direct antenas

8/8/2019 Direct Antenas

1/7

WJ Communications, Inc. 401 River Oaks Parkway San Jose, CA 95134-1918 Phone: 1-800-WJ1-4401 Fax:408-577-6620 e-mail: [email protected] Web site: www.wj.com

The Communications Edge Tech-note

Author: John E. Hill

Gain of Directional Antennas

Gain is an antenna property dealing with anantennas ability to direct its radiated powerin a desired direction, or synonymously, toreceive energy preferentially from a desireddirection. However, gain is not a quantity

which can be defined in terms of physicalquantities such as the Watt, ohm or joule,but is a dimensionless ratio. As a conse-quence, antenna gain results from the inter-action of all other antenna characteristics.This article will explore these interactionsusing elementary definitions of antenna

properties. Antenna characteristics of gain, beamwidthand efficiency are independent of the anten-nas use for either transmitting or receiving.Generally these characteristics are more sim-ply described for the transmitting antenna;however, the properties described in this arti-cle apply to both cases.

Gain definitions, and antenna characteristicsrelated to gain, are found in a glossary onpage 6, and will appear in italics within text.First, the concept of directive gain will beexamined, followed by related antenna fac-tors such as beamwidth and efficiency. Somesimple equations are listed at the conclusion

which permit approximate computations of directive gain and half-power beamwidth fordirectional type antennas.

DIRECTIVE GAIN FROM AHYPOTHETICAL ANTENNA

An antenna does not amplify. It only distrib-

utes energy through space in a manner which can best make use of energy available.Directive gain is related to and is a measureof this energy distribution.

To visualize the concept of directive gain,assume an elastic sphere is filled with anincompressible medium having a shape asshown in Figure 1a. A dot at the center of the sphere represents a hypothetical isotropicradiator which has equal radiation intensity

in all directions. Let the radius of the spherebe proportional to the power radiated by theisotropic radiator. Next, the sphere isdeformed to create a new shape as shown inFigure 1b. As a result of our assumption thatthe sphere is filled with an incompressiblemedium, the volume must remainunchanged regardless of the change in shape;the sphere surface must bulge outwardsomewhere if another area of the surface isdepressed.

For the surface shown in Figure 1b, the dis-tance from the center dot to all points onthe sphere surface is no longer everywhereequal, although the average distance, whichis equal to the original radius (ro), remainsthe same. The distance from the center to apoint on the deformed surface is now pro-portional to the radiation intensity in thatdirection. The ratio of the distance from thecenter to any particular point on the surface(rd), to the average distance (or originalsphere radius, ro) is the directive gain in that

direction. The value of the directive gain inthe direction of its maximum value is thedirectivity.

To accomplish this power distribution

change, the hypothetical antenna at thespheres center must be replaced by anantenna with the ability to direct radiatedpower in a desired direction. It is importantto note that directive gain, as just described,is related only to the shape of the antennasradiation pattern, and does not include effi-ciency factors.

DIRECTIVE GAIN ANDBEAMWIDTH

An antennas beamwidth is usually under-stood to mean the half-power beamwidth,that is, the angle between the two directionsin which the directive gain of the major radiation lobe is one half the maximum value(one half the directivity), and is shown inFigures 2a, 2b, and 2c. Each curve representthe same antenna radiation pattern, butplotted to a different scale: in watts, voltage,and decibels (dB).

For the power plot, the half-powerbeamwidth is measured at a value which isone half (.5) the peak of the beam, and is30 in the illustrated example. For the volt-age plot, the half-power beamwidth is mea-sured at a point which is .707 of the beam

Figure 1. Directive gain resulting from the shape of the radiation pattern in a cer tain direction.

a) Symmetric radiation pattern of an isotropic radiator. b) Directive radiation pattern.


