sampson@killer.DALLAS.TX.US (Steve Sampson) (09/18/88)
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I threw this together as an intro to police radar, for those interested.
Critique at will.
Public Domain (p) September 1988 by Steve R. Sampson
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POLICE RADAR, DETECTORS AND JAMMERS
INTRODUCTION
The radar systems used by police as well as detectors used by
the public, have matured and become more sophisticated over the
years. Some radars even have cameras attached now to photograph
the speeders. The cheapest radar detector on the market will
outperform the detector of even five years ago. All of them work
as advertised, that is, warn of radar emissions on two frequency
bands. Where you spend your money is in increased sensitivity and
optional features. The old crystal detector is fully obsolete and
superheterodyne detectors have become state of the art.
THE RADAR
The police radars operate in three frequency bands. The first
is X-Band with a frequency centered on 10.525 GHz (Giga-Hertz) and
13.45 GHz. The second is K-Band centered on 24.150 GHz. The third
is Ka-Band and is centered on 34.31 GHz. These radars are not very
sophisticated as far as frequency generation and transmission go.
They generally use a Gunn Diode in a tuned cavity connected to a
waveguide, circulator and antenna.
((Figure 1 ))
The circulator is simply a ferrite rod inserted into the waveguide.
The purpose of the circulator is to direct the transmitter power
out the antenna and the receive power to the mixer. In older
radars a Majic-T performed this duplexing function. The circulator
performs much better (by about 6 dB) and allows much smaller
antennas to be used. The mixer circuit is also quite simple,
usually consisting of a diode. The reflected target frequencys are
mixed with a sample of the transmitter frequency (which comes from
some of the power going around the circulator) producing an audio
frequency difference which is directly related to the velocity of
the target. Most of the improvements to the police radar have been
in the tracking circuitry.
This type of radar is called Continuous Wave (CW). Both the
transmitter and receiver are always on so there is no need for a
Local Oscillator (LO). The disadvantage of CW radars is that they
do not measure range. For police work however, the officer is only
concerned with immediate traffic and they can visually acquire the
target. With the radar tracking the fastest target, the officer
merely goes after the fastest moving vehicle. This procedure is
not complex or error prone as you might think. If an officer can't
decide who the offender is, they can wait for easier pickings or
provide a warning to both drivers to slow it down. The whole
purpose of traffic radar is to keep the traffic down at a safer
speed and penalize those who refuse. The fines come in handy when
it comes time to pay for all those that have killed or injured
themselves (gas for the fire trucks and ambulances, etc).
DOPPLER EFFECT
When a radar beam strikes a stationary target, such as the
ground or buildings, the same frequency returns as was transmitted.
When a radar beam strikes a moving target however, the frequency is
shifted relative to the speed of the target. The faster a target
is moving, the greater the frequency shift. This resulting
frequency shift is called a Doppler Shift. You can hear Doppler
shift in many activities. Race cars coming down the main stretch
for example, have an increasing frequency as they come towards you,
while decreasing in frequency as they go away. The formula for
Doppler shift in Hertz is:
((Formula 1 ))
The wavelength of the transmit frequency in centimeters can be
computed using:
((Formula 2 ))
For the police radar frequencies of 10.525 GHz, 24.150 GHz, the
wavelengths are 2.85, and 1.24 centimeters respectively. To find
the Doppler shift for each Mile Per Hour, simply substitute one (1)
for Velocity (V). This results in 31.35 Hz per MPH in X-Band and
72.06 Hz per MPH in K-Band. A car moving at 55 MPH would cause a
frequency shift of 1724.25 Hz at X-Band (55 x 31.35). This math is
done electronically using a frequency counter and gate divider in
the radar display.
To accurately measure the speed of a target the radar should
be pointed directly into the path of travel. The reason the Race
car frequency changes as it goes by, is because you are offset away
from the path of travel. The angle between you and the car are
constantly changing. If you get down next to the track, then only
one frequency will be heard as the car approaches, and one other as
it goes away. This principle is important to the police officer
also. They must point the radar into the traffic to get the true
speed. Any difference in angle results in an incorrect speed
(slower). The measured speed (Doppler shift) decreases as the
angle increases, until at 90 Degrees the speed is zero. An officer
pointing the radar at the side of your car would read zero even if
you were doing 200 MPH.
((Figure 2))
Engineers refer to this resulting speed as Range Rate. The symbol
for Range Rate is R (Dot Product, R with a dot over it), and the
formula to compute it is:
((Formula 3 ))
What this means is that the measured Range Rate is equal to the
ground speed at the speedometer; reduced by the radar angle. For
example a radar angle of 90 Degrees would result in zero Range Rate
(cosine of 90 degrees is zero). A radar angle of 0 Degrees, or
pointed directly into the oncoming traffic would be one (1) times
the cars speed, or the true speed (cosine of 0 Degrees is 1).
