UNIT -2
DOPLLER EFFECT
It is well known in the fields of optics and acoustics that if either the
source of oscillation or the observer of the oscillation is in motion, an
apparent shift in frequency will result. This is the doppler effect and is the
basis of CW radar
A radar detects the presence of objects and locates their position in space
by transmitting electromagnetic energy and observing the returned echo.
A pulse radar transmits a relatively short burst of electromagnetic
energy, after which the receiver is turned on to listen for the echo.
The echo not only indicates that a target is present, but the time that
elapses between the transmission of the pulse and the receipt of the
echo is a measure of the distance to the target.
Separation of the echo signal and the transmitted signal is made on the
basis of differences in time.
• The radar transmitter may be operated continuously
rather than pulsed if the strong transmitted signal can
be separated from the weak echo.
• The received-echo-signal power is considerably smaller
than the transmitter power; it might be as little as 10-
18
that of the transmitted power-sometimes even less.
• Separate antennas for transmission and reception help
segregate the weak echo from the strong leakage signal,
but the isolation is usually not sufficient.
• A feasible technique for separating the received signal
from the transmitted signal when there is relative
motion between radar and target is based on
recognizing the change in the echo-signal frequency
caused by the doppler effect.
If R is the distance from the radar to target, the total number of
wavelengths λ. contained in the two-way path between the radar and the
target is 2R/ λ The distance R and the wavelength λ are assumed to be
measured in the same units.
Since one wavelength corresponds to an angular excursion of 2π radians, the
total angular excursion ф, made by the electromagnetic wave during its
transit to and from the target is 4 π R/ λ radians
• If the target is in motion, R and the phase ф,
are continually changing. A change in ф , with
respect to time is equal to a frequency . This
is the doppler angular frequency wd, given by
The relative velocity may be written Vr, = v cos Ѳ,
where v is the target speed and Ѳ is the angle
made by the target trajectory and the line joining
radar and target. When Ѳ = 0, the doppler
frequency is maximum. The doppler is zero when
the trajectory is perpendicular to the radar line of
sight (Ѳ = 90°).
CW RADAR
• Consider the simple CW radar as illustrated by the block diagram of Fig. 3.2a.
• The transmitter generates a continuous (unmodulated) oscillation of
frequency .fo, which is radiated by the antenna. A portion of the radiated energy
is intercepted by the target and is scattered, some of it in the direction of the radar,
where it is collected by the receiving antenna.
Can the same antenna receive and
transmit signals at the same time?
• Yes, and often to save space and costs engineers
will do this (it’s less effective than having multiple
antennas, but there are plenty of factors that go
into design choices and often sacrificing the
second antenna is worth some other benefit).
• The interesting part happens behind the antenna.
We want to be able to separate the transmitted
and received signals, so that we can process the
received signal without interference. This is done
using what is known as a circulator
• A circulator is a passive (meaning unpowered) device that
typically uses ferrites (magnets) to make sure that signals can
only travel in one direction through it. It typically has three
‘ports’, labeled as 1, 2, and 3 above. So in the image above,
any signal coming in on port one can only go to port two.
Same for two to three, and three to one. Just follow the
arrow!
• Using this, we can set up our antenna and transmit and
receive signals as such. We put the antenna on one port, say
in our case we put it on port one. The transmit line would
then feed into port three, and the receive line would come
out from port two. The signal going into port three is
redirected entirely to port one containing the antenna,
which radiates out. Any radiation picked up by the antenna
on port one is redirected entirely to port two, which is what
we had designated as our receive line. Since we never send
information out on the receive line, a signal doesn’t go into
port two, and so nothing travels out of port three.
• In this way, the transmit and receive signals are isolated
from each other. This component usually happens at the
very front of a transceiver, perhaps after only the antenna
and a filter.
• If the target is in motion with a velocity v, relative to the radar, the
received signal will be shifted in frequency from the transmitted
frequency fo by an amount ± fd as given by Eq. (3.2).
• The plus sign associated with the doppler frequency applies if the
distance between target and radar is decreasing (closing target), that
is, when the received signal frequency is greater than the transmitted
signal frequency.
• The minus sign applies if the distance is increasing (receding target).
The received echo signal at a frequency fo ±.fd enters the radar via
the antenna and is heterodyned in the detector (mixer) with a
portion of the transmitter signal fo to product a doppler beat note
of frequency fd
• The purpose of the doppler amplifier is to
eliminate echoes from stationary targets and
to amplify the doppler echo signal to a level
where it can operate an indicating device.
