START-UP CHIRP — HERE'S THE MATH

The POP^tm burst works by cold starting the radar’s Gunn oscillator, and its 67 ms duration is shorter than the component’s warm-up time, so the entire POP takes place in a period of frequency transition. The chirp rate is a measure of frequency change per unit time during this POP. We tested the one MPH BEE III^tm available to us and determined the chirp rate of its Gunn oscillator.

What would be the chirp rate of other BEE IIIs? As a way to create an envelope of possibilities, we tested quite a few Gunn oscillators in our own stock (we buy them for test gear we design for use in our laboratory) and we confirmed that our BEE III sample falls within the range of commercially-produced components available to any manufacturer. Interestingly, we had never tested this parameter before, because it is irrelevant for the steady-state applications intended for these components.

The best rate (lowest) in our test is -0.0198 Hz/nsec; the worst is -1.069 Hz/nsec.

During a POP burst, this frequency change adds (or subtracts, depending upon direction of vehicle travel) to the Doppler shift, causing an error in the speed reading.

The Doppler shift used by the BEE III operating on a Ka band at 33.800 GHz to calculate speed of the target vehicle is based on the following formula: 1 mph = 100.803 Hz.

The Doppler shift error rate due to chirp is determined by the following formula: chirp rate in Hz/nsec multiplied by propagation delay of light (inverse of speed) in nsec/ft. The best (lowest) rate of Doppler shift error in our sample is -0.02015 Hz/ft of wave travel; the worst is -1.087 Hz/ft.

The actual Doppler shift error increases with distance the wave must travel (out to the target and back) as follows: Doppler shift error rate multiplied by total distance.

Distance matters here because radar works by comparing the frequency of a transmitted beam to the frequency of a returning echo of that beam. Since the echo is being returned from a moving target, the echo frequency is either higher (for approaching targets) or lower (for departing targets) by the amount of the Doppler shift. If the frequency being transmitted changes before the echo returns, then the returning frequency will be compared to a fictitious reference. Longer distances increase the time before return, allowing an out-of-control reference frequency to change more.

For the best Gunn oscillator we’ve tested, the error at 1/2-mile range calculates as follows: 0.02015 Hz/ft multiplied by 2640 ft multiplied by 2 (out and back) divided by 100.803 Hz/mph = 1.1 mph.

For the worst, 1.087 Hz/ft multiplied by 2640 ft multiplied by 2 (out and back) divided by 100.803 Hz/mph = 56.9 mph.

The following table shows the radar error for best- and worst-case Gunn oscillators we’ve tested.