Gain of Directional Antennas

Home , Antenna aperture, Antenna gain, Isotropic radiator, Side lobe

The Communications Edgeª Tech-note Author: John E. Hill

Gain is an antenna property dealing with an in all directions. Let the radius of the sphere change, the hypothetical antenna at the antenna’s ability to direct its radiated power be proportional to the power radiated by the sphere’s center must be replaced by an in a desired direction, or synonymously, to isotropic radiator. Next, the sphere is antenna with the ability to direct radiated receive energy preferentially from a desired deformed to create a new shape as shown in power in a desired direction. It is important direction. However, gain is not a quantity Figure 1b. As a result of our assumption that to note that directive gain, as just described, which can be defined in terms of physical the sphere is filled with an incompressible is related only to the shape of the antenna’s quantities such as the Watt, ohm or joule, medium, the volume must remain radiation pattern, and does not include effi- but is a dimensionless ratio. As a conse- unchanged regardless of the change in shape; ciency factors. quence, antenna gain results from the inter- the sphere surface must bulge outward action of all other antenna characteristics. somewhere if another area of the surface is DIRECTIVE GAIN AND This article will explore these interactions depressed. BEAMWIDTH using elementary definitions of antenna For the surface shown in Figure 1b, the dis- An antenna’s beamwidth is usually under- properties. tance from the center dot to all points on stood to mean the half-power beamwidth, Antenna characteristics of gain, beamwidth the sphere surface is no longer everywhere that is, the angle between the two directions and efficiency are independent of the anten- equal, although the average distance, which in which the directive gain of the major radi- na’s use for either transmitting or receiving. is equal to the original radius (ro), remains ation lobe is one half the maximum value Generally these characteristics are more sim- the same. The distance from the center to a (one half the directivity), and is shown in ply described for the transmitting antenna; point on the deformed surface is now pro- Figures 2a, 2b, and 2c. Each curve represents however, the properties described in this arti- portional to the radiation intensity in that the same antenna radiation pattern, but cle apply to both cases. direction. The ratio of the distance from the plotted to a different scale: in watts, voltage, Gain definitions, and antenna characteristics center to any particular point on the surface and decibels (dB). (r ), to the average distance (or original related to gain, are found in a glossary on d For the power plot, the half-power sphere radius, r ) is the directive gain in that page 6, and will appear in italics within text. o beamwidth is measured at a value which is direction. The value of the directive gain in First, the concept of directive gain will be one half (.5) the peak of the beam, and is the direction of its maximum value is the examined, followed by related antenna fac- 30º in the illustrated example. For the volt- directivity. tors such as beamwidth and efficiency. Some age plot, the half-power beamwidth is mea- simple equations are listed at the conclusion To accomplish this power distribution sured at a point which is .707 of the beam which permit approximate computations of directive gain and half-power beamwidth for directional type antennas.

DIRECTIVE GAIN FROM A HYPOTHETICAL 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 measure of this energy distribution. To visualize the concept of directive gain, assume an elastic sphere is filled with an incompressible medium having a shape as a) Symmetric radiation pattern of an isotropic radiator. b) Directive radiation pattern. shown in Figure 1a. A dot at the center of the sphere represents a hypothetical isotropic radiator which has equal radiation intensity Figure 1. Directive gain resulting from the shape of the radiation pattern in a certain direction.

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 Edgeª Tech-note Author: John E. Hill

that all the power radiated by a directional 30° 30° 30° radiator is constrained to flow through an area which is circular in cross section, as Beam shown in Figure 3c. Since the power radiated is constrained to flow through an area which is π/4 (78%) as large, the resulting directive gain will be greater. and is given by:

41,253 4 0 0 -40 gd = • θ1θ2 π 0.5 or 0.707 -3 52,525 1.0 1.0 0 gd = Power Ð Watts Voltage Ð Watts Decibels Ð dB θ1θ2

where θ1 and θ2 are orthogonal beamwidths, a) Power plot b) Voltage plot c) Decibel plot and represent the major and minor axis of

