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Fundamentals

of Radar7. Choice of Radio Frequency . . . . . . . . . . . . . . .97

8. Directivity and the Antenna Beam . . . . . . . .107

9. Electronically Scanned Array Antennas . . . .125

10. Electronically Scanned Array Design . . . . . .135

11. Pulsed Operation . . . . . . . . . . . . . . . . . . . . . . 149

12. Detection Range . . . . . . . . . . . . . . . . . . . . . . .159

13. The Range Equation: What It Doesand Doesnt Tell Us . . . . . . . . . . . . . . . . . . . . 179

14. Radar Receivers and Digitization . . . . . . . . . .195

15. Measuring Range and Resolving in Range . .215

16. Pulse Compression and High-Resolution Radar . . . . . . . . . . . . . . . . . . . . . .229

17. Frequency-Modulated ContinuousWave Ranging . . . . . . . . . . . . . . . . . . . . . . . .245

PART
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English Electric Canberra (1957)

The Canberra was Britains first-generation jet-powered light bomber

to be manufactured in large numbers. It entered service in 1951 and

served as a nuclear strike aircraft, tactical bomber, and reconnaissance

platform (photographic and electronic). Flying at Mach 0.88, its ability to

outpace the jet interceptors of the time and its adaptability made it highly

desirable for export. The Canberra set multiple flight records including

first nonstop unrefueled transatlantic crossing by a jet aircraft and thealtitude record twice (1955 and 1957).

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97

Ferranti AI23:the first airborne monopulse radar

(Courtesy of Selex ES.)

Aprimary consideration in the design of virtually

every radar is the frequency of the transmitted radio

wavesthe radars operating frequency. How close

a radar comes to satisfying many of the require-

ments imposed on itfor example, detection range, angular

resolution, Doppler performance, size, weight, costoften

hinges on the choice of radio frequency. This choice, in turn,

has a major impact on many important aspects of the design

and implementation of the radar. In this chapter we will sur-

vey the broad span of radio frequencies used by radars and

examine the factors that determine the optimum frequency for

particular applications.

7.1Frequencies Used for Radar

Todays radars operate at frequencies ranging from as low as a

few megahertz to as high as 300,000,000 MHz (Fig. 7-1).

At the low end are a few highly specialized radars. Sounders

measure the height of the ionosphere. Another is over-the-

horizon (OTH) radars, which take advantage of ionospheric

reflection to beyond line of sight and detect targets thousands

of kilometers away.

At the high end are laser radars, which operate in the visibleand infrared region of the spectrum. Such radars are used to

provide the angular resolution needed for such tasks as mea-

suring the ranges of individual targets on the battlefield.

Most radars, however, employ frequencies lying somewhere

between a few hundred megahertz and 100,000 MHz. Present

airborne radars used for search, surveillance, and multimode

operation are predominantly in the 425 MHz to 12 GHz range.

To make such large frequency values more manageable, it is

customary to express them in gigahertz. One gigahertz equals

1000 MHz, so a frequency of 100,000 MHz is 100 GHz.

100,000,000

Frequency

(MHz)

100,000

Laser Radars

Satellite

Communications

Most Airborne

Radars

Cellphones

10,000

1,000

400

TV

Over the Horizon

Radars

AM Radio

100

10

1

40,000

Figure 7-1.Shown here is the portion of the electromagnetic

spectrum used for radar.

Choice of RadioFrequency

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98 PART III: Fundamentals of Radar

Radar operating frequencies are also expressed in terms of

wavelengththe speed of light (3 108 m/s) divided by the

frequency in Hertz (Fig. 7-2).

Incidentally, a convenient rule of thumb for converting

from frequency to wavelength is wavelength in centime-

ters =30 frequency in gigahertz. The wavelength of a

10 GHz wave, for example, is 30 10 =3 cm.

To convert from wavelength to frequency you turn the rule

around, interchanging wavelength and frequency: frequency in

gigahertz =30 wavelength in centimeters. The frequency of a

3 cm wave is thus 30 3 =10 GHz.

7.2Frequency Bands

Besides being identified by discrete values of frequency and/or

wavelength, radio waves are also broadly classified as falling

within one or another of several arbitrarily established regions

of the radio frequency spectrum such as high frequency (HF),very high frequency (VHF), and ultra high frequency (UHF).

The frequencies commonly used by radars fall in the VHF,

UHF, microwave, and millimeter-wave regions (Fig. 7-3).