2/7




maximum .5 = .7072), and is 30. For thedecibel plot, the half-power beam-width is3dB from the beam maximum (10 log10 0.5= -3 dB), and is 30. Assuming that a signif-icant amount of radiated power is notdiverted into side lobes, then the directivegain is inversely proportional to beamwidth;as the beamwidth decreases, the directivegain increases.

A simplified approximation to an antennasdirective gain may be obtained by consider-ing a convenient spherical-shaped boundary at which the power radiated by a hypotheti-cal directional antenna can be measured. Allpower radiated from the hypothetical anten-na may be imagined to flow outward andthrough the surface shown in Figure 3a.

This surface may be divided into squareareas which are independent of radius, each

occupying one degree in the vertical planeand one degree in the horizontal plane, andcontaining a total of 41,253 square degrees.*If all the power radiated by a directionalradiator could be constrained to flow throughone square degree, shown in Figure 3b, thedirective gain in that direction would be41,253 times the average directive gain. Thedirective gain for this power distribution is;

that all the power radiated by a directionalradiator is constrained to flow through anarea which is circular in cross section, as

shown in Figure 3c. Since the power radiat-ed is constrained to flow through an area

which is/4 (78%) as large, the resultingdirective gain will be greater. and is given by

gd =

or

gd =

where 1 and 2 are orthogonal beamwidths

and represent the major and minor axis of the beam. For a circular beam shape,1 isequal to 2.

In practical antenna applications, the beamis usually circular in cross section with manyminor radiation lobes, or side lobes, presentTo account for power flow in directionsother than the beams direction, an assump-tion is made that approximately 55% of thepower radiated flows within the half-powerbeamwidth. The directive gain is now approximated by:

gd =

gd =

where all the power radiated is assumed toflow through an area of one square degree.Usually, directive gain is expressed in deci-bels, and for the directive gain just calculat-ed, is equal to:

Gd = 10 log10 gd = 46 dB. A more accurate approximation of the direc-tive gain from the radiated pattern assumes

Figure 2. Equivalent half-power beamwidth representations of an antennas radiation pattern.

41,253

1

41,253

12

52,525

12

29,000

12

4

0

0.5

1.0

Beam

30

Power Watts

a) Power plot

0

0.707

1.0

30

Voltage Watts

b) Voltage plot

-40

-3

0

30

Decibels dB

c) Decibel plot

Figure 3. Simplified assumptions as to the shape of the radiated power yield approximate calculations of directive gain.

a) Power flow through a con-venient spherical boundary

b) Power flow through asquare area of one squaredegree

c) Power flow through a circu-lar area of /4 squaredegrees

*4 square radians (steradians) = 4 (57.3) 2 square degrees = 41,253 square degrees.


3/7




illumination. It is most simply explained by considering the field distribution over a par-abolic reflector-horn feed antenna shown in

Figure 5. For the aperture illuminationshown in Figure 5a, a hypothetical feed pro-duces equal radiation intensity over the anglsubtended by the parabolic reflector, but

with no energy spilled past the edges. Although this uniform aperture illuminationis not achievable in practice, it is useful as areference, as is the hypothetical isotropicradiator. The side lobes of the radiation pat-tern produced by uniform circular apertureillumination are approximately 18 dB lowerin amplitude than the beam, which itself hasas high a directive gain as can be achieved

with a given aperture size.

Practical reflector-feed antennas, however,produce a tapered distribution of radiationintensity shown in Figure 5b. For thisnonuniformly illuminated aperture, the radi-ation intensity at the edges of the aperture isapproximately 10 dB less than at the center.

As a result, the edges contribute less to theresultant, or secondary pattern, than theedges of the uniformly illuminated aperture.

The side lobes of the radiation pattern pro-duced are less in amplitude, and are morethan 20 dB below the beam. However, thedirective gain of this pattern is less than theuniformly illuminated aperture.

The directive gains of the uniform andnonuniform illuminated apertures are relatedby aperture illumination efficiency, ai whichis the ratio of the two directive gains, or

where 1 and 2 are the orthogonal half-power beamwidths of an asymmetric beam.

