George W. Stimson introduction to Airborne Radar (Se)

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CHAPTER 7 Choice of Radio Frequency

quencies are widely used for surface search, detection of

low flying targets, and piloting. (The same phenomenon is

encountered on land when operating over a flat surface.)

Airborne Applications. In aircraft, the limitations on size

are considerably more severe. The lowest frequencies gener-

ally used here are in the UHF and S-bands. They provide

the long detection ranges needed for airborne early warning

in the E2 and AWACS aircraft, respectively (Fig. 10). One

look at the huge radomes of these planes, though, and it is

clear why higher frequencies are commonly used when nar-

row antenna beams are required in smaller aircraft, such as

fighters.

The next lowest-frequency applications are in the C-band.

Radar altimeters operate here. Interestingly, the band was

originally selected for this use because it made possible

light, cheap equipment that could use a triode transmitter

tube. These frequencies, of course, enable good cloud pene-

tration. Because altimeters are simple, require only modest

amounts of power, and do not need highly directive anten-

nas, they can use these frequencies and still be made conve-

niently small.

Weather radars, which require greater directivity, operate

in the C-band as well as in the X-band. The choice between

the two bands reflects a dual trade-off. One is between

storm penetration and scattering. If scattering is too severe,

the radar will not penetrate deeply enough into a storm to

see its full extent. Yet, if too little energy is scattered back to

the radar, storms will not be visible at all. The other trade-off

is between storm penetration and equipment size. C-band

radars, providing better penetration, hence longer-range per-

formance, are primarily used by commercial aircraft. X-band

radars, providing adequate performance in smaller pack-

ages, are widely used by private aircraft.

Most fighter, attack, and reconnaissance radars operate

in the X- and Ku-bands, with a great many operating in the

3-centimeter wavelength region of the X-band (Fig. 11).

The attractiveness of the 3-centimeter region is threefold.

First, atmospheric attenuation, though appreciable, is still

reasonably low—only 0.02 dB per kilometer for two-way

transmission at sea level. Second, narrow beamwidths, pro-

viding high power densities and excellent angular resolu-

tion, can be achieved with antennas small enough to fit in

the nose of a small aircraft. Third, because of their wide use,

microwave components for 3-centimeter radars are readily

available from a broad base of suppliers.

Where limited range is not a problem and both small

size and high angular resolution are desired, higher fre-

quencies may be used. Radars operating in the Ka-band, for

10. Operating in the S-band, AWACS radar provides early warn-

ing. But its antenna must be very large to provide desired

angular resolution.

11. At X-band reasonably high angular resolution can be obtained

with an antenna small enough to fit in the nose of a fighter.

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PART III Primary Design Considerations

example, have been developed to perform ground search

and terrain avoidance for some aircraft. But because of the

high level of attenuation at these frequencies, to date there

has been relatively little utilization of this band.

With the recent availability of suitable millimeter-wave

power-generating components, radar designers are develop-

ing extremely small, albeit short-range, radars which take

advantage of the atmospheric window at 94 gigahertz to give

small air-to-air missiles high terminal accuracies (Fig. 12).

At 94 gigahertz, a 3.8-inch antenna provides the same

angular resolution as a 36-inch antenna would at 10 giga-

hertz (3 centimeters).

Summary

Radio frequencies employed by airborne radars range

from a few hundred megahertz to 100 thousand megahertz,

the optimum frequency for any one application being a

trade-off among several factors.

In general, the lower the frequency, the greater the physi-

cal size and the higher the available maximum power. The

higher the frequency, the narrower the beam that may be

achieved with a given sized antenna.

At frequencies above about 0.1 gigahertz, attenuation

due to atmospheric absorption—mainly by water vapor and

oxygen—becomes significant. At frequencies of 3 gigahertz

and higher, scattering by condensed water vapor—rain,

hail, and, to less extent, snow—produces weather clutter. It

not only increases attenuation, but in radars not equipped

with MTI may obscure targets. Above about 10 gigahertz,

absorption and scattering become increasingly severe, and

attenuation due to clouds becomes important.