During World War II, the microwave region was broken into

comparatively narrow bands and assigned letter designations

for purposes of military security: L-band, S-band, C-band,

X-band, and K-band (military users tend not to like to talk

in terms of specific frequencies). To enhance security, the

designations were deliberately arranged out of alphabetical

sequence. Although long since declassified, these designations

have persisted to this day.

The K-band turned out to be very nearly centered on the

resonant frequency of water vapor, where absorption of

radio waves in the atmosphere is high. Consequently the

band was split into three parts. The central portion retained

the original designation. The lower portion was designated

the Ku-band while the higher portion was designated the

Ka-band. An easy way to keep these designations straight

is to think of the u in Ku as standing for underand the

a in Ka as standing for above the central band. Only a

portion of these bands are allocated by the International

Telecommunications Union (ITU) for radar use, and radar

bands are often further constrained by the bandwidth of

radio frequency components.

In the 1970s a completely new sequence of bands

neatly assigned consecutive letter designations from A to

Mwas devised for electronic countermeasures equipment

(Fig. 7-4). Attempts were made to apply these designations

to radars as well, but largely because the junctions of the

new bands occur at the centers of the traditional bands

about which many radars are clusteredthese attempts

were unsuccessful. In the United States the new band

3 GHz

(10 cm)

10 GHz

(3 cm)

37.5 GHz

(0.8 cm)

94 GHz

(0.28 cm)

Figure 7-2.These wavelengths used by airborne radars, are shown

in their relative size.

100

Millimeter

Wave

Microwave

UHF

VHF

HF

30

Frequency

(GHz)

0 0.1

Figure 7-3.Regions of the electromagnetic spectrum commonly

used for radar are plotted here on a linear scale. The bandwidth

available at millimeter-wave frequencies is much greater than at

microwave frequencies.

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CHAPT ER 7: Choice of Radio Frequency 99

designations are generally used, as originally intended, only

for countermeasures.

If you havent already done so, memorize the center frequen-

cies and wavelengths of these five radar bands:

Band GHz cm

Ka (above) 38 0.8

Ku (under) 15 2

X 10 3

C 6 5

S 3 10

7.3Influence of Frequency on Radar Performance

The best frequency to use depends on the job the radar is

intended to perform. Like most other design decisions, the

choice involves trade-offs involving several factors: physical

size, transmitted power, antenna beamwidth, and atmospheric

attenuation are among the most important.

Physical Size.The dimensions of the hardware used to gener-

ate and transmit radio frequency power are in general pro-

portional to wavelength. At the lower frequencies (longer

wavelengths), the hardware is usually large and heavy. At the

higher frequencies (shorter wavelengths), radars can be put into

smaller packages and thus operate in more compact spaces at a

lighter weight (Fig. 7-5). The limited space requires more tightly

packed electronics, which can present design challenges.

Transmitted Power.Because of its impact on hardware size,

the choice of wavelength indirectly influences the ability ofradar to transmit large amounts of power. The levels of power

that can be handled by a radar transmitter are largely limited

by voltage gradients (volts per unit of length) and heat dissipa-

tion requirements. It is not surprising, therefore, that the larger,

heavier radars operating at wavelengths of the order of meters

can transmit megawatts of average power, whereas millimeter-

wave radars may be limited to only a few hundred Watts of

average power.

Most often, though, within the range of available power the

amount of power actually used is decided by size, weight, reli-

ability, cost, and detection range considerations.

Beamwidth.As will be explained in Chapter 8, the angular

width of a radars antenna beam is directly proportional to the

ratio of the wavelength to the width of the antenna. To achieve

a given beamwidth, the longer the wavelength, the wider the

antenna must be. At low frequencies, very large antennas must

be used to achieve acceptably narrow beams. At high frequen-

cies, small antennas will suffice (Fig. 7-6). The narrower the

beam, of course, the greater the power that is concentrated in

a particular direction at any one time, and thus the finer the

angular resolution.

100

Radar Countermeasures

40

26.5

Frequency

(GHz)

Wavelength

(cm)

18.0

12.010

8

6

4

3

2

1CUHF

L D

ES

CG

H

IX

JKu

KK

Ka

L0.8

2

3

5

10

15

30

M

Millimeter

F

Figure 7-4.Radar and countermeasures band letter designations

are shown here with their corresponding wavelengths.

Figure 7-5.The physical size and power-handling capacity of radio

frequency components decreases with frequency. A transmitter

tube for a 30 cm radar is shown on top while the transmitter tube

for a 0.8 cm radar is below it.

Wavelength

6 cm

Wavelength

3 cm

Figure 7-6.For the same size antenna, the angular width of its

beam is proportional to wavelength.

