How Does a Chirp Signal Detect Range of an Object?

 

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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

f(t) = f_c

The carrier frequency remains constant.

📈

Chirp Signal

f(t) = f₀ + Kt

The transmitted frequency continuously changes with time.

1️⃣ Steady-Frequency Radar

Suppose the radar continuously transmits a carrier at:

f_c = 10 GHz

If an object is moving toward or away from the radar, the reflected signal experiences a Doppler shift.

f_D = 2v / λ

λ = c / f_c

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.

5 GHz 1 GHz

Time →

1 GHz → 5 GHz

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.

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Radar

───────────────→

↓

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Target

←───────────────

↓

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Echo

If the target is at distance R , the signal travels to the target and back.

τ = 2R / c

Here τ 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.

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Transmitted Chirp

×

📥

Delayed Echo

Result

Beat Frequency

f_b = Kτ

5️⃣ From Beat Frequency to Range

We know:

f_b = Kτ

τ = 2R / c

Therefore:

R = c f_b / 2K

🎯 Main Idea

The radar converts a very small propagation delay into a measurable beat frequency.

🧮 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

f_b = 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.

f_b = Range Component + Doppler Component

📍 Range

Kτ

Depends on target distance.

🚗 Velocity

f_D

Depends on target motion.

🔬 FMCW Radar Signal Flow

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Chirp Generator

→

📤

Transmit

→

🎯

Target

→

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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

f_b = Kτ + f_D

Beat frequency contains information about both target distance and motion.