Chirp
Understanding Chirp Signals
Chirp (also called linear frequency modulation, LFM) is the most important radar waveform after simple CW and pulsed CW. By transmitting a long duration signal with frequency sweep, the radar achieves both high energy (for detection range) and fine range resolution (from the bandwidth). The matched filter at the receiver compresses the chirp into a short pulse.
Chirp Parameters
- Bandwidth (B): Frequency sweep range. Determines range resolution: delta_R = c/(2B).
- Duration (T): Pulse length. Determines energy and uncompressed range extent.
- Time-bandwidth product (TB): Processing gain in pulse compression. TB = 10-10,000 typical.
- Chirp rate: B/T (Hz/s). Rate of frequency change.
Pulse Compression
The matched filter correlates the received signal with a replica of the transmitted chirp. This compresses the long pulse into a short pulse of width 1/B, improving range resolution by a factor of TB while maintaining the energy of the long pulse.
f(t) = f0 + (B/T) x t (increasing frequency)
Range resolution: delta_R = c / (2B)
100 MHz bandwidth: delta_R = 1.5 m
1 GHz bandwidth: delta_R = 0.15 m
Processing gain: PG = TB (time-bandwidth product)
T = 10 us, B = 100 MHz: TB = 1000 = 30 dB
Frequently Asked Questions
What is a chirp signal?
A chirp is a signal whose frequency sweeps linearly over time. In radar, a chirp pulse provides both high energy (long duration) and fine range resolution (wide bandwidth). The matched filter at the receiver compresses the chirp into a short pulse.
What determines range resolution?
Range resolution = c/(2B), where B is the chirp bandwidth. Wider bandwidth gives finer resolution. 100 MHz bandwidth provides 1.5 m resolution. 1 GHz provides 15 cm resolution. This is independent of the pulse duration.
What is pulse compression gain?
Pulse compression gain = time-bandwidth product (TB). A 10 us pulse with 100 MHz bandwidth has TB = 1000 (30 dB). This means the compressed pulse has the same peak power as a 10 ns pulse but 30 dB more energy, improving detection range.