• It might have a frequency-response
characteristic similar to that of Fig. 3.2b.
• The low-frequency cutoff must he high
enough to reject the d-c component caused
by stationary targets.
• The upper cutoff frequency is selected to pass
the highest doppler frequency expected.
• The indicator might be a pair of earphones or
a frequency meter
• Earphones are not only simple devices. but
the ear acts as a selective bandpass filter with
a passband of the order of 50 Hz centered
about the signal frequency.
• The narrow-bandpass characteristic of the
ear results in an effective increase in the
signal-to-noise ratio of the echo signal
• the doppler frequencies usually fall within
the passband of the ear
ISOLATION BETWEEN TRANSMITTER AND RECEIVER
A single antenna serves the purpose of transmission and
reception in the simple CW radar described above.
A single antenna may be employed since the necessary
isolation between the transmitted and the received
signals is achieved via separation in frequency as a result
of the doppler effect.
In practice, it is not possible to eliminate completely the
transmitter leakage. However, transmitter leakage is not
always undesirable.
A moderate amount of leakage entering the receiver
along with the echo signal supplies the reference
necessary for the detection of the doppler frequency
shift
• There are two practical effects which limit the
amount of transmitter leakage power which can
be tolerated at the receiver. These are
• ( 1) the maximum amount of power the
receiver input circuitry can withstand before it is
physically damaged or its sensitivity reduced
(burnout) and
• (2) the amount of transmitter noise due to hum,
microphonics, stray pick-up, and instability
which enters the receiver from the transmitter.
• The additional noise introduced by the transmitter
reduces the receiver sensitivity
• The amount of isolation required depends on the
transmitter power and the accompanying transmitter
noise as well as the ruggedness and the sensitivity of
the receiver. For example, if the safe value of power
which might be applied to a receiver were 10 mW and
if the transmitter power were l kW, the isolation
between transmitter and receiver must be at least 50
dB.
• If complete elimination of the direct leakage signal at
the receiver could be achieved, it might not entirely
solve the isolation problem since echoes from nearby
fixed targets (clutter) can also contain the noise
components of the transmitted signal
• the receiver of a pulsed radar is isolated and protected from the
damaging effects of the transmitted pulse by the duplexer, which
short-circuits the receiver input during the transmission period.
Turning off the receiver during transmission with a duplexer is not
possible in a CW radar since the transmitter is operated continuously.
• Isolation between transmitter and receiver might be obtained with a
single antenna by using hybrid junction, circulator, turnstile
junction, or with separate polarizations. Separate antennas for
transmitting and receiving might also be used.
• The amount of isolation which can be readily achieved between the
arms of practical hybrid junctions such as the magic-T, rat race, or
short-slot coupler is of the order of 20 to 30 dB.
• In some instances, when extreme precision is exercised, an isolation
of perhaps 60 dB or more might be achieved. One limitation of the
hybrid junction is the 6-dB loss in overall performance
• Ferrite isolation devices such as the circulator
do not suffer the 6-dB loss inherent in the
hybrid junction. Practical devices have isolation
of the order of 20 to 50 dB. Turnstile junctions
achieve isolations as high as 40 to 60 dB.
• An important factor which limits the use of
isolation devices with a common antenna is the
reflections produced in the transmission line by
the antenna. The antenna can never be
perfectly matched to free space, and there will
always be some transmitted signal reflected
back toward the receiver
The largest isolations are obtained with two antennas-one for
transmission, the other for reception-physically separated from
one another.
Isolations of the order of 80 dB or more are possible with high-
gain antennas. The more directive the antenna beam and the greater
the spacing between antennas, the greater will be the· isolation.
When the antenna designer is restricted by the nature of the
application, large isolations may not be possible. For example, typical
isolations. between transmitting and receiving antennas on
missiles might be about 50 dB at X band, 70 dB at K band and as
low as 20 dB at L band. 9 Metallic baffles, as well as absorbing
material, placed between the antennas can provide additional
The separate antennas of the AN/MPQ 46 CW tracker-illuminator
of.the Hawk missile system are shown in Fig.
The transmitter noise that enters the radar receiver via
backscatter from the clutter is sometimes called transmitted
clutter.It can appear at the same frequencies as the doppler
shifts from moving targets and can mask desired targets or cause
spurious responses. This extraneous noise is produced by ion
oscillations in the tube (usually a klystron amplifier) rather than
INTERMEDIATE-FREQUENCY RECEIVER
Receivers of this type are called homodyne receivers, or
superheterodyne receivers with zero IF. The function
of the local oscillator is replaced by the leakage signal
from the transmitter. Such a receiver is simpler than
one with a more conventional intermediate frequency
since no IF amplifier or local oscillator is required.
