George W. Stimson introduction to Airborne Radar (Se)

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CHAPTER 8 Directivity and the Antenna Beam

Sidelobes. An antenna’s sidelobes are not limited to the

forward hemisphere. They extend in all directions, even to

the rear, for a certain amount of radiation invariably “spills

over” around the edges of the antenna. Moreover, when the

antenna is placed in a radome, the backward radiation is

increased. For the radome scatters some energy from the

mainlobe, much as the frosted glass of a light bulb diffuses

light from the filament.

Nor are the sidelobes neatly defined, with sharp nulls

in between. As can be seen from Fig. 16, the nulls tend to

fill in.

For a uniformly illuminated circular aperture, the gain of

the strongest (first) sidelobe is only about

/64 that of the

mainlobe. Stated in decibels, the first sidelobe has 18 dB

less gain than the mainlobe—it is down 18 dB. The gain of

the other sidelobes is substantially lower.

Nevertheless, in aggregate the sidelobes rob the mainlobe

of a substantial amount of power. Because of the large solid

angle they cover, roughly 25 percent of the total power

radiated by a uniformly illuminated antenna is radiated out-

side the mainlobe.

Against most small targets even the strongest sidelobes

are sufficiently weak that they can generally be ignored.

But against the ground, even the weakest sidelobes may

produce considerable return. And, as will be explained in

Chap. 22, buildings and other structures on the ground

form corner reflectors which can return tremendously

strong echoes, even when illuminated only by sidelobes.

In military applications, the sidelobes also increase both

the radar’s susceptibility to detection by an enemy and its

vulnerability to jamming. Interference from a powerful

noise jammer, for example, can be much stronger than the

echoes of a small or distant target in the mainlobe. Conse-

quently, it is generally desirable for the gain of the first side-

lobes to be reduced to at least 80dB below that of the main-

lobe.

Sidelobe Reduction. The degree to which the radiated

power is concentrated into the mainlobe is called solid

angle efficiency. To make it acceptably high, as well as to

minimize problems of ground clutter and jamming, the gain

of the sidelobes must generally be reduced. As explained

earlier, the sidelobes are produced by radiation from the

portion of the aperture near its edges. Consequently, they

may be reduced by designing the antenna to radiate more

power per unit area through the central portion of the aper-

ture (Fig. 17). This technique is called illumination taper-

ing. It increases the beamwidth somewhat, hence it reduces

the peak gain of the mainlobe. But usually this is an accept-

able price to pay for reduced sidelobes.

16. An antenna’s sidelobes extend in all directions, even to the rear.

3. However, for some targets

which in certain aspects

reflect a large fraction of the

incident energy back in the

direction of the radar, side-

lobe return can be substantial.

17. Sidelobes may be reduced by tapering illumination at edges of

aperture.

PART III Radar Fundamentals

100

20. Antenna for air-to-ground radar in which fan-shaped beam is electronically steered in azimuth. Antenna is carried in pod beneath aircraft; by

rotating antenna about its longitudinal axis, it can be made to look out on either side of the aircraft.

Electronic Beam Steering

In most airborne radars, the antenna beam is positioned

by physically moving the antenna through the desired

azimuth and elevation angles (Fig. 18). An alternative

method, possible with array antennas, is to differentially

shift the phases of the radio waves emitted by the individ-

ual radiators. This technique is called electronic beam steer-

ing (or electronic scanning).

As with the simple linear array described earlier, the

direction of maximum radiation from the array—i.e., direc-

tion of the mainlobe—is that for which the waves from all

of the radiators are in phase. If the phases of the emitted

waves are all the same, this direction is perpendicular to the

plane of the array. However, if the phases are progressively

shifted from one radiator to the next, the direction of maxi-

mum radiation will be correspondingly shifted (Fig. 19). By

appropriately shifting the phases of the inputs to the indi-

vidual radiators, therefore, the beam can be steered in any

desired direction within a large solid angle.

Electronic steering has the advantage of being extremely

flexible and remarkably fast. The beam can be given any

shape, swept in any pattern at a very high rate, or jumped

almost instantaneously to any position. It can even be split

into two or more beams which radiate simultaneously on

different frequencies and can be trained simultaneously on

different targets (at the expense of a reduction in detection

range).

Depending upon the application, electronic steering may

be provided in one (Fig. 20) or two dimensions. Moreover,

it may be combined with either mechanical beam steering

or mechanical rotation of the antenna, as in the AWACS

radar (see Chap. 44).