((Figure 2 ))
THE DETECTOR
Since the police radar is transmitting a signal, any receiver
tuned to the same frequency can detect it. In the early days
crystal diodes were used with an oscillator. The diodes were
placed in a waveguide cavity and caused the circuit to oscillate
when the radar frequency was detected. I bought one and the
sensitivity was poor, with range less than 1/4 of a mile. False
alarms were also a major problem. Various circuits and diodes were
used and sensitivity slowly increased over the years. It wasn't
until the advent of the superheterodyne detector that realistic
long ranges became available. The comparison in performance is not
unlike a crystal radio to a transistor radio. With the
superheterodyne circuit, a mixing signal is used to produce a high
frequency IF. This IF is then filtered and amplified resulting in
much better sensitivity and selectivity. Increasing range and
reducing false alarms.
((Figure 3))
The circuit complexity and microwave devices are still quite
expensive however, and that is the reason you pay about $150.00 for
this type of detector.
One problem with the detectors is there are many X-Band
transmitters out there. This frequency is very popular with
intrusion detectors and automatic door openers which will also set
off the alarm. For this reason many detectors provide a 'city' and
'highway' sensitivity. What this does is reduce the X-Band
sensitivity while leaving the K-Band alone. In my experience I've
found K-Band alarms were 99% associated with police radar, while
X-Band has many false alarms in the city. Every grocery store has
installed the new automatic sliding doors and the detectors can
pick them out over a block away. By using the 'city' position you
can knock many of these false alarms out. There is no way for the
detector to determine whether it's a police officer or a door; both
emit a CW signal that look identical. These sources of false
alarms do not go unnoticed by the police officers, and make a
perfect spot to nab someone with a radar detector.
The detectors have good sensitivity from behind also. Sooner or
later your detector will go off, and like everyone you'll start
looking for the source. Check that rear view mirror every now and
then!
THE JAMMER
In recent years many radar jammers have hit the streets in an
attempt to create an Electronic Counter-Measures (ECM) war. These
are totally ineffective without a high power level. The most
common jammer found is called an Amplitude Modulated (AM) CW
jammer. It usually consists of a Gunn diode modulated by a
selectable frequency (Doppler shift). The purpose of this type of
jammer is so a police officer would not suspect anything while you
reduced your speed. It's very easy to see why this type of jammer
provides limited offensive capability however. Just like an AM CB
radio, 50% of the power is in the carrier. The sidebands with the
jamming information contain only a fraction of the transmitter
power. That's why most radio operators use Single Sideband (SSB)
radios now. On top of that, the newer police radars lock on to the
highest speed when confronted with two signals of approximately the
same amplitude. The effective jamming power will probably be about
the same amplitude as your echo. The radar ignores the jammer and
locks on to the vehicle. These low power (100 milliwatt) jammers
only become effective at very close range. The fines for radar
jamming can run a small city for the rest of the year however, and
basically there is just no reasonable excuse for jamming tactics.
CONCLUSION
As we have seen, the CW police radar is quite simple in design
and has a significant ECM advantage due to its short operating
range. It performs its function easily with few errors or
limitations. The radar provides the police officer with an easy
method of measuring speed. The alternative is to put marks on the
highway, and using a stop-watch; manually calculate each vehicles
speed. This method takes time and gets quite boring after a few
minutes. Buying yourself a radar detector is easy insurance that
you won't be caught funding your state, county, or cities motor
pool. It's surprising that many habitual speeders do not invest in
detectors. Jammers are expensive and provide no advantage over
plain detection. The result is that jammer manufacturers are now
trying to sell their contraptions as radar calibrators for lack of
any other market. A two dollar tuning fork will perform that
function just as well.
Figure 1
A Block Diagram of a CW radar showing the basics
Figure 2
A picture of aiming the radar and the Range Rate (R Dot) error
Figure 3
A Block diagram of a superheterodyne detector
Formula 1
89.36 V
Fd = --------
L
V = Velocity in MPH
L = Wavelength of Transmitter in centimeters
Fd = Doppler Frequency in Hertz
Formula 2
30
L = ----
F
F = Transmitter Frequency in Giga-Hertz
L = Wavelength in centimeters
Formula 3
R = cos(theta) * V
V = Speedometer reading of target (true ground speed)
theta = Radar angle off the targets heading (negative for
closing, and positive for opening).
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EOF