Although this last equation is very useful inobtaining an antennas directive gain know-ing the beamwidth, it must be rememberedthat it serves only as an approximation. Thedirective gain which results is based upon aradiation pattern exhibiting low-power lossesin the side lobes. This is not always a goodassumption. It is possible for a radiation pat-tern to have the same beamwidth as for the55% assumption, but have a large amountof power appear in the minor lobes. Forexample, if an additional 10% of the radiat-

ed power is lost to side lobe radiation, thedirective gain is approximated by:

gd =

where it is now assumed that 45% of theradiated power flows through the half-powerbeamwidth. This last equation yields themost realistic value for the directive gain of reflector-type antennas. For horn-typeantennas, it may be assumed that 60% of the power radiated flows within thebeamwidth and the directive gain is:

gd =

EFFICIENCIES RELATED TOPOWER GAIN, REALIZED GAINAND DIRECTIVE GAIN

A quantity closely related to directive gain ispower gain, gp. For an ideal antenna with aradiation efficiency of 100%, directive gain

is equal to power gain. For an antenna withlosses (excluding reflection losses arisingfrom impedance mismatch), power gain willbe lower than directive gain, and is given by the equation:

Gp = gd

where is the radiation efficiency, and isalways less than unity.

Radiation efficiency is a measure of those

losses internal to the antenna, such as I2R losses in imperfect conductors anddielectrics. It is the ratio of the total power

radiated by an antenna to the net poweraccepted by the antenna from a connectedtransmitter. Excluded from these losses is thepower reflected back to the transmitterbecause of impedance mismatch. The impli-cation is that an antenna tested for efficiency by the method described under the gainmeasurements paragraph to follow must beperfectly matched to the transmitter. This isa condition realizable under test conditionsand at a single frequency, but is not a condi-tion likely to exist under normal operatingconditions, especially in a system whichmust operate over a wide frequency band.

When mismatch loss occurs, as it usually does, this loss must be subtracted from thepower gain of the antenna to yield realizedgain. Realized gain is important to the sys-tems engineer, for it reveals how much signal

will be available at the input to the receiverfor a given field strength.

The aperture of an antenna is a planar sur-

face near the antenna that is perpendicularto the direction of maximum radiation, andthrough which the major portion of theradiation passes. For parabolic reflector-typeand horn-type antennas, the aperture is thearea of the paraboloid, or horn opening,respectively, as shown in Figure 4.

The manner in which energy is distributedover the aperture is referred to as aperture

27,000

12

31,000

12

Aperture

Aperture

a) Parabolic reflector antenna b) Horn antenna

Figure 4. Physical apertures of parabolic reflector- and horn-type antennas.


4/7




ai =

It is possible, and in fact common, for theillumination taper across an aperture to bedifferent for the feed patterns orthogonalplanes, particularly when the antenna mustoperate over a broad frequency range.

It is important to note that aperture illumi-nation efficiency is related to directive gain,

which, in turn, is related only to the shapeof the radiation pattern and not to radiationefficiency. An antenna may simultaneously exhibit a low radiation efficiency and a high

aperture illumination efficiency.

ANTENNA EFFICIENCY-APERTURE-TYPE ANTENNAS

Antenna efficiency is concerned with theeffectiveness of an antennas aperture indirecting, or collecting, radiated power. It isnot related to radiation efficiency or mis-match loss, and need not be subtracted fromdirective gain.

length). Therefore, it is necessary to under-illuminate the reflector at the high-end fre-quency in order to not over-illuminate at the

low-end frequency of the band.

GAIN MEASUREMENTS

The most generally used method for measuring an antennas power gain is shown inFigure 6, and involves substituting a stan-dard gain horn for the antenna under testand comparing the power received by each.The power gain of the standard gain hornused as reference is computed from thehorns geometry. If the measurement is per-formed properly, which is extremely difficulto do, an accuracy approaching 0.1 dB ispossible.

