George W. Stimson introduction to Airborne Radar (Se)

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PART II Essential Groundwork

8. Gain is the ratio of output power to input power.

Using Decibels

A common use of decibels in radar work is expressing

power gains and power losses.

Gain is the term for an increase in power level. In the

case of an amplifier—such as might raise a low power

microwave signal to the desired level for radiation by an

antenna—gain is the ratio of the power of the signal coming

out of the amplifier to the power of the signal going into it.

Gain =

Output power

Input power

If the output power is 250 times the input power, the gain

is 250. This ratio (250 to 1) is 24 dB (Fig. 8).

Loss is the term for a decrease in power. According to

convention, it is the ratio of input power to output power—

just the opposite of gain.

Loss =

Input power

Output power

To illustrate, let us assume that the amplifier of the pre-

ceding example is connected to the antenna by a waveguide

that absorbs some 20 percent of the power. The ratio of

input to output power, therefore, is 10 to 8 (1.25), making

the loss 1 dB (Fig. 9).

(Some people prefer to consider gain and loss as being

synonymous and think only in terms of the ratio of output

to input. Looked at this way, a 1 dB loss is a gain of –1 dB.)

Suppose, now, that we wish to find the total gain (G

)

between the input to the amplifier and the input to the

antenna. To do this in terms of straight power ratios, we

divide the gain of the amplifier (250) by the loss of the

waveguides (1.25).

= G

AMP

÷L

W.G.

= 250 ÷ 1.25

= 200

On the other hand, to determine the gain and loss in dB

(Fig. 10), we simply subtract the loss from the gain.

= 24 dB – 1 dB

= 23 dB

A decibel value of 23 dB is a power ratio of 200. So the

answer is the same either way.

9. Loss is the ratio of input power to output power.

1. Assuming properly

matched source and

load impedances.

10. In decibels, the overall gain is the gain minus the loss.

CHAPTER 6 The Ubiquitous Decibel

12. Expressed in terms of voltage, gain = (V

)

, provided input

and output resistances are the same.

Following this same general procedure, we could take

into account any number of gains and losses—additional

stages of amplification inserted on either side of the original

amplifier, losses in the antenna, losses in the radome, reduc-

tions in gain (losses) due to degradation in the field, etc.

(Fig. 11). And by multiplying the total gain by the input

power, we could quickly tell how much power would be

supplied to the antenna.

Power Gain in Terms of Voltage

Sometimes it is convenient to express power in terms of

voltages. The power dissipated in a resistance equals the

voltage, V, applied across the resistance times the current, I,

flowing through it: P = VI. But the current is equal to the

voltage divided by the resistance: I = V/R. So the power is

equal to (V

/R).

Accordingly, the power output of a circuit equals (V

)

/R,

and the power input equals (V

)

/ R. If the circuit’s input

and output impedances are the same, the gain is (V

)

/(V

)

(Fig. 12). Expressed in decibels, then, the gain is

G = 10 log

(

)

= 20 log

(

)

Decibels as Absolute Units

While decibels were originally used only to express

power ratios, they can also be used to express absolute val-

ues of power. All that is necessary is to establish some

absolute unit of power as a reference. By relating a given

value of power to this unit, that value can be expressed with

decibels.

An often used unit is 1 watt. A decibel relative to 1 watt is

called a dBW. A

power of 1 watt is 0 dBW

;

a power of 2 watts is

3 dBW; a

power of 1 kilowatt (10

watts) is 30 dBW

(Fig. 13).

Another common reference unit is 1 milliwatt. A decibel

relative to 1 milliwatt is called a dBm. The dBm is widely

used for expressing small signal powers, such as the powers

of radar echoes. They vary over a tremendous range. Echoes

from a small, distant target may be as weak as –130 dBm, or

less; while echoes from a short range target may be as strong

as 0 dBm, or more. The dynamic range of echo powers is

thus at least 130 dB. Considering that –130 dBm is 10

–13

or 0.000,000,000,000,1 millliwatt, the convenience of

expressing absolute powers in dBm is striking (Fig. 14).

