Maximum Range vs. Chirp-up Time

A lower slope extends the maximum measurable range.

 

 

c  speed of light S  chirp slope B_BB  baseband signal bandwidth

 

 

 

 

 

1. Chirp slope and  T_UP

The chirp slope is determined by the RF signal bandwidth and Tup,

and when B_RF is fixed, the slope decreases as T_UP increases.

 

 

 

 

 

 

2. Design Consideration

The maximum beat frequency must satisfy the ADC constraint.

 

B_BB is the bandwidth of baseband or IF signal and should be equal to or lager than f_b, max.

In practical FMCW radar design, f_b, max is typically designed with sufficient margin below the Nyquist frequency

to account for anti-aliasing filter roll-off, non-ideal analog behavior, and implementation tolerance.

 

 

f_s = 2.5MHz → f_Nyquist = f_s/2 = 1.25MHz
Beat Frequency Utilization	100%	80%	70%	50%	2.03%
Maximum Beat Frequency	1.25 MHz	1.00 MHz	0.875 MHz	0.625 MHz	25.4 kHz

 

 

 

 

 

3. Example

 

Items	Parameter	Value	Unit
RF/Chirp Bandwidth	B_RF	200	MHz
ADC Sampling Rate	f_s	2.5	MHz
Nyquist Frequency	f_Nyquist	1.25	MHz
Beat Frequency Utilization		2.03	%
Max Range	R_max	8	m

 

 

 

 

T_UP examples

Beat Frequency Max	1.25 MHz	0.875 MHz	25.4 kHz
T_UP @ Max range 8 m	8.53 µs	12.19 µs	420 µs
T_UP @ Max range 150m	160 µs	228.57 µs	7,874 µs