Noise is minimum between about 0.3 and 10 gigahertz,

but becomes increasingly severe at 20 gigahertz and higher

frequencies.

Doppler shifts increase with frequency, and this may also

be a consideration.

12. Operating at 94 gigahertz, this tiny antenna of an air-to-air

missile provides the same angular resolution as the much larg-

er antenna pictured in Fig. 11.

Typical Frequency Selections

• Early warning radars.... UHF and S-band

• Radar altimeters.......... C-band

• Weather radars............ C- and X-bands

• Fighter/Attack .............. X- and Ku-bands

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Directivity and the

Antenna Beam

1. Three-dimensional plot of the strength of the radiation from a

pencil beam antenna.

he degree to which the antenna concentrates the

radiated energy in a desired direction—broadly

referred to here as directivity—is a key characteris-

tic of virtually every airborne radar. Besides

determining the radar’s ability to locate targets in angle,

directivity can vitally affect the ability to deal with ground

clutter and is a major factor governing detection range.

In this chapter, we will learn how the energy radiated by

an antenna is distributed in angle and examine the salient

characteristics of the radiation pattern—beamwidth, gain,

and sidelobes. We will then see how the sidelobes may be

reduced; how fast, versatile beam positioning may be

accomplished with electronic scanning; and how high

angular resolution and angular measurement accuracy

may be achieved. Finally, we will learn how the beam may

be optimized for ground mapping.

Distribution of Radiated Energy in Angle

From common simplistic illustrations, it might be sup-

posed that a radar antenna concentrates all of the transmit-

ted energy into a narrow beam within which the power is

uniformly distributed; that if a pencil beam were trained

like a flashlight on an imaginary screen in the sky, it would

illuminate a single round spot with uniform intensity.

While this might be desirable, it is even less true of an

antenna than of a flashlight.

Like all antennas, a pencil beam antenna radiates some

energy in almost every direction. As illustrated in the

three-dimensional plot of Fig. 1, most of the energy is con-

centrated in a more or less conical region surrounding the

PART III Radar Fundamentals

3. Lobular distribution of power is due to diffraction–the process

that causes a beam of light projected through a tiny hole to

spread and become fringed with concentric rings of light.

4. To determine the distribution of energy radiated by array, a

field-strength meter is moved along arc of constant radius. The

array consists of a row of closely spaced vertical radiators.

5. Line AB marks off differences in distance from individual array

elements to meter. The angle that AB makes with array equals

azimuth angle (

θ) of meter.

central axis, or boresight line, of the antenna. This region is

called the mainlobe. If we slice the plot in two through the

central axis of this lobe (the boresight line), we find that it

is flanked on either side by a series of weaker lobes (Fig. 2).

These are called sidelobes.

This lobular structure is due to diffraction—the phenom-

enon observed when a beam of light passes through a small

circular hole (Fig. 3). The beam spreads and, if the light is

all of one wavelength, becomes fringed with concentric

rings of light of progressively decreasing intensity.

The phenomenon is most easily explained if we consider

a type of horizontally oriented, one-dimensional antenna

called a linear broadside array. It consists of a row of closely

spaced radiators, each emitting in all azimuth directions a

wave of the same amplitude, phase, and frequency. To mea-

sure the combined strength of these waves at various

azimuth angles, we place a field strength meter far enough

away that the lines of sight from the meter to all radiators

are very nearly parallel (Fig. 4). Starting at a point on the

perpendicular bisector of the array (boresight line), we

move the meter along an arc of constant radius from the

array center.

At any one point, the field strength depends upon the

relative phases of the received waves. The relative phases, in

turn, depend on the differences in distance to the individual

radiators. These differences can best be visualized if we

draw a line from one end of the array, perpendicular to the

line of sight to the meter—the line AB in Fig. 5. The angle

this line makes with the array equals the azimuth angle, θ,

of the meter.

2. A slice taken through 3-dimensional plot. Note the series of

lesser lobes on either side of the mainlobe.

Now, if θ is zero, the distance from the meter to all of the

radiators is essentially the same. (The lines of sight to all

radiators, remember, are essentially parallel.) The waves are

in phase, and their fields add up to a large sum.