This advantage of decibels is so compelling that they

have been applied to other variables than power. One exam-

ple is radar cross section.

14. Power received from a large, short-range target can be

10,000,000,000,000 or more times that received from a small

distant target. Advantage of expressing such powers in deci-

bels relative to a milliwatt is obvious.

13. A decibel relative to 1 watt is called a dBW.

11.

Any number of gains and losses can readily be compounded.

PART II Essential Groundwork

REMEMBERING THE BASIC POWER RATIOS

Whole Decibels. The table of equivalent power ratios has two

characteristics that make it surprisingly easy to remember.

First, 3 dB corresponds almost exactly to a ratio of 2. Since

adding decibels has the same effect as multiplying the ratios

they represent, we can obtain the ratios for 6 dB and 9 dB direct-

ly from that for 3 dB.

3 dB  2

6 dB  3 dB  3 dB  2  2  4

9 dB  6 dB  3 dB  4  2  8

Second, 1 dB corresponds to about 11/

4 (5/4). Since a nega-

tive sign inverts the ratio, –1 dB corresponds to 4/5 = 0.8. On

the basis of these two ratios—1

/4 and 0.8—we can determine

all of the remaining ratios.

2 dB  3 dB  1 dB  2  0.8  1.6

4 dB  3 dB  1 dB  2  1

/4  2.5

5 dB  6 dB  1 dB  4  0.8  3.2

7 dB  6 dB  1 dB  4  1

/4  5

8 dB  9 dB  1 dB  8  0.8  6.4

Fractions of a decibel. When you round off to the nearest

whole decibel, the error in the power ratio is at most only 1 part

in 7. While such accuracy is usually sufficient, greater precision

is often required—as, for example, in compounding radar losses,

which though small individually may be significant collectively.

So, it is helpful to have a way of remembering the ratios for

fractions of a decibel. A plot of decibels versus power ratio in

the interval between 0 and 1 dB is practically a straight line.

Since 0 dB corresponds to a ratio of 1 and 1 dB to a ratio of 1

/4,

the power ratio corresponding to any fraction of a decibel

between 0 and 1 very nearly equals 1 plus

/4th of the fraction.

Power ratio  1 

Fraction of dB

The ratio for

/2 dB, for example, is 1 +

/2 /4 = 1

/8, or

approximately 1.12.

So, if you were stranded on a desert island and the batteries in

your pocket calculator were dead, if you could remember just:

two ratios—those for 1 dB and 3 dB—you could reconstruct the

entire table right in your head. You might starve, but you could

talk in decibels until you did.

Oh yes . . . in case you forgot the ratio for 1 dB, you could

find it by subtracting 9 dB from 10 dB.

1 dB  10 dB  9 dB  10  8  1

Remembering the “quarter-dB rule,” you not only can round

off to the nearest half dB, but could easily scratch out a table

like this in the sand of a desert island.

0.8 dB  1.2

0.6 dB  1.15

0.5 dB  1.12

0.4 dB  1.10

0.2 dB  1.05

CHAPTER 6 The Ubiquitous Decibel

The radar cross section of a typical target can easily vary

from 1 to 1000 square meters as the aspect of the target

changes. A decibel relative to 1 square meter of radar cross

section is called a dBsm (Fig. 15).

Another example is antenna gain. It is the ratio of the

power per unit of solid angle radiated in a given direction to

the power per unit of solid angle which would have been

radiated had the same total power been distributed uni-

formly in all directions, i.e., isotropically. A decibel relative

to isotropically radiated power is called a dBi.

Summary

The decibel was devised to express power ratios. Being

logarithmic, it greatly compresses the numbers needed to

express values having a wide dynamic range.