18. Beam is conventionally steered by mechanically deflecting the

antenna.

19. With electronic steering, beam is steered by progressively

shifting the phases of the signals radiated by the individual

radiators.

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CHAPTER 8 Directivity and the Antenna Beam

101

21. With electronic steering, length of aperture L decreases as

cosine of look angle, θ. With mechanical steering, no such

reduction occurs.

22. Ability to resolve targets in angle is determined primarily by

antenna beamwidth. Targets can be resolved if beamwidth is

less than their angular separation.

Naturally, electronic steering also has disadvantages.

Among these are increased complexity and degraded perfor-

mance at large look angles.

The degradation in performance is due to foreshortening

of the aperture when viewed from angles off dead center

(Fig. 21). The length of the foreshortened dimension

decreases as the cosine of the angle. The effect is negligible

at small scan angles, but it becomes increasingly severe at

large angles. The result of the foreshortening (effectively

smaller aperture in the direction of illumination) is an

increase in beamwidth and more importantly, a decrease in

gain, limiting the maximum practical look angle to ±60˚.

With mechanical steering, no such limitation occurs: the

plane of the aperture is perpendicular to the direction of the

mainlobe for all look angles.

Angular Resolution

The ability of a radar to resolve targets in azimuth and

elevation is determined primarily by the azimuth and eleva-

tion beamwidths. This is illustrated simplistically by the two

diagrams in Fig. 22.

In the first diagram, two identical targets, A and B, at

nearly the same range are separated by slightly more than

the width of the beam. As the beam sweeps across them, the

radar receives echoes first from Target A, then from Target

B. Consequently, the targets can easily be resolved.

In the second diagram, the same two targets are separat-

ed by less than the width of the beam. As the beam sweeps

across them, the radar again receives echoes first from

Target A. However, long before it stops receiving echoes

from this target, it starts receiving echoes from Target B. The

echoes from the two targets, therefore, meld together.

Superficially, angular resolution would appear to be lim-

ited to the null-to-null width of the mainlobe. But it is actu-

ally better than that, because the resolution depends not

only upon the width of the lobe but on the distribution of

power within it.

The graph in Fig. 23 is a plot of strength of the received

signal as the mainlobe sweeps across an isolated target.

When the leading edge of the lobe passes over the target,

the echoes are so weak that they are undetectable. However,

their strength increases rapidly. It reaches a maximum when

the lobe is centered on the target, then drops to an unde-

tectable value again as the trailing edge approaches the target.

This curve, you should note, is not the same shape as the

radiation pattern plotted in similar coordinates, but is more

sharply peaked. The reason is that the antenna’s directivity

applies equally to transmission and reception—a character-

istic called reciprocity.

23. Angular accuracy is sharpened by peaking of receiver output

as beam sweeps across target. Unless target echoes are very

strong, azimuth angle over which return is detected is much

less than null-to-null beamwidth, θ

PART III Radar Fundamentals

102

26. With sequential lobing, during reception the angular tracking

error is determined by alternately placing mainlobe on one side

and then the other of antenna boresight line.

24. Since antenna‘s directivity is applied to both transmitted and

received waves, the plot of received signal strength versus

angle is more sharply peaked.

25. As separation between two closely spaced targets is

increased, a notch develops in the plot of receiver output ver-

sus azimuth angle.

To illustrate, suppose the position of a target is such

that the power radiated in its direction is half that radiated

in the center of the lobe (down 3 dB). When the target

echoes are received, their power will again be cut in half.

As a result, the received echoes will by only

/4 as strong

(down 6 dB) as when the target is in the center of the lobe

(Fig. 24).

Because of this compounding, the plot or received signal

power is narrower than the radiation pattern. And because

the echoes received when the target is near the edges of the

lobe are too weak to be detected (unless the target is at

short range), the azimuth angle over which the target is

detected is narrower than the null-to-null beamwidth.

The net effect of this narrowing on angular resolution is

illustrated by the three plots of Fig. 25. They show a com-

posite of the bell-shaped curves for two equally strong tar-

gets, A and B.

When the targets are closely spaced, the curves combine

to produce a single broad hump. As the spacing increases, a

notch develops in the top of this hump. The notch grows

until the hump splits in two.

In practice, the notch becomes apparent at a target spac-

ing of 1 to 1

/2 times the antenna’s 3 dB beamwidth. The 3

dB beamwidth, therefore, has come to be used as the mea-

sure of the angular resolution of a radar.

