POP RADAR 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
warmup 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 commerciallyproduced components available to any manufacturer.
Interestingly, we had never tested this parameter before,
because it is irrelevant for the steadystate 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 outofcontrol reference frequency to change more.
For
the best Gunn oscillator we’ve tested, the error at 1/2mile
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 worstcase
Gunn oscillators we’ve tested.