Decibels also make compounding ratios easy. Ratios can

be multiplied by adding their decibel equivalents, divided

(inverted) by giving them a negative sign, and raised to a

power by multiplying them by that power.

A ratio expressed in dB can be thought of as consisting of

two parts. The digit in the one’s place expresses the basic

ratio. The digit to the left of it is the power of 10. To trans-

late from dB to a power ratio in your head, you convert the

basic ratio; then, place a number of zeros to the right of it

equal to the power of ten. To translate to decibels, you do

the reverse.

Positive decibels correspond to ratios >1; zero decibels to

a ratio of 1; negative decibels, to ratios <1. There is no deci-

bel equivalent for a ratio of 0.

Decibels are commonly used to express gains and losses.

Gain is output divided by input. Loss is input divided by

output.

Referenced to absolute units, decibels are also used to

express absolute values.

15.

Because they vary widely in value, radar cross sections are con-

veniently expressed in decibels relative to 1 square meter.

Some Relationships To Keep In Mind

• Power ratio

dB = 10 log

• Power ratio in terms of voltages

dB = 20 log

• 1 dB = 1

• 3 dB = 2

• dBW = dB relative to 1 watt

• dBm = dB relative to 1 milliwatt

• dBsm = dB relative to 1 square meter

of radar cross section

• dBi = dB relative to isotropic radiation

Choice of Radio

Frequency

1. Portion of electromagnetic spectrum used for radar.

primary consideration in the design of virtually

every radar is the frequency of the transmitted

radio waves—the radar’s operating frequency.

How close a radar may come to satisfying many

of the requirements imposed on it—detection range, angu-

lar resolution, doppler performance, size, weight, cost,

etc.—often 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 survey the broad span of radio

frequencies used by radars and examine the factors which

determine the optimum choice of frequency for particular

applications.

Frequencies Used for Radar

Today, radars of various kinds operate at frequencies

ranging from as low as a few megahertz to as high as

300,000,000 megahertz (Fig. 1).

At the low end are a few highly specialized radars:

sounders that measure the height of the ionosphere, as

well as radars that take advantage of ionospheric reflection

to see over the horizon and detect targets thousands of

miles away.

At the high end are laser radars, which operate in the

visible region of the spectrum and are used to provide the

angular resolution needed for such tasks as measuring the

ranges of individual targets on the battlefield.

Most radars, however, employ frequencies lying some-

where between a few hundred megahertz and 100,000

megahertz.

To make such large values more manageable, it is cus-

tomary to express them in gigahertz. One gigahertz, you

3. Regions of the electromagnetic spectrum commonly used for

radar, plotted on a linear scale.

PART III Primary Design Considerations

will recall, equals 1000 megahertz. A frequency of 100,000

megahertz, then, is 100 gigahertz.

As often as not, radar operating frequencies are expressed

in terms of wavelength—the speed of light divided by the

frequency (Fig. 2).

Incidentally, a convenient rule of thumb for converting

from frequency to wavelength is wavelength in centimeters =

30 divided by frequency in gigahertz. The wavelength of a 10

gigahertz wave, for example, is 30 ÷ 10 = 3 cm.

To convert from wavelength to frequency, you turn the

rule around, interchanging wavelength and frequency: fre-

quency in gigahertz = 30 divided by wavelength in centimeters.

The frequency of a 3-cm wave is thus 30 ÷ 3 = 10 GHz.

In English units, the rule is wavelength in feet = 1 divided

by frequency in gigahertz, and vice versa. The wavelength of a

10 gigahertz wave is 1 ÷ 10 = 0.1 foot.

Frequency Bands

Besides being identified by discrete values of frequency

and wavelength, radio waves are also broadly classified as

falling within one or another of several arbitrarily estab-

lished regions of the radio frequency spectrum—high fre-

quency (HF), very high frequency (VHF), ultra high fre-

quency (UHF), and so on. The frequencies commonly used

by radars fall in the VHF, UHF, microwave, and millimeter-

wave regions (Fig. 3).