Angle Measurement

The foregoing should not be taken to imply that the

accuracy with which a radar can determine a target’s direc-

tion is limited to the beamwidth. Since the amplitude of the

received echoes varies symmetrically as the beam sweeps

across a target, the direction of an isolated target can be

determined to within a very small fraction of the

beamwidth.

By stopping the antenna’s search scan, target angle can be

determined with still greater precision. One technique for

accomplishing this is lobing.

Lobing. During reception, the center of the mainlobe is

alternately placed on one side of the target and then the

other (Fig 26). If the target is centered between lobes, the

received echoes will be the same strength for both lobes. If

it is not, the echoes will be stronger for one lobe than for

the other.

Normally, the lobes are separated just enough to intersect

at their half-power points. Since the slope of the radiation

pattern in this region is relatively steep, a slight displace-

ment of the target from a line through the crossover point

results in a large difference in the strength of the echoes

received through the two lobes (Fig. 27). By positioning the

antenna to reduce this difference to zero (i.e., to eliminate

the angular error), the antenna can be precisely lined up on

the target.

Because the lobing is sequential, however, short-term

changes in the strength of the target echoes—caused by

scintillation or electronic countermeasures—can introduce

large, spurious differences in the returns received through

the two lobes and so degrade tracking accuracy. This prob-

lem may be avoided by designing the antenna to produce

the lobes simultaneously, a technique called simultaneous

lobing.

Since all the necessary angular tracking information is

obtained from one reflected pulse, it is more commonly

called monopulse operation.

Monopulse. Monopulse systems are of two general types.

They differ both in regard to the direction of the lobes and

in regard to the way the returns received through opposing

lobes are compared.

The first type, called amplitude comparison monopulse,

essentially duplicates sequential lobing with simultaneously

formed lobes (Fig. 28).

Because the lobes point in slightly different directions, if

a target is not on the boresight line of the antenna, the

amplitude of the return received through one lobe differs

from the amplitude of the return simultaneously received

through the other lobe. The difference is proportional to the

angular error.

By subtracting the output of one feed from the output of

the other, an angular tracking error signal—often termed

the different signal—is produced. The sum of the two out-

puts—termed the sum signal—is used for range tracking.

CHAPTER 8 Directivity and the Antenna Beam

27. If the target is off the boresight line, return received through

one lobe will be stronger than that received through the other.

Magnitude of difference corresponds to magnitude of tracking

error; sign of difference, to direction of error.

28. In essence, amplitude comparison monopulse duplicates

sequential lobing in every respect except that return is received

simultaneously through both lobes. Error signal is difference

between outputs A and B.

103

PART III Radar Fundamentals

104

The second type of monopulse is phase-comparison. In it,

the array is divided into halves. The lobes produced by

both halves point in the same direction. Consequently, the

return received through one lobe has the same amplitude

as that received through the other regardless of the angle of

the target relative to the antenna boresight line. However, if

an angular error exists, the phases of the returns will differ

because of the difference in mean distance from the target

to each half (Fig. 29).

An error signal proportional to the phase difference may

be obtained by introducing a 180˚ phase shift in the output

from one half and summing the two outputs. If no tracking

error exists, the outputs cancel. If an angular error exists,

the resulting phase difference partially offsets the external

phase shift, and a difference output proportional to the

tracking error is produced (Fig. 30).

By combining the two outputs without the external

phase shift, a sum signal is provided for range tracking.

For monopulse tracking in both azimuth and elevation,

the antenna is typically divided into quadrants. The azimuth

difference signal is obtained by separately summing the

outputs of the two left quadrants and the two right quad-

rants and taking the difference between the two sums. The

elevation difference signal is similarly produced by taking

the difference between the sum of the outputs of the two

upper quadrants and the sum of the outputs of the two

lower quadrants.

Conventionally, three receiver channels would be provid-

ed: one, for the azimuth difference signal; a second, for the

elevation difference signal; and a third, for the sum signal.

The receiving system can, however, be simplified consider-

ably, by alternately forming the azimuth and elevation dif-

ference signals (Fig. 31) and feeding them on a time-share

basis through a single receiver channel.

29. Phase-comparison monopulse. Since lobes of two antenna

halves point in the same direction, amplitudes of outputs A

and B are equal. But their phases differ by angle φ, which is

proportional to angle error, θ.