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Atmos pheric Atte nuation. In passing through the atmo-

sphere, radio waves are attenuated by two basic mechanisms:

absorption and scattering (see blue panel). The absorption is

mainly due to oxygen (60 GHz) and water vapor (21 GHz).

The scattering is due almost entirely to condensed water

vapor (e.g., raindrops). Both absorption and scattering

increase with frequency. Below about 0.1 GHz, atmospheric

attenuation is negligible; above about 10 GHz it becomes

increasingly significant.

Moreover, above about 10 GHz the radars performance is

increasingly degraded by weather clutter competing with

desired targets. Even when the attenuation is reasonably low,

if enough transmitted energy is scattered back in the direc-

tion of the radar, it will be detected. In simple radars that do

not employ moving target indication (MTI), this returncalled

weather cluttermay obscure targets.

While usually not a concern for airborne radars, the effects

of the ionosphere on radar signals at UHF and below pass-ing through the ionosphere (attenuation, refraction, dispersion,

and Faraday rotation) may also be significant.

Foliage Penetration.In some specialized applications an air-

borne radar may be required to detect targets hidden under

trees. The ability to do this depends on the attenuation prop-

erties of the foliage canopy, which are found to increase with

frequency. In practice, frequencies of L-band or below are nec-

essary for foliage penetration radars.

Fractional Bandwidth.The fractional bandwidth of a radar is

defined as the bandwidth of its signal divided by the centerfrequency. Well see later that the bandwidth of a radar signal

defines its range resolution, so the greater the bandwidth, the

finer the range resolution. However, for a given radar band-

width, the lower the center frequency, the greater the frac-

tional bandwidth. High fractional bandwidths (greater than

about 15%) pose problems for the radar hardware, especially

the antenna.

Coexistence with Other Users. The electromagnetic spec-

trum is used for many other purposesparticularly com-

munications, broadcast, and radionavigationbesides radar.

By international agreement the spectrum is allocated amongthe different users, so some frequency bands are allocated to

a particular application on an exclusive basis, while others

are shared. All users of the spectrum have requirements for

greater and greater bandwidth, yet the electromagnetic spec-

trum is a strictly finite resource. So even with this regula-

tory framework, mutual interference can become a problem.

Special techniques to improve transmitter spectral purity and

to suppress interference, as well as work to understand and

quantify the degree of interference that can be tolerated, are

active areas of research.

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CHAPTE R 7: Choice of Radio Frequency 101

Ambient Noise. Electrical noise from sources outside the

radar is high in the HF band. It decreases with frequency (Fig.

7-7), reaching a minimum between about 0.3 and 10 GHz,

depending on the level of galactic noise, which varies with

solar conditions. From that point, atmospheric noise predom-

inates. It gradually becomes stronger and grows increasingly

at K-band and higher frequencies. In many radars, internally

generated noise predominates. However, when low-noise

receivers are used to meet long-range requirements, external

noise can be an important consideration in the selection of

frequency.

Doppler Considerations.Doppler shifts are proportional not

only to the closing rate of the target, but also to radio fre-

quency. The higher the frequency, the greater the Doppler

shift that a given closing rate will produce. As will be made

clear in later chapters, excessive Doppler shifts can cause

problems. In some cases these tend to limit the frequencies

that can be used. On the other hand, Doppler sensitivity to

small differences in closing rate can be increased by selectinghigher frequencies.

Sky Noise

Galactic

0.1 1 10 100

Atmospheric

Frequency, GHz

Noise

Power

(Log Scale)

Figure 7-7.Ambient noise reaches a minimum between 0.3 GHz

and 10 GHz, depending on the level of galactic noise, which varies

with solar conditions.

Atmospheric Attenuation

Absorption. Energy is absorbed from radio waves passing

through the atmosphere primarily by the gases comprising it.

Absorption increases dramatically with frequency.

50

.

50 100 30010

Fr quen y GHz

1.

Loss

(dB/km)

Fraction o Si nal Gettin throu h 1 km o Atmosphere

Below about 0.1 GHz, absorption is negligible, while above

5 GHz it becomes increasingly significant. Beyond about

20 GHz, it becomes severe. Typical windows are around

35 GHz and 94 GHz.

Most of the absorption is due to oxygen and water vapor.

Consequently, it not only decreases at the higher altitudes

where the atmosphere is thinner but also with decreasing

humidity.

The molecules of oxygen and water vapor have resonant

frequencies.

