with radar presents several engineering challenges:

Blade Aspect Angle: Only the velocity component parallel to the radar beam contributes to Doppler shift: v_eff = v_tip · cos(θ), where θ is the angle between the blade tip velocity vector and the radar beam.
Multiple Returns: Different parts of the blade (hub, mid-span, tip) return signals with different Doppler shifts, creating a spread spectrum.
Blade Flashing: Rotating blades periodically present their broadside to the radar, causing strong but intermittent returns.
Micro-Doppler: The rotation creates sidebands around the main Doppler frequency, revealing the rotational signature.

4. Continuous Wave (CW) Doppler Radar Architecture

A basic CW Doppler radar for speed measurement consists of:

RF Oscillator: Generates a stable continuous wave at the carrier frequency (typically 1–24 GHz for laboratory applications).
Transmitter Antenna: Radiates the CW signal toward the target.
Receiver Antenna: Captures the reflected signal (often shared with transmitter via circulator).
Mixer: Combines transmitted and received signals to extract the Doppler frequency.
Low-Pass Filter: Removes high-frequency components, leaving only the Doppler shift.
Signal Processor: Performs FFT to identify peak Doppler frequency and calculate speed.

Measured Speed from Doppler Shift:

v = (f_d · c) / (2 · f_c)

Or in practical units:
v (m/s) = (f_d (Hz) × 0.15) / f_c (GHz)
v (km/h) = (f_d (Hz) × 0.54) / f_c (GHz)

5. Signal Processing

The received signal is processed using:

Fast Fourier Transform (FFT): Converts time-domain beat signal to frequency spectrum.
Windowing: Applies Hamming or Hanning windows to reduce spectral leakage.
Peak Detection: Identifies the dominant frequency component corresponding to the blade tip.
Clutter Rejection: Uses high-pass filtering to remove stationary object returns (DC component).

Important: In practical systems, the maximum unambiguous Doppler frequency is limited by the sampling rate (Nyquist criterion): f_s > 2 · f_d,max. For high-speed fans and high carrier frequencies, this requires fast analog-to-digital converters.

🔬 Interactive Simulation

Adjust the parameters below to simulate a Doppler radar measuring fan speed. Observe how carrier frequency, fan RPM, and blade radius affect the Doppler shift and calculated velocity.

Fan Speed (RPM): 1500

Radar Carrier Frequency: 10.0 GHz

Fan Blade Radius: 25 cm

Aspect Angle (θ): 0°

Simulation Speed: 1x

Tip Velocity

0.0

m/s

Doppler Shift

Measured Speed

0.0

m/s

Wavelength

0.0

Doppler Shift vs. Fan Speed Characteristic

📝 Experimental Procedure

Part A: Setup and Calibration

Equipment Check: Verify that the CW Doppler radar module is functioning correctly. Ensure the transmitter and receiver antennas are properly aligned and the oscillator frequency is stable.
Frequency Calibration: Using a spectrum analyzer, confirm that the transmitted carrier frequency matches the nominal value (e.g., 10.525 GHz for X-band modules). Record any deviation.
Zero-Velocity Test: Point the radar at a stationary metallic plate. Verify that the mixer output shows minimal signal (ideally DC only), confirming proper clutter rejection.
Distance Setup: Position the radar at a distance of 1–2 meters from the fan, ensuring the beam illuminates the blade tips. The radar boresight should be perpendicular to the fan rotation axis for maximum Doppler shift (θ = 0°).

Part B: Data Collection

Set the fan to its lowest speed setting (e.g., 500 RPM). Allow 30 seconds for the speed to stabilize.
Record the Doppler frequency from the spectrum analyzer or signal processor display. Take 5 consecutive readings and calculate the average.
Increase the fan speed in increments of 250 RPM. At each setting, repeat the measurement process.
Record the ambient temperature and humidity, as these affect air density and may slightly influence fan loading.
Repeat the entire measurement sequence for three different aspect angles: 0°, 30°, and 60°. Note how the effective velocity component changes.
Capture screenshots of the frequency spectrum at each operating point for your report.