31. Monopulse antenna feed provides sum signal for range tracking;

difference signals for angle tracking. Difference signals for azimuth

and elevation tracking may be processed on a time-shared basis.

30. Phase difference between outputs of two antenna halves is

converted to error signal by introducing 180° of phase shift in

one output and adding the two together.

CHAPTER 8 Directivity and the Antenna Beam

105

HOW TO CALCULATE THE RADIATION PATTERN FOR A LINEAR ARRAY

If you wish, you can readily calculate the radiation pattern for a

linear array consisting of any number of radiators having any

spacing and any illumination taper.

For successive values of the angle,

, you merely sum the

contribution of the individual radiators to the total field strength in

the direction,

. If the array is symmetrical about its central axis,

the summation only needs to be performed for half the array.

As was illustrated with phasors on page 93 of the text, the

contribution of any given radiator, say No. 2, to the total field

strength in a given direction is proportional to the amplitude of

the signal (a

) supplied to the radiator times the cosine of the

phase of the radiation from this radiator relative to the radiation

from the radiator at the center of the array (in this example a

hypothetical oentral radiator).

The relative phase, of course, depends upon the difference ∆d

between the distance from radiator No. 2 to an observer (a long

way off) in the direction

and the distance from the center of the

array to the same observer. That difference equals the distance

of the radiator from the array center (d

) times sin

Dividing Ad2 by the wavelength ()~) and multiplying by 2’r

yields the phase in radians.

Thus, the contribution of radiator No. 2 to the total field strength

in the direction

The total field strength, then, can be found by performing the

following summation.

By repeating the summation for values of

from zero to 90°, you

can obtain the radiation pattern for the array.

In case you’re wondering how the above summation is related to

the sin x/x equation given in the text, the relationship is direct. If

we assume that the total excitation (A) is uniformly distributed

over the length of the array (L), we can obtain the total field

strength simply by integrating this same expression with respect

to d over the length of the array.

PART III Radar Fundamentals

106

Antenna Beams for Ground Mapping

For ground mapping, the entire region being mapped

must be illuminated by the antenna’s mainlobe (Fig. 32). If

the radar is operating at low altitudes, or if the range inter-

val being mapped is relatively narrow, adequate illumina-

tion can be provided by a pencil beam. Otherwise, the

antenna must radiate a fan-shaped beam.

Ideally, it is shaped so that the strength of the returns

received from equivalent ground patches will be indepen-

dent of their range. For that, the one-way gain of the anten-

na must be proportional to the square of the range, R, to

the ground. This may be achieved by making the gain in

the vertical plane proportional to the square of the cosecant

of the look-down angle, φ (Fig. 33). Hence the beam is

called a cosecant-squared beam.

It should be noted that multipurpose antennas, which

are not exclusively designed for ground mapping, normally

do not have a cosecant-squared beam but a pencil beam. In

this case, reduction in strength of the return with range is

compensated by increasing the receiver sensitivity with

range, a process called sensitivity time control (STC)

described in Chap. 25.

Summary

A directional antenna radiates a mainlobe surrounded by

progressively weaker sidelobes. The width of the mainlobe

(beamwidth) is inversely proportional to the width of the

antenna aperture in wavelengths.

Antenna gain is the ratio of the power radiated in a spe-

cific direction to the power that would be radiated in that

direction if the total power were radiated isotropically (uni-

formly in all directions). The gain on the axis of the main-

lobe is proportional to the area of the aperture in square

wavelengths.

Sidelobes rob the mainlobe of substantial power and are

a source of undesirable ground clutter. Their gain can be

reduced by radiating more power per unit area from the

central portion of the aperture than from its edges.

Where extreme versatility and speed are required, the

mainlobe of an array antenna may be steered by progres-

sively shifting the phases of the waves radiated by succes-

sive radiating elements.

Angular resolution is determined by beamwidth. Angular

measurement accuracy is much finer than the beamwidth

and, in single-target tracking, can be made extremely fine

through lobing. By designing the antenna to produce the

lobes simultaneously (monopulse), angle tracking degrada-

tion due to short term variations in amplitude of the target

return can be avoided.

33. To illuminate ground at all ranges uniformly, power radiated

at angle

must be proportional to R

; hence to the cosecant

squared of the lookdown angle.

32. For ground mapping, if the radar is at a low altitude, or the

range interval being mapped is narrow, a pencil beam can

be used. Otherwise, a fan beam is required.