To measure realized gain, measurement forthe antenna under test is made as it wouldbe used in the field, with no special imped-ance matching, but with the standard gainhorn always matched to the transmissionline.

If the antenna under test is circularly polar-ized, the measurement becomes more com-

plex, for there is no agreed-upon easily con-structed gain standard that is circularly polarized and whose gain can be calculatedfrom its geometry. Either specially designedreference antennas must be constructed andcalibrated, or the antenna must be tested

with reference to linear polarization (thestandard gain horn) and suitably corrected

Antenna efficiency is often sacrificed toobtain other desirable characteristics, such asa low side-lobe level, or wide bandwidth per-formance. For example, if it is necessary toilluminate a parabolic reflector with a hornfeed over a band of frequencies, it is appar-ent the reflectors illumination will vary withfrequency since a horn radiators beamwidthis inversely proportional to frequency (or theaperture dimensions in terms of wave-

Figure 5. FIeld dlstrlbutlons, and radiation patterns produced, when a parabolic reflector s aperture is uniformly andnonuniformly illumInated.

Uniformillumination

Feed

(a) Uniform aperture illumination

0.dB

Radiation(Secondary pattern)

Nonuniformillumination

Feed

(a) Nonuniform aperture illumination

0.dB

Radiation(Secondary pattern)

-10 dB Taper

-10 dB Taper

0 dB

Detector

To measurepower gain

To measurerealized gain

Transmission line

Transmission line

Losslessmatchingnetwork

Antennaundertest

Standardgain horn

Transmissionantenna

Figure 6. Power gain and realized gain measurements.

gd (nonuniform)

gd (uniform)


5/7




for polarization mismatch. A discussion of these techniques is beyond the scope of thisarticle.

Optimum antenna performance is often acompromise between the conflicting require-ments of maximum realized gain andbeamwidth. The maximum possible realizedgain is always desirable, of course, but thenarrow beamwidth required to produce itrequires precise positioning of the beam.Gain in the wrong direction is of little use.

Measurement of gain, difficult though itmay be, is necessary to confirm that anantenna meets specification. Measured real-ized gain is the last word of performance,revealing the essence of the antenna, and isthe most significant factor for any wirelesslink, be it the local TV station or the mostexotic of spacecraft sending pictures of Marsto Earth.

ANTENNA GAIN ANDPOLARIZATION

When antenna gain is specified or tested,generally the assumption made is that thepolarization of the field is optimum-that is,the characteristic polarization of the antennaand the field in which it is measured, are thesame. If the wave is polarized differently from the antenna receiving it, then thepower available at the antenna terminals willbe less than maximum. Loss resulting frompolarization mismatch can have any valuebetween infinity and zero. Losses associated

with some of the more common polarizationmismatches are listed in Table 1.

Attenuation for the three polarizations listedis based on the polarization being either purelinear (vertical or horizontal) or pure circu-lar. In practice, however, there is some cou-pling between orthogonal polarizations. If the polarizations are coincident, no attenua-tion (0 dB) occurs due to coupling mis-match between field and antenna.Polarizations which are either orthogonallinear or opposite-hand circular suffer infi-

nite attenuation () between field andantenna. Since a circular polarized wave canbe resolved into two equal vertical and hori-

zontal components, each containing one half the total power radiated, only one half thepower (3 dB) of a circularly polarized field iscoupled to a linearly polarized antenna.

GAIN COMPUTATIONS

Approximate solutions of beamwidth anddirective gain for most directional type anten-nas can be obtained from the equations listedin Table 2. Also included is the approximateside-lobe level if the antenna is of the aper-ture-type shown. Side-lobe levels are notincluded in the equations for the uniformly illuminated apertures. Directive gain deter-mined by either method should be used withcaution; however, estimates of performanceare adequate for preliminary system analysis.