During World War II, the microwave region was broken

into comparatively narrow bands and assigned letter desig-

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

C-band, X-band, and K-band. To enhance security, the des-

ignations were deliberately put out of alphabetical

sequence. Though long since declassified, these designa-

tions 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 up. The central portion retained the original

designation. The lower portion was designated the Ku-

band; the higher portion, the Ka-band. An easy way to keep

these designations straight is to think of the “u” in Ku as

2. Some wavelengths used by airborne radars, actual size.

UHF 300 – 900 MHz

VHF 30 – 300 MHz

HF 3 – 30 MHz

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CHAPTER 7 Choice of Radio Frequency

standing for under and the “a” in Ka as standing for above,

the central band.

In the 1970s, a complete new sequence of bands—neatly

assigned consecutive letter designations from A to M—was

devised for electronic countermeasures equipment (Fig. 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 clustered—these attempts proved abortive.

In the U.S. the “new” band designations are generally used,

as originally intended, only for counter measures.

If you haven’t already done so, memorize the center fre-

quencies and wavelengths of five of these radar bands:

Band GHz cm

Ka (above) 38 0.8

Ku (under) 15 2

X103

C65

S310

Influence of Frequency on Radar Performance

The best frequency to use depends upon the job the

radar is intended to do. Like most other design decisions,

the choice involves trade-offs among several factors—physi-

cal size, transmitted power, antenna beamwidth, atmos-

pheric attenuation, and so on.

Physical Size. The dimensions of the hardware used to

generate and transmit radio frequency power are in general

proportional 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 in smaller packages and operate in more

limited spaces, and they weigh correspondingly less (Fig. 5).

Transmitted Power. Because of its impact on hardware

size, the choice of wavelength indirectly influences the abil-

ity of radar to transmit large amounts of power. The levels

of power that can reasonably be handled by a radar trans-

mitter are largely limited by voltage gradients (volts per unit

of length) and heat dissipation requirements. It is not sur-

prising, therefore, that the larger, heavier radars operating at

wavelengths on 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

4. Radar and countermeasures band letter designations.

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

quency components decreases with wavelength. Transmitter

tube for 30 centimeter radar, top; transmitter tube for 0.8 cen-

timeter radar, bottom.

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PART III Primary Design Considerations

the amount of power actually used is decided by size,

weight, reliability, and cost considerations.)

Beamwidth. As will be explained in Chap. 8, the width

of a radar’s 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 generally be used to achieve acceptably nar-

row beams. At high frequencies, small antennas will suffice

(Fig. 6). The narrower the beam, of course, the greater the

power that is concentrated in a particular direction at any

one time, and the finer the angular resolution.

Atmospheric Attenuation. In passing through the atmos-

phere, radio waves may be attenuated by two basic mecha-

nisms: absorption and scattering (see panel, right). The

absorption is mainly due to oxygen and water vapor. The

scattering is due almost entirely to condensed water vapor

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

with frequency. Below about 0.1 gigahertz, atmospheric

attenuation is negligible. Above about 10 gigahertz, it

becomes increasingly important.

Moreover, above that frequency, the radar’s 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

direction of the radar, it will be detected. In simple radars

which do not employ moving target indication (MTI), this

return—called weather clutter—may obscure targets.

Ambient Noise. Electrical noise from sources outside the

radar is high in the HF band. But it decreases with frequen-

cy (Fig. 7), reaching a minimum somewhere between about

0.3 and 10 gigahertz—depending upon the level of galactic

noise, which varies with solar conditions. From there on,

atmospheric noise predominates. It gradually becomes

stronger and grows increasingly so at K-band and higher

frequencies. In many radars internally generated noise pre-

dominates. But, when low-noise receivers are used to meet

long range requirements, external noise can be an impor-

tant consideration in the selection of frequency.