When excited at these frequencies, they absorb more energy

hence the peaks in the absorption curve. The peaks are broad-

ened by molecular collisions and thus are sharper at high

altitudes, where the atmosphere is less dense, but their fre-

quencies are the same. (Plot B has the same horizontal axis as A.

The vertical axis is shifted down to encompass the lower curve.)

10

1

Loss

(dB/km).

.

Fr quency (GHz

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The peaks at 22 and 185 GHz are due to water vapor; those at

60 and 120 GHz are due to oxygen. The regions between peaks,

where the attenuation is lower, are called windows.

Energy is also absorbed by particles suspended in the atmo-

sphere, but their principal effect is scattering.

Scattering.Radio waves are scattered by particles suspended

in the atmosphere. Scattering increases with the particles

dielectric constant and size relative to wavelength. Scattering

becomes severe when the size is comparable to a wavelength.

The principal scatterers are raindrops and, to a lesser extent,

hail (because of its much lower dielectric constant). Snow-

flakes, which contain less water and have slower fall rates, scat-

ter less energy. Clouds, which consist of tiny droplets, scatter

even less. Smoke and dust are usually negligible scatterers

because of their small particle size and low dielectric constant.

10

dB/km

0.1

0.010

Frequen y (GHz100

Scattering becomes noticeable in the S-band (3 GHz). At those

frequencies and higher, backscattering is sufficient to make

rain visible.

Both absorption and scattering by clouds are still negligible

in the S-band. Therefore, meteorological radars operating

there can measure rainfall rates without being hampered by

attenuation or backscatter due to clouds.

Above 10 GHz, scattering and absorption by clouds becomes

appreciable. The attenuation is proportional to the amount of

water in the clouds.

dB/

km

0.1

0.011

Frequen y (GHz)

0

Attenuation increases with decreasing temperature since the

dielectric constant of water is inversely proportional to tem-

perature. Ice clouds, however, attenuate less because of the

low dielectric constant of ice.

7.4Selecting the Optimum Frequency

From the preceding, it is evident that selection of the radio

frequency is influenced by several factors: the functions the

radar is intended to perform, the environment in which the

radar will be used, the physical constraints of the platform on

which it will operate, and cost. To illustrate, lets consider some

representative applications. To put the selection in context we

will consider not only airborne applications, but ground andshipboard applications, too.

Ground-Based Applications.These run the gamut of operating

frequencies. At one extreme are the long-range multimegawatt

surveillance radars. Unfettered by size and weight limitations,

they can be made large enough to provide acceptably high

angular resolution while operating at relatively low frequencies.

OTH radars, as weve seen, operate in the HF band where the

ionosphere is suitably reflective. Space surveillance and early

warning radars operate in the UHF and VHF bands, where ambi-

ent noise is minimal and atmospheric attenuation is negligible.

Atmospheric Attenuation continued

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CHAPTE R 7: Choice of Radio Frequency 103

However, these bands are crowded with communication signals,

so their use by radars (whose transmissions generally occupy a

comparatively broad band of frequencies) is restricted to special

applications and geographic areas. Where such long ranges are

not required and some atmospheric attenuation is therefore tol-

erable, ground radars may be reduced in size by moving up to

L-, S-, and C-band frequencies or higher (Fig. 7-8).

Shipboard Applications.Aboard ships, physical size becomes

a limiting factor in many applications. At the same time, the

requirement that ships be able to operate in the most adverse

weather puts an upper limit on the frequencies that can be

used. This limit is relaxed, however, where extremely long

ranges are not required. Furthermore, higher frequencies must

be used when operating against surface targets and targets at

low elevation angles.

At grazing angles approaching zero, the return received directly

from a target is very nearly cancelled by the return from the

same target reflected off the watera phenomenon called mul-tipath propagation(Fig. 7-9). Cancellation is due to a 180 phase

reversal occurring when the return is reflected. As the graz-

ing angle increases, a difference develops between the lengths

of the direct and indirect paths, and cancellation decreases.

The shorter the wavelength, the more rapidly the cancella-

tion disappears. For this reason, the shorter wavelength S- and

X-band frequencies are widely used for surface search, detec-

tion 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

considerable. The lowest frequencies generally used here are

in the UHF, L, and S-bands, and only for very specific appli-

cations. They provide the long detection ranges needed for

airborne early warning in the E2 and airborne warning and

control system (AWACS) aircraft, respectively (Fig. 7-10). One

look at the huge radomes of these aircraft and it is clear why

higher frequencies are commonly used when narrow 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 because its use made possible light, cheap

equipment that could use a triode transmitter tube. These fre-

quencies also enable good cloud penetration. Because altim-eters are simple, require only modest amounts of power, and

do not need highly directive antennas, they can use these

frequencies and still be made conveniently small.