CHAPTER 8 Directivity and the Antenna Beam

However, if θ is greater than zero, the distance to each

successive radiator down the line is progressively greater.

As a result, the phases of the received waves are all slightly

different, and the sum is not as great.

As the azimuth angle increases, the differences in dis-

tance increase. A point is ultimately reached (Fig. 6) where

the distance from the meter to the first radiator beyond the

center of the array (No. 7) is half a wavelength greater than

the distance to the radiator at the near end (No. 1).

Consequently, the wave received from radiator No. 1 is can-

celled by the wave received from radiator No. 7. The same

is true of the waves received from radiators No. 2 and No.

8, and so on.

The sum of the waves received from all of the radiators,

therefore, is zero. The meter has reached an azimuth angle

where there is a null in the total radiation from the

antenna.

If θ is increased further, the waves from the radiators at

the ends of the array no longer cancel exactly, and the sum

increases. As the difference in distance from the meter to

the ends of the array approaches 1

/2 wavelengths, another

peak is reached (Fig. 7). The waves from the radiators in

the central portion of the array—Nos. 3 through 10—still

cancel. But the waves from the radiators at either end—

Nos. 1 and 2, and Nos. 11 and 12—add up to an apprecia-

ble sum. The meter is now in the center of the array’s first

sidelobe.

If θ is increased still further, the portion of the array for

which cancellation occurs increases, and the same general

process repeats. The meter thus moves through a succes-

sion of nulls and progressively weaker lobes.

The field strength measured in an excursion through

several lobes on either side of the mainlobe is plotted ver-

sus azimuth angle in Fig. 8. The shape of this plot is

approximated by the equation

E = K

sin x

where E is the field strength and x is proportional to θ. This

is called a “sine-x-over-x” shape.

Actually, x = π (L/λ) sin θ. So x is directly proportional

to θ only for small values of θ. As θ increases, sin θ

becomes progressively less than θ, with the result that the

higher-order sidelobes are spaced progressively farther

apart.

The directivity of an array antenna has been explained

here in terms of field strength, since that is both easily mea-

sured and easily visualized.

6. When distance from meter to radiator No. 7 becomes half a

wavelength longer than distance to radiator No. 1, the signals

received from these radiators cancel. So do all the others.

As difference in distance from meter to ends of array approaches

/2 wavelengths, only those signals from elements 3 through

10 cancel.

8. Field strength measured in an excursion through several lobes

on either side of boresight line. (Radio frequency phase of odd

numbered sidelobes—1, 3, etc.—is reversed; hence, these

sidelobes are plotted as negatives.)

PART III Radar Fundamentals

9. Directivity of a linear array expressed in terms of power.

In a radar, however, what is important is the amount of

energy radiated per unit of time: the power of the radiated

waves (Fig. 9). Power is proportional to field strength

squared. Expressed in terms of power, therefore, the equa-

tion for the distribution of the radiated energy in angle is

Power = K’

(

sin x

)

Two-dimensional planar arrays, such as are commonly

used in airborne radars, consists essentially of a number of

linear arrays stacked on top of one another.

THE SIN X/X SHAPE

As the angle, 8, between the line of sight to a distant point

and the boresight line of a linear array antenna increases,

phasors representing the signals received from the individ-

ual radiators fan out and their sum decreases.

CHAPTER 8 Directivity and the Antenna Beam

TWO COMMON TYPES OF AIRBORNE RADAR ANTENNAS

Parabolic reflector antenna—for years the most common

type used in airborne radars. Feed located at focus of

parabola directs radiation into dish, which reflects it.

Curvature of parabola is such that distance from feed to

dish to plane across mouth (aperture) of dish is the same for

every path the radiation can take. Consequently, the phase

of the radiation at every point in the plane of the aperture is

the same, and a narrow pencil beam is formed. Antenna is

simple and relatively inexpensive to fabricate.

Planar array antenna—for an advanced fighter radar.