Doppler Considerations. Doppler shifts are proportional

not only to closing rate but to radio frequency. The higher

the frequency, the greater the doppler shift 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 may be used. On the

other hand, doppler sensitivity to small differences in clos-

6. For same sized antenna, width of beam is proportional to

wavelength.

7. Ambient noise reaches a minimum somewhere between 0.3

gigahertz and 10 gigahertz, depending upon the level of the

galactic noise, which varies with solar conditions.

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CHAPTER 7 Choice of Radio Frequency

ATMOSPHERIC ATTENUATION

Absorption. Energy is absorbed from radio waves passing

through the atmosphere primarily by the gases comprising it.

Absorption increases dramatically with the waves’ frequency.

Below about 0.1 gigahertz, absorption is negligible. Above 5

gigahertz, it becomes increasingly significant. Beyond about 20

gigahertz, it becomes severe.

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 decreases 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

broadened by molecular collisions and so are sharper at high

altitudes, where the atmosphere is less dense, but their

frequencies are the same. (Plot B is drawn to the same scale as A;

but is shifted down to encompass the lower curve.)

The peaks at 22 gigahertz and 185 gigahertz are due to water

vapor. Those at 60 gigahertz and 120 gigahertz are due to oxygen.

The regions between peaks are called windows.

Energy is also absorbed by particles suspended in the atmos-

phere, but their principal effect is scattering.

Scattering. Radio waves are scattered by particles suspended in

the atmosphere. Scattering increases with the particies’ 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). Snowflakes,

which contain less water and have lower fali rates, scatter less

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

Smoke and dust are negligible scatterers because of their small

particle size and low dielectric constant.

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

those frequencies and higher, backscattering is sufficient to make

rain visibie.

Both absorption and scattering by clouds are still negligible in

the S-band. So meteorological radars operating there can

measure rainfall rates without being hampered by attenuation

due to clouds or by receiving enough backscatter from them to

be confused with precipitation.

Above 10 gigahertz, scattering and absorption by clouds

becomes appreciable. The attenuation is proportional to the

amount of water in the clouds.

Attenuation increases with decreasing temperature since the

dielectric constant of water is inversely proportional to

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

low dielectric constant of ice.

FREQUENCY, GHz

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PART III Primary Design Considerations

9. At small grazing angles, return received directly from the tar-

get is very nearly cancelled by return reflected off the water.

ing rate can be increased by selecting reasonably high fre-

quencies.

Selecting the Optimum Frequency

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

radio frequency is influenced by several factors: the func-

tions 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, let

us consider some representative applications. To put the

selection in context, we will consider not only airborne

applications, but ground and shipboard 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 limi-

tations, they can be made large enough to provide accept-

ably high angular resolution while operating at relatively

low frequencies. Over-the-horizon radars, as we’ve seen,

operate in the HF-band where the ionosphere is suitably

reflective. Space surveillance and early warning radars oper-

ate in the UHF and VHF bands, where ambient noise is

minimal and atmospheric attenuation is negligible. These

bands, however, are crowded with communication signals.

So their use by radars (whose transmissions generally occu-

py 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 tolerable, ground

radars may be reduced in size by moving up to L-, S-, and

C-band frequencies or higher (Fig. 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 frequen-

cies that may 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.

For, at grazing angles approaching zero, the return

received directly from a target is very nearly cancelled by

return from the same target, reflected off the water—a

phenomenon called multipath propagation (Fig. 9).

Cancellation is due to a 180º phase reversal occurring when

the return is reflected. As the grazing angle increases, a dif-

ference develops between the lengths of the direct and indi-

rect paths, and cancellation decreases. The shorter the

wavelength, the more rapidly the cancellation disappears.

For this reason, the shorter wavelength S- and X-band fre-

8. While ground-based radars commonly operate at lower fre-

quencies, where long range is not important—as for this radar

which traces the source of mortar fire—X-band may be used

for small size.

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