Weather radars, which require greater directivity, operate in

C-band as well as in 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 vis-

ible at all. The other trade-off is between storm penetration and

Figure 7-8.Ground-based radars commonly operate at lower

frequencies where long range is not important. This radar traces

the source of mortar fire. X-band and Ku-band may be used for

small size and better measurement accuracy. (Courtesy of THALES.)

Figure 7-10.Operating in S-band, the AWACS radar provides an

early warning, its antenna is very large to provide the desired

angular resolution.

Figure 7-9.At small grazing angles, the return received directlyfrom the target is very nearly cancelled by the return reflected off

the water.

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equipment size. C-band radars, providing better penetration and

hence longer-range performance, are primarily used by com-

mercial aircraft. X-band radars, providing adequate performance

in smaller packages, 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 cm wave-

length region of X-band (Fig. 7-11) and the 2 cm wavelengthregion of Ku-band (Fig. 7-12).

The attractiveness of the 3 cm region is threefold. First, atmo-

spheric attenuation, though appreciable, is still reasonably

lowonly 0.02 dB/km for two-way transmission at sea level.

Second, narrow beamwidths, providing high power densities

and excellent angular resolution, can be achieved with anten-

nas small enough to fit in the nose of a small aircraft. Third,

because of their wide use, microwave components for 3 cm

radars are readily available from a wide range of suppliers.

Where limited range is not a problem and both small size and

high angular resolution are desired, higher frequencies can beused. Radars operating in the Ka-band, for 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 utiliza-

tion of this band.

With the availability of suitable millimeter-wave power-

generating components, radar designers are developing

extremely small, albeit short-range, radars that take advan-

tage of the atmospheric window at 94 GHz to give small air-

to-air missiles high terminal accuracies (Fig. 7-12). At 94 GHz,

a 10 cm antenna provides the same angular resolution as a0.94 m antenna would at 10 GHz (3 cm).

Typical Frequency Selections

Early warning radars UHF, L, and S-bands

Radar altimeters C-band

Weather radars C- and X-bands

Fighter/attack X- and Ku-bands

7.5Summary

Radio frequencies employed by airborne radars range from a

few hundred megahertz to 100,000 MHz (100 GHz), the opti-

mum frequency for any one application being a trade-off

among several factors.

In general, the lower the frequency, the greater the physical

size of the hardware and the higher the available maximum

power. The higher the frequency, the narrower the beam that

may be achieved with a given size antenna.

At frequencies above about 0.1 GHz, attenuation due to atmo-

spheric absorptionmainly by water vapor and oxygen

becomes significant. At frequencies of 3 GHz and higher,

Figure 7-11.At X-band, reasonably high angular resolution can

be obtained with an antenna small enough to fit in the nose of a

fighter.

Figure 7-12.Operating at 94 GHz, this tiny antenna of an air-to-air

missile provides the same angular resolution as the much larger

antenna pictured in Figure 7-11.

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CHAPT ER 7: Choice of Radio Frequency 105

scattering by condensed water vaporrain, hail, and to lesser

extent, snowproduces weather clutter. It not only increases

attenuation, but in radars not equipped with MTI, it can

obscure targets. Above about 10 GHz, absorption and scatter-

ing become increasingly severe and attenuation due to clouds

becomes important.

Noise is minimal between about 0.3 GHz and 10 GHz, butbecomes increasingly severe at 20 GHz and higher frequencies.

Doppler shifts increase with frequency, and this may also be a

consideration in certain applications.

Further Reading

D. E. Kerr,Propagation of Short Radio Waves, IEEE Press, 1986.

M. E. Davis, Foliage Penetration Radar: Detection and

Characterization of Objects under Trees, SciTech-IET, 2011.

L. W. Barclay,Propagation of Radiowaves, 3rd ed., IET, 2012.

Test your understanding

1. Explain the mechanisms by whichelectromagnetic waves are attenuated

when passing through the atmosphere.

2. A particular radar has a center frequency

of 15 GHz and a bandwidth of 3 GHz.What is its fractional bandwidth?

3. The Swedish CARABAS FOPEN radaroperates over the band 2090 MHz.

What is its fractional bandwidth?

4. An X-band radar signal passes through asevere rainstorm with a horizontal extentof 10 km and an attenuation of 2 dB/km.

What is the two-way attenuation of thesignal through the rainstorm?

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