Useful Relationships To Remember

• For a circular uniformly illuminated X-

band antenna of diameter d:

3dB

= (d in inches)

G = d

η (d in cm)

(If illumination is tapered, substitute 85°

for 70° in expression for beamwidth.)

• For circular, uniformly illuminated

antenna and wavelength λ:

3dB

= radians

(d and λ in

same units)

G = 9

• Angular resolution = θ

3dB

70°

107

Pulsed Operation

2. Where doppler shift may be negligible, transmitted signal

can be kept from interfering with reception by continuously

shifting transmitter frequency.

1. In applications where doppler frequency of return is large,

doppler shift can keep transmitted signal from interfering with

reception.

adars are of two general types: continuous

wave—called CW—and pulsed. A CW radar

transmits continuously and simultaneously lis-

tens for the reflected echoes. A pulsed radar, on

the other hand, transmits its radio waves intermittently in

short pulses, and listens for the echoes in the periods

between transmissions.

Pulsed radars fall into two categories: (1) those that

sense doppler frequencies and (2) those that do not. The

former have come to be called pulse-doppler radars; the

latter, simply pulsed radars. Here, though, pulsed will be

used in a general sense to refer to any radar that transmits

pulses.

In this chapter, we’ll consider the advantages of pulsed

transmission, characteristics of the pulsed waveform, and

effects of pulsed transmission on transmitted power and

energy.

Advantages of Pulsed Transmission

With the exception of doppler navigators, altimeters,

and VT proximity fuses, most airborne radars are pulsed.

The chief reason is that with pulsed operation, one avoids

the problem of the transmitter interfering with reception.

The transmitter’s intended output—the signal—is not,

of course, the problem. In doppler navigators, for example

(Fig. 1) the doppler shift provides sufficient frequency sep-

aration to keep the transmitted signal from interfering

with reception. And in altimeters (Fig. 2), where the

doppler shift is usually near zero, interference from the

transmitted signal is avoided by continuously shifting the

transmitter’s frequency. Because of the time the radio

waves take to reach the ground and return, the frequency

of the received signal lags behind the frequency of the

transmitter; so, the signal is not interfered with.

108

Noise sidebands blanket broad band of frequencies above

and below transmitted signal and are vastly stronger than

echoes of typical airborne targets. Interference from them can

be avoided by transmitting pulses.

4. When the same antenna must be used for both transmis-

sion and reception, pulsed transmission avoids problem of

transmitter noise leaking into receiver.

5. Basic characteristics of transmitter waveform.

The problem in most airborne applications is electrical

noise. Unavoidably generated in every transmitter, it modu-

lates the transmitter output. In so doing, it creates sidebands

(see Chap. 5), which blanket a broad band of frequencies

above and below the transmitter frequency (Fig. 3). Although

the power of the noise sidebands may seem infinitesimal (and

is negligible compared to that of echoes from the ground at

short range), it can be many orders of magnitude stronger

than the echoes from the average airborne target.

To keep the noise from interfering with reception, the

receiver must be isolated from the transmitter. Adequate isola-

tion can be obtained by physically separating the transmitter

and receiver and providing separate antennas for each (as in

ground and shipborne CW radars).

In airborne radars, however, because of space limitations it

is usually necessary to use a single antenna for both transmis-

sion and reception (Fig. 4). When this is done, it is extremely

difficult—hence costly—to prevent some of the noise in the

transmitter output from leaking through the antenna into the

receiver.

If the transmission is pulsed, neither the transmitted signal

nor transmitter noise is a problem; the radar does not transmit

and receive at the same time.

Pulsed operation has the further advantage of simplifying

range measurement. If the pulses are adequately separated, a

target’s range can be precisely determined merely by measur-

ing the elapsed time between the transmission of a pulse and

the reception of the echo of that pulse.

Pulsed Waveform

Overall, the form of the radio waves radiated by a pulsed

radar—the transmitted signal—is referred to as the transmit-

ted waveform (Fig. 5). It has four basic characteristics:

• Carrier frequency

• Pulse width

• Modulation (if any) within or between the pulses

• Rate at which the pulses are transmitted (pulse repetition

frequency)

Carrier Frequency. This is not always constant, but may be

varied in different ways to satisfy specific system or opera-

tional requirements. It may be increased or decreased from

one pulse to the next. It may be changed at random or in

some specified pattern. It may even be increased or decreased

in some prescribed pattern during each pulse—intrapulse

modulation.

PART IV Detection and Ranging

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