Part C: Data Analysis

For each measurement, calculate the theoretical tip velocity using: v = 2πNr/60
Calculate the expected Doppler shift using: f_d = 2vf_c/c
Compare measured Doppler shifts with theoretical predictions. Compute percentage error for each data point.
Plot measured Doppler shift vs. theoretical velocity. Perform linear regression and determine the slope. Compare with theoretical slope (2f_c/c).
Analyze the spectrum at each point. Identify any sidebands or harmonics and explain their origin (blade passing frequency, motor vibrations).

                Safety Note: Although this is a virtual laboratory, in physical implementations, ensure RF exposure limits are respected. X-band radar modules typically emit low power (<20 dBm), but prolonged exposure should be minimized. Never look directly into transmitting waveguides or antennas.
            

🧪 Knowledge Assessment Quiz

Answer the following questions to test your understanding of Doppler radar principles and fan speed measurement. Click "Show All Answers" when ready to review.

📋 Laboratory Report Guidelines

A well-written laboratory report demonstrates your understanding of the theoretical principles, your ability to collect and analyze data, and your capacity to draw meaningful conclusions. Follow this structure:

1. Title Page & Abstract 5%

Title: "Measurement of Rotational Speed Using Doppler Radar"
Abstract (150-200 words): Briefly state the objective, methodology (CW Doppler radar at X-band), key results (measured vs. theoretical velocity correlation), and main conclusion (accuracy achieved, error sources identified).

2. Introduction & Objectives 10%

Explain the relevance of non-contact speed measurement in industrial applications.
State the specific objectives of this experiment (as listed in the Objectives section).
Include a brief literature review of Doppler radar applications (traffic monitoring, industrial process control, sports).

3. Theoretical Background 15%

Derive the Doppler shift equation for monostatic radar from first principles (wavelength compression).
Explain the relationship between angular velocity (RPM) and linear tip velocity.
Discuss the effect of aspect angle on measured velocity.
Include all relevant equations with proper variable definitions.

4. Experimental Setup & Procedure 10%

Provide a block diagram of the CW Doppler radar system (hand-drawn or using software).
List all equipment with specifications (radar module, spectrum analyzer, fan model, tachometer for reference).
Describe the measurement procedure in sufficient detail that another student could replicate it.
Include a photograph or diagram of the physical arrangement.

5. Results & Data Presentation 20%

Present your data in organized tables and graphs:

Fan Setting	Theoretical RPM	Measured f_d (Hz)	Calculated v (m/s)	Theoretical v (m/s)	Error (%)
Low	500	...	...	...	...
Medium	1500	...	...	...	...
High	3000	...	...	...	...

Plot Doppler shift vs. theoretical velocity with error bars.
Include representative spectrum screenshots at minimum, medium, and maximum speeds.
Show the effect of aspect angle in a separate plot or table.

6. Analysis & Discussion 25%

This is the most critical section. Address the following:

Error Analysis: Calculate systematic and random errors. Discuss sources: oscillator frequency drift, aspect angle uncertainty, blade flexing at high RPM, spectral leakage in FFT processing.
Linearity: Is the relationship between Doppler shift and velocity truly linear? Explain any deviations.
Spectrum Interpretation: What do the sidebands represent? Can you identify the blade passing frequency (BPF = RPM × N_blades/60)?
Aspect Angle: Does v_measured = v_tip·cos(θ) hold? Compare experimental and theoretical cosine dependence.
Limitations: What is the minimum detectable speed? What limits the maximum speed? How would you modify the system to measure a jet engine turbine (50,000 RPM)?

7. Conclusion 10%

Summarize whether the experiment successfully demonstrated Doppler radar speed measurement.
State the achieved accuracy quantitatively (e.g., "within ±3% for speeds above 5 m/s").
Suggest two specific improvements to the experimental method or equipment.

8. References & Appendices 5%

Cite at least 3 peer-reviewed sources or standard textbooks (e.g., Skolnik's Radar Handbook, Richards' Fundamentals of Radar Signal Processing).
Include raw data tables, additional spectra, and calibration records in appendices.

Formatting Requirements: 12-point Times New Roman or Arial, 1.5 line spacing, numbered equations, labeled figures and tables, page numbers, and professional binding or PDF submission. Maximum length: 15 pages excluding appendices.