• Flicker Noise :- Flicker noise is also known
as 1/f noise in view of the fact that is power density
decreases with increasing frequency or increasing
offset from a signal. It follows a 1/f characteristic,
having what is termed a pink noise spectrum.,
• However, the simpler receiver is not as sensitive
because of increased noise at the lower intermediate
frequencies caused by flicker effect.
• Flicker-effect noise occurs in semiconductor devices
such as diode detectors' and cathodes of vacuum
tubes. The noise power produced by the flicker effect
• at the lower range of frequencies (audio or video
region), where the doppler frequencies usually are
found, the detector of the CW receiver can introduce
a considerable amount' of flicker noise, resulting in
reduced receiver sensitivity.
• But for maximum efficiency with CW radar, the
reduction in sensitivity caused by the simple doppler
receiver with zero IF, cannot be tolerated
• The effects of flicker noise are overcome in the
normal super heterodyne receiver by using an
intermediate frequency high enough to render. the
flicker noise small compared with the normal
receiver noise
•
Receiver bandwidth
• One of the requirements of the doppler-frequency amplifier in
the simple CW radar (Fig. 3.2) or the IF amplifier of the sideband
superheterodyne (Fig. 3.4) is that it be wide enough to pass the
expected range of doppler frequencies.
• In most cases of practical interest the expected range of doppler
frequencies will be much wider than the frequency spectrum
occupied by the signal energy.
• Consequently, the use of a wideband amplifier covering the
expected doppler range will result in an increase in noise and a
lowering of the receiver sensitivity.
• If the frequency of the doppler-shifted echo signal were known
beforehand, a narrowband filter-one just wide enough to reduce
the excess noise without eliminating a significant amount of
signal energy-might be used
• its frequency spectrum would be a delta function (Fig. 3.5a)
and the receiver bandwidth would be infinitesimal
• The more normal situation is an echo signal which is a
sine wave of finite rather than infinite duration. The
frequency spectrum of a finite-duration sine wave has a
shape of the form [sin π(f- f0) ᵟ]/π(f - fo), where fo and ᵟ
are the frequency and duration of the sine wave,
respectively, and f is the frequency variable over which the
spectrum is plotted (Fig. 3.5b).
• In many instances, the echo is not a pure sine wave of
finite duration but is perturbed by fluctuations in cross
section, target accelerations, scanning fluctuations, etc.,
which tend to broaden the bandwidth still further. Some
of these spectrum-broadening effects are considered
below.
• The fluctuations widen the spectrum by modulating the
echo signal
• In a particular case, it has been reported that the aircraft
cross section can change by 15 dB for a change in target
aspect of as little as 1.33 degrees.
• The echo signal from a propeller-driven aircraft can
also contain modulation components at a frequency
proportional to the propeller rotation. The spectrum
produced by propeller modulations is more like that
produced by a sine-wave signal and its harmonics rather
• This could be a potential source of difficulty in a CW
radar since it might mask the target's doppler signal
or it might cause an erroneous measurement of
doppler frequency. In some instances, propeller
modulation can be of advantage. It might permit the
detection of propeller-driven aircraft passing on a
tangential trajectory, even though the doppler
frequency shift is zero.
• If the target's relative velocity is not constant, a
further widening of the received signal spectrum can
occur
• When the doppler-shifted echo signal is known to lie
somewhere within a relatively wide band of frequencies, a
bank of narrowband filters (Fig. 3.6) spaced throughout
the frequency range permits a measurement of frequency
and improves the signal-to noise ratio
• bandwidth of each individual filter is wide enough to
accept the signal energy, but not so wide as to introduce
more noise than need be
• If the filters are spaced with their half-power points
overlapped. the maximum reduction in signal-to-noise ratio
of a signal which lies midway between adjacent channels
compared with the signal-to-noise ratio at mid band is 3 dB
• When the system requirements permit a time sharing of the
doppler frequency range, the bank of doppler filters may be
replaced by a single narrowband tunable filter which
searches in frequency over the band of expected doppler
frequencies until a signal is found.
• After detecting and recognizing the signal, the filter may
be programmed to continue its search in frequency for
additional signals
Sign of the radial velocity
In some applications of CW radar it is of interest to know whether the
target is approaching or receding.