Figure 2. Equivalent half-power beamwidth representations of an antenna’s radiation pattern. the beam. For a circular beam shape, θ1 is equal to θ2. maximum .5 = .7072), and is 30º. For the 41,253 In practical antenna applications, the beam gd = decibel plot, the half-power beam-width is 1 is usually circular in cross section with many 3dB from the beam maximum (10 log 0.5 minor radiation lobes, or side lobes, present. 10 where all the power radiated is assumed to = -3 dB), and is 30º. Assuming that a signif- To account for power flow in directions flow through an area of one square degree. icant amount of radiated power is not other than the beam’s direction, an assump- diverted into side lobes, then the directive Usually, directive gain is expressed in deci- tion is made that approximately 55% of the gain is inversely proportional to beamwidth; bels, and for the directive gain just calculat- power radiated flows within the half-power as the beamwidth decreases, the directive ed, is equal to: beamwidth. The directive gain is now gain increases. approximated by: Gd = 10 log10 gd = 46 dB. A simplified approximation to an antenna’s A more accurate approximation of the direc- 29,000 directive gain may be obtained by consider- gd = tive gain from the radiated pattern assumes θ1θ2 ing a convenient spherical-shaped boundary at which the power radiated by a hypothetical directional antenna can be measured. All power radiated from the hypothetical antenna may be imagined to flow outward and through the surface shown in Figure 3a. This surface may be divided into square areas which are independent of radius, each occupying one degree in the vertical plane and one degree in the horizontal plane, and containing a total of 41,253 square degrees.* If all the power radiated by a directional radiator could be constrained to flow through a) Power flow through a con- b) Power flow through a c) Power flow through a circu- one square degree, shown in Figure 3b, the venient spherical boundary square area of one square lar area of π/4 square directive gain in that direction would be degree degrees 41,253 times the average directive gain. The directive gain for this power distribution is; Figure 3. Simplified assumptions as to the shape of the radiated power yield approximate calculations of directive gain.

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

2 where θ1 and θ2 are the orthogonal half- losses internal to the antenna, such as I R illumination. It is most simply explained by power beamwidths of an asymmetric beam. losses in imperfect conductors and considering the field distribution over a par- dielectrics. It is the ratio of the total power abolic reflector-horn feed antenna shown in Although this last equation is very useful in radiated by an antenna to the net power Figure 5. For the aperture illumination obtaining an antenna’s directive gain know- accepted by the antenna from a connected shown in Figure 5a, a hypothetical feed pro- ing the beamwidth, it must be remembered transmitter. Excluded from these losses is the duces equal radiation intensity over the angle that it serves only as an approximation. The power reflected back to the transmitter subtended by the parabolic reflector, but directive gain which results is based upon a because of impedance mismatch. The impli- with no energy spilled past the edges. radiation pattern exhibiting low-power losses cation is that an antenna tested for efficiency Although this uniform aperture illumination in the side lobes. This is not always a good by the method described under the “gain is not achievable in practice, it is useful as a assumption. It is possible for a radiation pat- measurements” paragraph to follow must be reference, as is the hypothetical isotropic tern to have the same beamwidth as for the perfectly matched to the transmitter. This is radiator. The side lobes of the radiation pat- 55% assumption, but have a large amount a condition realizable under test conditions tern produced by uniform circular aperture of power appear in the minor lobes. For and at a single frequency, but is not a condi- illumination are approximately 18 dB lower example, if an additional 10% of the radiat- tion likely to exist under normal operating in amplitude than the beam, which itself has ed power is lost to side lobe radiation, the conditions, especially in a system which as high a directive gain as can be achieved directive gain is approximated by: must operate over a wide frequency band. with a given aperture size. 27,000 Practical reflector-feed antennas, however, gd = When mismatch loss occurs, as it usually θ1θ2 does, this loss must be subtracted from the produce a tapered distribution of radiation where it is now assumed that 45% of the power gain of the antenna to yield realized intensity shown in Figure 5b. For this nonuniformly illuminated aperture, the radi- radiated power flows through the half-power gain. Realized gain is important to the sys- ation intensity at the edges of the aperture is beamwidth. This last equation yields the tems engineer, for it reveals how much signal approximately 10 dB less than at the center. most realistic value for the directive gain of will be available at the input to the receiver As a result, the edges contribute less to the reflector-type antennas. For horn-type for a given field strength. resultant, or secondary pattern, than the antennas, it may be assumed that 60% of The aperture of an antenna is a planar sur- edges of the uniformly illuminated aperture. the power radiated flows within the face near the antenna that is perpendicular The side lobes of the radiation pattern pro- beamwidth and the directive gain is: to the direction of maximum radiation, and duced are less in amplitude, and are more 31,000 through which the major portion of the than 20 dB below the beam. However, the gd = radiation passes. For parabolic reflector-type directive gain of this pattern is less than the θ1θ2 and horn-type antennas, the aperture is the uniformly illuminated aperture. area of the paraboloid, or horn opening, EFFICIENCIES RELATED TO The directive gains of the uniform and respectively, as shown in Figure 4. POWER GAIN, REALIZED GAIN nonuniform illuminated apertures are related AND DIRECTIVE GAIN The manner in which energy is distributed by aperture illumination efficiency, ηai which A quantity closely related to directive gain is over the aperture is referred to as aperture is the ratio of the two directive gains, or power gain, gp. For an ideal antenna with a radiation efficiency of 100%, directive gain is equal to power gain. For an antenna with losses (excluding reflection losses arising from impedance mismatch), power gain will be lower than directive gain, and is given by the equation: Aperture Gp = gd η Aperture where η is the radiation efficiency, and is a) Parabolic reflector antenna b) Horn antenna always less than unity.