Field PolarizationVertical Horizontal Right hand Left hand

Circular Circular

Vertical

0 dB 3 dB 3 dB

Horizontal

0 dB 3 dB 3 dB

Right handCircular

3 dB 3 dB 0 dB

Left handCircular

3 dB 3 dB 0 dB

A n

t e n n a

P o

l a r i z a

t i o n

Table 1. Attenuation resulting from polarization mismatchbetween field and antenna.

Beamwidth Directive Gain Directive Gain Antenna EfficiencyAperture-Type (From Aperture) (From Aperture) (From Beamwidth) (Aperture IlluminationEfficiency)

Uniformly IlluminatedCircular Aperture-hypothetical parabola =

gd

=gd =

= 1 = 2gd = = 1 = 2

18 dB side-lobe level

Uniformly IlluminatedRectangular Aperture 1 =or Linear Array

gd = g d =

2 =13 dB Side-lobe Level

Rectangular Horn(a) Polarization Plane:

E-plane1 =

13 dB Side-lobe Levelgd = g d =

(b) Orthogonal PolarizationPlane: H-plane

2 =

26 dB side-lobe Level

Nonuniformly IlluminatedCircular Aperture (10 dBTaper) Normal Parabola = g d =

gd =

= 1 = 2 = 1 = 226 dB Side-lobe Level

a >> G d = 10 log 10gd dB G d = 10 log 10gd dB

Table 2. Computations of directive gain end beamwldth for representative aperture-type

100%

58 a

100%

60%

50%

72 a

51 a

51 b

15a 2

2

5a 2

2

1.6ab 2

9.87a 2

2

52,525 2

27,000 2

41,25312

31,000

12

56 a E

67 a H

7.5a Ea H

a

ba

a E

a H

a


6/7




SELECTED BIBLIOGRAPHY

1. Antenna Standards Committee of theIEEE Antennas and Propagation Group,IEEE Standard Definitions of Terms for

Antennas, IEEE Std 145-1973.

2. Jasik, H. (ed.) Antenna EngineeringHandbook, McGraw-Hill Book Co.,New York, First Edition. (Sections 2.6and 2.7 discuss gain, directivity and effec-tive aperture area.)

3. Kraus, J. D., Antennas, McGraw-HillBook Co., 1950.

4. Ramo, S., J. R. Whinnery, Fields and

Waves in Modern Radio, John Wiley &Sons, Inc., 1953. (Discussion of antennagain with respect to half-wave dipole.)

5. Reich, H. J.. (ed.), Very High-Frequency Techniques, McGraw-Hill Book Co.,New York, 1947. (Derivation of theequation for beamwidth in Chapter 1.)

6. Silver, S. (ed.), Microwave AntennaTheory and Design, Boston TechnicalPublishing, Inc., 1964. (Discussion of gain and absorption cross section.)

7. Southworth, G. C., Principles and Applications of Waveguide TransmissionD. Van Nostrand Co., 1950. (Discussionof gain from effective aperture area pointof view.)

8. Weeks, W. L., Antenna Engineering,McGraw-Hill Book Co., New York.(Discussion of gain with respect to radia-tion resistance.)

9. Wolff, E. A., Antenna Analysis, John

Wiley & Sons, Inc., New York.(Discussion of gain in terms of admit-tance, current and effective aperture area.)

minals of a receiving antenna to the powerper unit area of a plane wave incident on theantenna from that direction, polarized coin-

cident with the polarization that the antenna would radiate.

Half-power beamwidth.In a plane containingthe direction of the maximum of a beam,the angle between the two directions in

which the radiation intensity is one half themaximum value of the beam.

Isotropic radiator. A hypothetical antennahaving equal radiation intensity in all direc-tions. Note: An isotropic radiator representsa convenient reference for expressing thedirective properties of actual antennas.