Radiation of equal phase is emitted from 2-dimensional array

of slots in face. Planar arrays provide relatively high aperture

efficiency and low back radiation (spillover). By controlling

excitation of slots with nondissipating attenuators on back of

antenna, distribution of energy across aperture can be

shaped to minimize sidelobes. Principal disadvantages are

relatively narrow bandwidth (

≅

10 percent) and higher cost.

Also, circular polarization, if desired, is more difficuit to obtain.

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PART III Radar Fundamentals

11. Beamwidth is commonly measured between points where

power has dropped to one half of maximum (–3 dB). Three dB

beamwidth, θ

3dB

, is roughly

/2 null-to-null beamwidth, θ

10. Radiation pattern is normally plotted in rectangular coordinates in

dB relative to gain at center of mainlobe.

1. This pattern has a J

(x)-over-x

shape, where J

is the Bessel

function of the first order.

To give an antenna a circular or elliptical shape, the

arrays above and below the central ones are progressively

shortened. The total radiation from the antenna is the com-

posite of the radiation from the individual arrays. Even if

the radiation from every element were the same—which it

never is—a plot of the total radiation would not have a sim-

ple sin x/x shape. Nevertheless, the general shape is much

the same. (Incidentally, the shape for a uniformly illuminat-

ed circular array is exactly the same as the diffraction pat-

tern mentioned earlier for light passing through a small

round hole.

)

Characteristics of the Radiation Pattern

A plot of the power (or field strength) of the radiation

from an antenna in any one plane versus angle from the

antenna’s central axis is called a radiation pattern. In con-

sidering directivity, the power at the center of the mainlobe

is taken as a reference and the power radiated in every

other direction is taken in ratio to this value. The ratio is

normally expressed in decibels and plotted in rectangular

coordinates as in Fig. 10.

Since the pattern is usually not symmetrical about the

center of the mainlobe, “cuts” must be taken through many

different planes to describe an antenna’s directivity fully.

Also, patterns are generally measured in two polarizations:

that for which the antenna was designed and the polariza-

tion at right angles to this—the cross polarization.

Generally, three characteristics of a radiation pattern are

of interest: the width of the mainlobe, the gain of the main-

lobe, and the relative strengths of the sidelobes.

Beamwidth. The width of the mainlobe is called the

beamwidth. It is the angle between opposite edges of the

beam. The beam is generally not symmetrical, so it is com-

mon to refer to azimuth beamwidth and elevation

beamwidth.

Since the strength of the mainlobe falls off increasingly as

the angle from the center of the beam increases, for any

value of beamwidth to have meaning, one must specify

what the edges of the beam are considered to be.

The edges are perhaps most easily defined as the nulls on

either side of the mainlobe. However, from the standpoint of

the operation of a radar (Fig. 11), it is generally more realis-

tic to define them in terms of the points where the power

has dropped to some arbitrarily selected fraction of that at

the center of the beam. The fraction most commonly used is

/2. Expressed in decibels,

/2 is –3 dB. Beamwidth mea-

sured between these points, therefore, is called the 3-dB

beamwidth.

Regardless of how it is defined, beamwidth is determined

primarily by the size of the antenna’s frontal area. This area

is called the aperture. Its dimensions—width, height, or

diameter—are gauged not in inches or centimeters, but in

wavelengths of the radiated energy (Fig. 12).

The larger the appropriate dimension is in relation to the

wavelength, the narrower the beam in a plane through that

dimension will be. As we saw earlier, the nulls on either

side of the mainlobe of a linear array occur at angles for

which the distance from the observer to one end of the

array is one wavelength longer than to the other end.

Therefore, for either a linear array or a rectangular aper-

ture over which the illumination is uniformly distributed,

the null-to-null beamwidth in radians is twice the ratio of

the wavelength to the length of the array (Fig. 13).

= 2

radians

where

λ = wavelength of radiated energy

L = length of aperture (same units as λ)

The 3-dB beamwidth is a little less than half the null-to-

null width.

3 dB

= 0.88

For a uniformly illuminated circular aperture of diameter

d, the 3-dB beamwidth is a bit greater.

3 dB

= 1.02

A circular antenna 60 centimeters in diameter, radiating

energy of 3-centimeter wavelength, for example, has a

beamwidth of 1.02 x

/60 = 0.051 radian.