Radiation efficiency is a measure of those Figure 4. Physical apertures of parabolic reflector- and horn-type antennas.

length). Therefore, it is necessary to under- Uniform illumination illuminate the reflector at the high-end frequency in order to not over-illuminate at the low-end frequency of the band. 0.dB GAIN MEASUREMENTS Feed The most generally used method for measur- ing an antenna’s power gain is shown in Radiation Figure 6, and involves substituting a stan- (Secondary pattern) (a) Uniform aperture illumination dard gain horn for the antenna under test and comparing the power received by each. Nonuniform -10 dB Taper The power gain of the standard gain horn illumination used as reference is computed from the horn’s geometry. If the measurement is per- formed properly, which is extremely difficult 0.dB 0 dB to do, an accuracy approaching 0.1 dB is

Feed possible. To measure realized gain, measurement for -10 dB Taper Radiation the antenna under test is made as it would (Secondary pattern) (a) Nonuniform aperture illumination be used in the field, with no special impedance matching, but with the standard gain Figure 5. FIeld dlstrlbutlons, and radiation patterns produced, when a parabolic reflector’s aperture is uniformly and nonuniformly illumInated. horn always matched to the transmission line. gd (nonuniform) Antenna efficiency is often sacrificed to If the antenna under test is circularly polar- ηai = obtain other desirable characteristics, such as gd (uniform) ized, the measurement becomes more com- a low side-lobe level, or wide bandwidth per- It is possible, and in fact common, for the plex, for there is no agreed-upon easily con- formance. For example, if it is necessary to illumination taper across an aperture to be structed gain standard that is circularly illuminate a parabolic reflector with a horn different for the feed pattern’s orthogonal polarized and whose gain can be calculated feed over a band of frequencies, it is appar- planes, particularly when the antenna must from its geometry. Either specially designed operate over a broad frequency range. ent the reflector’s illumination will vary with reference antennas must be constructed and frequency since a horn radiator’s beamwidth calibrated, or the antenna must be tested It is important to note that aperture illumi- is inversely proportional to frequency (or the with reference to linear polarization (the nation efficiency is related to directive gain, aperture dimensions in terms of wave- standard gain horn) and suitably corrected which, in turn, is related only to the shape of the radiation pattern and not to radiation efficiency. An antenna may simultaneously Transmission line exhibit a low radiation efficiency and a high Transmission antenna Standard aperture illumination efficiency. gain horn

To measure ANTENNA EFFICIENCY- realized gain Detector

APERTURE-TYPE ANTENNAS Transmission line Antenna efficiency is concerned with the Antenna effectiveness of an antenna’s aperture in under directing, or collecting, radiated power. It is test Lossless matching To measure not related to radiation efficiency or mis- network power gain match loss, and need not be subtracted from directive gain. Figure 6. Power gain and realized gain measurements.

for polarization mismatch. A discussion of nite attenuation (∞) between field and Field Polarization Vertical Horizontal Right hand Left hand these techniques is beyond the scope of this antenna. Since a circular polarized wave can Circular Circular article. be resolved into two equal vertical and horizontal components, each containing one half Optimum antenna performance is often a Vertical the total power radiated, only one half the 0 dB 3 dB 3 dB compromise between the conflicting require- ∞ power (3 dB) of a circularly polarized field is ments of maximum realized gain and Horizontal coupled to a linearly polarized antenna. ∞ 0 dB 3 dB 3 dB beamwidth. The maximum possible realized Right hand gain is always desirable, of course, but the GAIN COMPUTATIONS Circular narrow beamwidth required to produce it 3 dB 3 dB 0 dB ∞ Approximate solutions of beamwidth and Antenna Polarization requires precise positioning of the beam. Left hand Gain in the wrong direction is of little use. directive gain for most directional type anten- Circular nas can be obtained from the equations listed 3 dB 3 dB ∞ 0 dB Measurement of gain, difficult though it in Table 2. Also included is the approximate Table 1. Attenuation resulting from polarization mismatch may be, is necessary to confirm that an side-lobe level if the antenna is of the aper- between field and antenna. antenna meets specification. Measured real- ture-type shown. Side-lobe levels are not ized gain is the last word of performance, included in the equations for the uniformly revealing the essence of the antenna, and is illuminated apertures. Directive gain deter- the most significant factor for any wireless mined by either method should be used with link, be it the local TV station or the most caution; however, estimates of performance exotic of spacecraft sending pictures of Mars are adequate for preliminary system analysis. to Earth.