This might be determined with separate filters located on either side
of the intermediate frequency.
If the echo-signal frequency lies below the carrier, the target is
receding; if the echo frequency is greater than the carrier, the target
is approaching (Fig. 3.7).
• If the transmitter signal is given by
E1 = Eo COS w0 t
• the echo signal from a moving target will be
The sign of the doppler frequency, and therefore the direction of
target motion, may be found by splitting the received signal into two
channels as shown in Fig. 3.8.
• In channel A the signal is processed as in the simple CW radar of Fig. 3.2. The received
signal and a portion of the transmitter heterodyne in the detector (mixer) to yield a difference
signal
• The other channel is similar. except for a 90° phase delay introduced
• The output of the channel B mixer is
• The sign of ωd and the direction of the target's motion
may be determined according to whether the output
of channel B leads or lags the output of channel A.
• One method of determining the relative phase
relationship between the two channels is to apply the
outputs to a synchronous two-phase motor. The
direction of motor rotation is an indication of the
direction of the target motion
Applications of CW radar
• The chief use of the simple, unmodulated CW radar is for the
measurement of the relative velocity of a moving target, as in the police
speed monitor or in the previously mentioned rate-of-climb meter for
vertical-take-off aircraft
• CW radar has been suggested for the control of traffic lights, regulation of
toll booths, vehicle counting, as a replacement for the" fifth-wheel"
speedometer in vehicle testing, as a sensor in antilock braking systems,
and for collision avoidance.
• For railways, CW radar can be used as a speedometer to replace the conventional
axle-driven tachometer
• CW radar is also employed for monitoring the docking speed of large ships.
• The principal advantage of a CW doppler radar over other (nonradar) methods of
measuring speed is that there need not be any physical contact with the object
whose speed is being measured.
• In industry this has been applied to the measurement of turbine-blade vibration,
the peripheral speed of grinding wheels, and the monitoring of vibrations in the
cables of suspension bridges.
LIMITATION of CW RADAR
• Perhaps one of the greatest shortcomings of the simple CW radar is its
inability to obtain a measurement of range.
• As opposed to pulsed radar systems, continuous wave (CW) radar systems
emit electromagnetic radiation at all times. Conventional CW radar cannot
measure range because there is no basis for the measurement of the time
delay. Recall that the basic radar system created pulses and used the time
interval between transmission and reception to determine the target's
range. If the energy is transmitted continuously then this will not be
possible.
CW radar can measure the instantaneous rate-of-change in the target's
range. This is accomplished by a direct measurement of the Doppler
shift of the returned signal.
• This limitation can be overcome by modulating the CW carrier, as in the
frequency-modulated radar described in the next section.
FREQUENCY MODULATED CW RADAR
• The inability of the simple CW radar to measure not able to
measure the range.
• To overcome that Some sort of timing mark must be applied to
a CW carrier if range is to be measured.
• The timing mark permits the time of transmission and the time
of return to be recognized
• FMCW radar is a special type of radar sensor which radiates
continuous transmission power like a simple continuous wave
radar . In contrast to this CW radar FMCW radar can change its
operating frequency during the measurement: that is, the
transmission signal is modulated in frequency (or in phase).
Possibilities of Radar measurements through runtime
measurements are only technically possible with these changes
in the frequency (or phase).
• time reference for measuring the distance of
stationary objects, but can be generated using of
frequency modulation of the transmitted signal.
• In this method, a signal is transmitted, which
increases or decreases in the frequency
periodically. When an echo signal is received, that
change of frequency gets a delay Δt (by runtime
shift) like to as the pulse radar technique. In pulse
radar, however, the runtime must be measured
directly. In FMCW radar are measured the
differences in phase or frequency between the
actually transmitted and the received signal instead.
Range and Doppler Measurement
A block diagram illustrating the principle of the FM-CW radar is shown in
Fig. 3.11. A portion of the transmitter signal acts as the reference
signal required to produce the beat frequency
In the frequency-modulated CW radar (abbreviated FM-CW), the
transmitter frequency is changed as a function of time in a known
manner
• Assume that the transmitter frequency increases linearly with time,
as shown by the solid line in Fig. 3.10a.
• If there is a reflecting object at a distance R, an echo signal will return
after a time T = 2R/c. The dashed line in the figure represents the
echo signal
• If there is no doppler
frequency shift, the
beat note (difference
frequency) is a
measure of the target's
range and Fb = Fr,
where Fr is the beat
frequency due only to
the target's range. If the
rate of change of the
carrier frequency is fo,
the beat frequency is
• In any practical CW radar, the frequency cannot be continually changed in
one direction only.