Power gain.In a given direction, 4( times theratio of the radiation intensity in that direc-tion to the net power accepted by the anten-na from the connected transmitter.Notes: (1) When the direction is not stated,

the power gain is usually taken tobe the power gain in the directionof its maximum value.

(2) Power gain does not includereflection losses arising from mismatch of impedance.

Power gain in physical media.In a givendirection and at a given point in the farfield, the ratio of the power flux per unitarea from an antenna to the power flux perunit area from an isotropic radiator at aspecified location with the same power inpuas the subject antenna.Note: The isotropic radiator must he within

the smallest sphere containing theantenna. Suggested locations areantenna terminals and points of sym-metry, if such exist.

Power gain referred to a specified polarizatiThe power gain of an antenna, reduced by the ratio of that portion of the radiationintensity corresponding to the specifiedpolarization to the radiation intensity.

Radiation efficiency.The ratio of the totalpower radiated by an antenna to the net

GLOSSARY OF STANDARDANTENNA TERMS

The IEEE Standard Definitions of Term for Antennas represent a consistent and compre-hensive vocabulary suited for the effective com-munication and understanding of antenna the-ory. General use of these definitions of terms would eliminate much of the wide-spread inconsistency concerning antenna characteristics, particularly with regard to the basic parameters of gain, beamwidth, polarization and efficiency.For convenience, IEEE antenna terms used inthis article are listed in this glossary.

Antenna efficiency of an aperture-type anten-na. For an antenna with a specified planaraperture, the ratio at the maximum effectivearea of the antenna to the aperture area.

Aperture of an antenna. A surface, near or onan antenna, on which it is convenient tomake assumptions regarding the field valuesfor the purpose of computing fields at exter-nal points.Note: The aperture Is often taken as that

portion of a plane surface near theantenna, perpendicular to the direc-

tion of maximum radiation, through which the major part of the radiationpasses.

Aperture illumination.The field over theaperture as described by amplitude, phase,and polarization distributions.

Aperture illumination efficiency.For a planarantenna aperture, the ratio of its directivity to the directivity obtained when the apertureillumination is uniform.

Beam.The major lobe of the radiation pattern.Directive gain.In a given direction, 4 timesthe ratio of the radiation intensity in thatdirection to the total power radiated by theantenna.

Directivity.The value of the directive gain inthe direction of its maximum value.

Effective area of an antenna.In a given direc-tion, the ratio of power available at the ter-


7/7




Copyright 1976 Watkins-Johnson CompanyVol. 3 No. 4 July/August 1976

Revised and reprinted 2001 WJ Communications, Inc.

power accepted by the antenna from theconnected transmitter.

Radiation, electromagnetic.The emission of energy in the form of electromagnetic waves.

Radiation intensity. In a given direction, thepower radiated from an antenna per unitsolid angle.

Radiation lobe. A portion of the radiationpattern bounded by regions of relatively

weak radiation intensity.

Radiation pattern (antenna pattern). A graphical representation of the radiation

properties at the antenna as a function of

impedance to a specified impedance.

Realized radiation efficiency.The efficiency ofan antenna in its environment reduced by alllosses suffered by it, including: ohmic lossemismatch losses, feedline transmission losseand radome losses. (This term is not definedin the IEEE STD 145).

Relative power gain.The ratio of the powergain in a given direction to the power gain of a reference antenna in its reference direction.Note: Common reference antennas are half-

wave dipoles, electric dipoles, mag-netic dipoles, monopoles, and cali-

brated horn antennas.

space coordinates.Notes: (1) In the usual case the radiation

pattern is determined in the far-field region and is represented asa function of directional coordi-nates.

(2) Radiation properties includepower flux density, field strength,phase, and polarization.

Radiator. Any antenna or radiating elementthat is a discrete physical and functional entity.

Realized gain.The power gain of an antennain its environment, reduced by the losses due

to the mismatch of the antenna input

direct antenas

Documents