One radian equals 57.3° (Fig. 14). So the beamwidth in

degrees is 0.051 x 57.3 = 2.9°.

If the antenna has tapered illumination, such as is typi-

cally used in radars for fighter aircraft, the beamwidth will

be somewhat greater.

3 dB

= 1.25

A 60-centimeter antenna with tapered illumination

would thus have a beamwidth of about 3.6º.

A rule of thumb for estimating the beamwidths of

tapered circular antennas is this: at X-band, the 3-dB

beamwidth is roughly 85º divided by the diameter in inches.

The 3-dB beamwidth of a 20-inch diameter antenna is

thus about 85°÷20 = 4.25°. If the illumination is not

CHAPTER 8 Directivity and the Antenna Beam

12. Beamwidth is determined primarily by dimensions of antenna

aperture, in wavelengths.

13. For a linear array, angle (in radians) from boresight line to first

null equals ratio of wavelength to length of array. Null-to-null

beamwidth is twice this angle.

14. A radian is the angle subtended by an arc the length of the

radius (R). The circumference of a circle equals 2πR.

Therefore, 2π = 360°, and 1 radian = 360°/2π = 57.3°.

X-Band Beamwidth Rule of Thumb

For tapered illumination:

3dB

≈

85°

70°

For untapered illumination:

3dB

≈

d = diameter in inches

PART III Radar Fundamentals

tapered, 70° should be substituted for 85° in this rule. (See

bottom of next page for an explanation of “tapering.”)

Antenna Gain. The gain of an antenna is the ratio of the

power per unit of solid angle radiated in a specific direction

to the power per unit of solid angle that would have been

radiated had the same total power been radiated uniformly

in all directions—i.e., isotropically (Fig. 15).

An antenna

thus has gain in almost every direction. In most directions,

though the gain is less than one, since the average gain in

all directions is, by the law of conservation of energy, one.

The gain in the center of the mainlobe is thus a measure

of the extent to which the radiated energy is concentrated in

the direction the antenna is pointing. The narrower the

mainlobe, the higher this gain will be.

The maximum gain that can be achieved with a given

size antenna is proportional to the area of the antenna aper-

ture in square wavelengths times an illumination efficiency

factor. If the aperture were uniformly illuminated—a practi-

cally impossible condition, even if it were desired—the fac-

tor would equal one.

Actually, it ranges somewhere between 0.6 and 0.8 for

planar arrays and may be as low as 0.45 for parabolic reflec-

tors. In either case, for a given design, the factor tends to

vary with the width of the band of frequencies the antenna

is designed to pass. Typically, the greater the bandwidth, the

lower the efficiency.

Because of the difficulty of determining the efficiency fac-

tor analytically, in practice the gain is determined experi-

mentally and expressed in terms of an effective aperture

area.

G = 4π

where

G = antenna gain at center of mainlobe

λ = wavelength of radiated energy

= effective area of aperture (same units as λ

)

Effective area is equal to physical area times aperture effi-

ciency (which as noted above is virtually always less than

100 percent); so an alternate expression for antenna gain is

G = 4π

Aη

where

A = physical area of aperture

η = aperture efficiency

15. Antenna directive gain is the ratio of power radiated in the

direction of interest to power which would be radiated in that

direction by an isotropic antenna, i.e., one that radiates

waves of equal power in all directions.

2. Strictly speaking, the gain re-

ferred to here is directivity

gain. More commonly, anten-

na gain connotes directivity

gain less whatever power is

lost in the antenna.

Estimating Antenna Gain

X-Band Rule of Thumb:

G ≈ d

d = diameter in cm

η = aperture efficiency

Example:

Diameter = 60 cm

Aperture efficiency = 0.7

G ≈ 60 x 60 x 0.7

≈ 2520

≈ 34 dB

General Rule of Thumb:

G ≈ 9 d

d = diameter in wave-

lengths

Example:

Wavelength = 3 cm

Diameter = 60 cm = 20 λ

Aperture efficiency = 0.7

G ≈ 9 x (20)

x 0.7

≈ 2520

≈ 34 dB