How Does a Chirp Signal Detect an Object?
Understanding the difference between steady-frequency radar and chirp-based FMCW radar.
The Basic Idea
A radar can transmit a radio-frequency signal and listen for the signal reflected from an object. The important difference is whether the transmitted frequency is constant or changes with time.
Steady-Frequency Signal
The carrier frequency remains constant.
Chirp Signal
The transmitted frequency continuously changes with time.
1️⃣ Steady-Frequency Radar
Suppose the radar continuously transmits a carrier at:
If an object is moving toward or away from the radar, the reflected signal experiences a Doppler shift.
fD = 2v / Ī»
Ī» = c / fc
What can we learn?
The Doppler frequency can tell us the target's radial velocity.
⚠️ Limitation of a Single CW Frequency
A simple continuous-wave radar is very good at measuring Doppler velocity, but it does not naturally provide the target's range.
Velocity
Can be obtained from Doppler frequency.
Range
Not directly obtained from a single CW frequency.
2️⃣ Chirp Radar
Instead of transmitting one constant frequency, the radar continuously changes its frequency.
f(t) = f0 + Kt
K = chirp slope
3️⃣ The Echo Is Delayed
When the chirp reaches an object, part of the signal is reflected back toward the radar.
Radar
Target
Echo
If the target is at distance R , the signal travels to the target and back.
Here Ļ is the round-trip propagation delay and c is the speed of light.
4️⃣ The Mixer Creates a Beat Frequency
The radar knows exactly what frequency it transmitted. It compares the current transmitted signal with the delayed received echo.
Transmitted Chirp
Delayed Echo
Result
Beat Frequency
fb = KĻ
5️⃣ From Beat Frequency to Range
We know:
fb = KĻ
Ļ = 2R / c
Therefore:
R = c fb / 2K
šÆ Main Idea
The radar converts a very small propagation delay into a measurable beat frequency.
š§® Example: Finding Target Distance
Start Frequency
1 GHz
End Frequency
2 GHz
Chirp Duration
1 ms
K = (2 GHz − 1 GHz) / 1 ms
K = 1012 Hz/s
Suppose the measured beat frequency is
fb = 100 kHz
R = (3 × 108 × 100 × 103) / (2 × 1012)
R = 15 m
6️⃣ What Happens When the Target Moves?
A moving target introduces an additional Doppler frequency shift.
š Range
KĻ
Depends on target distance.
š Velocity
fD
Depends on target motion.
š¬ FMCW Radar Signal Flow
Chirp Generator
Transmit
Target
Echo
Mixer
Beat Frequency
Range + Velocity
⚖️ Steady Frequency vs Chirp
| Feature | CW / Steady Frequency | Chirp / FMCW |
|---|---|---|
| Frequency | Constant | Changes with time |
| Doppler velocity | ✓ Yes | ✓ Yes |
| Target range | Difficult | ✓ Yes |
| Beat-frequency ranging | Not the normal approach | ✓ Main principle |
Remember This
CW Radar
Frequency difference → Doppler → Velocity
FMCW Radar
Chirp + Echo Delay → Beat Frequency → Range
Moving Target
Range information + Doppler information → Range + Velocity
fb = KĻ + fD
Beat frequency contains information about both target distance and motion.