• Periodicity in the modulation is necessary, as in the triangular frequency-
modulation waveform shown in Fig. 3.10b. The modulation need not
necessarily be triangular; it can be sawtooth, sinusoidal·, or some other
shape. The resulting beat frequency as a function of time is
• shown in Fig. 3.10c for triangular modulation.
• The beat note is of constant frequency except at the turn-around region. If
the frequency is modulated at a rate fm over a range Ϫf, the beat
frequency
• The doppler frequency shift causes the frequency-time plot of the
echo signal to be shifted up or down (F ig. 3.12a).
• On one portion of the frequency-modulation cycle. the beat
frequency (Fig. 3.1 2b) is increased by the doppler shift, while on
the other portion, it is decreased.
• If for example, the target is approaching the radar, the beat
frequency fb(up) produced during the increasing, or up, portion of
the FM cycle will be the difference between the beat frequency due
to the range fr, and the doppler frequency shift fd [Eq. (3.12a)].
• Similarly, on the decreasing portion, the beat frequency
Fb(down) is the sum of the two [ Eq. (3.12b)].
•
• The range frequency fr, may be extracted by measuring the average
beat frequency; that is,
½[fb(up) + fb(down)] = fr,. If fb(up) and fb(down) are measured
separately
When more than one target is present within the view of the radar, the
mixer output will contain more than one difference frequency.
In principle, the range to each target may be determined by measuring
the individual frequency components and applying Eq . (3.11) to
each .
To measure the individual frequencies , they must be separated from
one another. This might he accomplished with a bank of narrowband
filters, or alternatively, a single frequency corresponding to a single
target may be singled out and continuously observed with a narrow
band tunable filter.
• The FM-CW radar principle was known and used at about the same time
as pulse radar, although the early development of these two radar
techniques seemed to be relatively independent of each other. FM-CW
was applied to the measurement of the height of the ionosphere in
FM-CW Altimeter
• The FM-CW radar principle is used in the aircraft radio altimeter to
measure height above the surface of the earth. The large backscatter
cross section and the. relatively short ranges required of
altimeters permit low transmitter power and low antenna gain.
• Backscattering cross section is a property of an object that
determines what proportion of incident wave energy is scattered
from the object, back in the direction of the incident wave.
•
•
• Since the relative motion between the aircraft
and ground is small, the effect of the doppler
frequency shift may usually be neglected.
• The band from 4.2 to 4.4 GHz is reserved for radio
altimeters
• The altimeter can employ a simple homodyne
receive r, but for better sensitivity and stability
the super heterodyne is to be preferred
whenever its more complex construction can
be tolerated.
• A block diagram of the FM-CW radar with a
sideband super heterodyne receiver is shown in
Fig. 3.13
•
• FM Modulator − It produces a Frequency Modulated (FM) signal having
variable frequency, fo(t) and it is applied to the FM transmitter.
• FM Transmitter − It transmits the FM signal with the help of transmitting
Antenna. The output of FM Transmitter is also connected to Mixer-I.
• Local Oscillator − In general, Local Oscillator is used to produce an RF signal.
But, here it is used to produce a signal having an Intermediate
Frequency, fIF. The output of Local Oscillator is connected to both Mixer-I
and Balanced Detector.
• Mixer-I − Mixer can produce both sum and difference of the frequencies
that are applied to it. The signals having frequencies of fo(t) and fIF are
applied to Mixer-I. So, the Mixer-I will produce the output having frequency
either fo(t)+fIF , or fo(t)−fIF
• Side Band Filter − It allows only one side band frequencies, i.e., either
upper side band frequencies or lower side band frequencies. The side band
filter shown in the figure produces only lower side band frequency. i.e., fo(t)
−fIF
• Mixer-II − Mixer can produce both sum and difference of the frequencies
that are applied to it. The signals having frequencies of fo(t)
−fIF and fo(t−T)are applied to Mixer-II. So, the Mixer-II will produce the
output having frequency either fo(t−T)+fo(t)−fIF or fo(t−T)−fo(t)+fIF
•
• IF Amplifier − IF amplifier amplifies the Intermediate
Frequency (IF) signal. The IF amplifier shown in the figure
amplifies the signal having frequency of fo(t−T)−fo(t)+fIF
This amplified signal is applied as an input to the Balanced
detector.
• Balanced Detector − It is used to produce the output signal
having frequency of fo(t−T)−fo(t) from the applied two
input signals, which are having frequencies of fo(t−T)−fo(t)
+fIF and fIF The output of Balanced detector is applied as
an input to Low Frequency Amplifier.
• Low Frequency Amplifier − It amplifies the output of Balanced detector to the
required level. The output of Low Frequency Amplifier is applied to both
switched frequency counter and average frequency counter.
• Switched Frequency Counter − It is useful for getting the value of Doppler
velocity.
• Average Frequency Counter − It is useful for getting the value of Range.
• Only the averaging frequency counter need be used in an altimeter
application, since the rate of change of altitude is usually small.
• A target at short range will generally result in a strong signal at low frequency,
while one at long range will result in a weak signal at high frequency.
• Therefore the frequency characteristic of the low-frequency amplifier in the FM-
CW radar may be shaped to provide attenuation at the low frequencies
corresponding to short ranges and large echo signals. Less attentuation is
applied to the higher frequencies, where the echo signals are weaker
• The low-frequency-amplifier bandwidth must
be sufficiently wide to encompass the
expected range of beat frequencies.
• Since tile bandwidth is broader than need be
to pass the signal energy, the signal-to-noise
ratio is reduced and the receiver sensitivity
degraded.
Measurement errors
The absolute accuracy of radar altimeters is usually of
more importance at low altitudes than at high
altitudes. Errors of a few meters might not be of
significance when cruising at altitudes of 10 km, but
are important if the altimeter is part of a blind
landing system.
errors caused by multiple reflections and transmitter
leakage, and the frequency error due to the turn-
around of the frequency modulation
Figure 3.14 shows some of the unwanted signals that
might occur in the FM altimeter. The wanted signal is
shown by the solid line. while the unwanted signals
are shown by the broken arrows.
• The unwanted signals include:
1. The reflection of the transmitted signals at the antenna caused by impedance mismatch.
2. The standing-wave pattern on the cable feeding the reference signal to the receiver, due
to poor mixer match.
3. The leakage signal entering the receiver via coupling between transmitter and receiver
antennas. This can limit the ultimate receiver sensitivity, especially at high altitudes.
4. The interference due to power being reflected back to the transmitter,
5. The double-bounce signal.
MULTIPLE – FREQUENCY CW RADAR
• Although it has been said in this chapter that CW radar does not
measure range, it is possible under some circumstances to do so by
measuring the phase of the echo signal relative to the phase of the
transmitted signal.
• Consider a CW radar radiating a single-frequency sine wave of the
form sin 2πfot, (The amplitude of the signal is taken to be unity since
it does not influence the result.)
• The signal travels to the target at a range R and returns to the radar
after a time T = 2R/c. where c is the velocity of propagation.
• The echo signal received at the radar is sin [ 2 π f0 ( t - T)]. If the
transmitted and received signals are compared in a phase detector.
• The region of unambiguous range may be extended considerably by
utilizing two separate CW signals differing slightly in frequency. The
unambiguous range in this case corresponds to a half wavelength at
the difference frequency
• The transmitted waveform is assumed to consist of two continuous
sine waves of frequency f1 and f 2 For convenience, the
amplitudes of all signals are set equal to unity. The voltage
waveforms of the two components of the transmitted signal
• V 1T and V 2T may be written as
• whereф 1 and ф 2 are arbitrary (constant) phase angles. The echo
signal is shifted in frequency by the doppler effect. The form of the
doppler-shifted signals at each of the two frequencies f1 and f2 may
be written
• The multiple-frequency CW radar technique has been applied to the
accurate measurement of distance in surveying and in missile guidance.
The Tellurometer is the name given to a portable electronic surveying
instrument which is based on this principle.
• The remote unit at the other end of the line receives the signals from
the master unit and amplifies and retransmits them. The phases of the
returned signals at the master unit are compared with the phases of the
outgoing signals.
• Since the master and the remote units are stationary, there is no
doppler frequency shift.
• The function of the doppler frequency is provided by modulating the
retransmitted signals at the remote unit in such a manner that a 1-k Hz
beat frequency is obtained from the heterodyning process at the
receiver of the master unit. The phase of the 1-k Hz signals contaii1s the
same information as the phase of the multiple frequencies.
• MRB 201 Tellurometer is capable of measuring distances from 200 to
250 km, assuming reasonable line of sight conditions, with an
accuracy of ±0.5 m ± 3 x 10- 6 d, where d is the distance being
measured.