ANTENNA GAIN AND

POLARIZATION Beamwidth Directive Gain Directive Gain Antenna Efficiency Aperture-Type (From Aperture) (From Aperture) (From Beamwidth) (Aperture Illumination When antenna gain is specified or tested, Efficiency) Uniformly Illuminated generally the assumption made is that the Circular Aperture- 2 58λ g = 15a 52,525 hypothetical parabola θ = d 2 g = polarization of the field is optimum-that is, a λ d 2 θ 100% a 9.87a2 the characteristic polarization of the antenna gd = 2 θ = θ1 = θ2 λ θ = θ1 = θ2 and the field in which it is measured, are the 18 dB side-lobe level same. If the wave is polarized differently Uniformly Illuminated 51λ Rectangular Aperture θ = 1 a from the antenna receiving it, then the or Linear Array 1.6ab 41,253 gd =g2 d = 100% power available at the antenna terminals will b λ θ1θ2 a 51λ θ2 = be less than maximum. Loss resulting from 13 dB Side-lobe Level b polarization mismatch can have any value Rectangular Horn between infinity and zero. Losses associated (a) Polarization Plane: E-plane 56λ = θ1 a with some of the more common polarization aE E mismatches are listed in Table 1. 13 dB Side-lobe Level 7.5aEaH 31,000 60% gd =gd = Attenuation for the three polarizations listed (b) Orthogonal Polarization λ θ1θ2 Plane: H-plane is based on the polarization being either pure 67λ θ2 = aH a linear (vertical or horizontal) or pure circu- H 26 dB side-lobe Level lar. In practice, however, there is some cou- Nonuniformly Illuminated pling between orthogonal polarizations. If Circular Aperture (10 dB 72λ 27,000 Taper)ÐNormal Parabola =g2 = θ 5a d 2 the polarizations are coincident, no attenua- a g = θ d λ2 50% tion (0 dB) occurs due to coupling mis- a θ = θ1 = θ2 θ = θ1 = θ2 match between field and antenna. 26 dB Side-lobe Level a >> G = 10 log g dB G = 10 log g dB Polarizations which are either orthogonal λ d 10 d d 10 d linear or opposite-hand circular suffer infi- Table 2. Computations of directive gain end beamwldth for representative aperture-type

SELECTED BIBLIOGRAPHY GLOSSARY OF STANDARD minals of a receiving antenna to the power 1. Antenna Standards Committee of the ANTENNA TERMS per unit area of a plane wave incident on the IEEE Antennas and Propagation Group, The “IEEE Standard Definitions of Term for antenna from that direction, polarized coin- IEEE Standard Definitions of Terms for Antennas” represent a consistent and compre- cident with the polarization that the antenna Antennas,” IEEE Std 145-1973. hensive vocabulary suited for the effective com- would radiate. munication and understanding of antenna the- 2. Jasik, H. (ed.) Antenna Engineering Half-power beamwidth. In a plane containing ory. General use of these definitions of terms Handbook, McGraw-Hill Book Co., the direction of the maximum of a beam, would eliminate much of the wide-spread New York, First Edition. (Sections 2.6 the angle between the two directions in inconsistency concerning antenna characteristics, and 2.7 discuss gain, directivity and effec- which the radiation intensity is one half the particularly with regard to the basic parameters tive aperture area.) maximum value of the beam. of gain, beamwidth, polarization and efficiency. Isotropic radiator. A hypothetical antenna 3. Kraus, J. D., Antennas, McGraw-Hill For convenience, IEEE antenna terms used in having equal radiation intensity in all direc- Book Co., 1950. this article are listed in this glossary. tions. Note: An isotropic radiator represents 4. Ramo, S., J. R. Whinnery, Fields and Antenna efficiency of an aperture-type anten- a convenient reference for expressing the Waves in Modern Radio, John Wiley & na. For an antenna with a specified planar directive properties of actual antennas. Sons, Inc., 1953. (Discussion of antenna aperture, the ratio at the maximum effective Power gain. In a given direction, 4( times the gain with respect to half-wave dipole.) area of the antenna to the aperture area. ratio of the radiation intensity in that direc- 5. Reich, H. J.. (ed.), Very High-Frequency Aperture of an antenna. A surface, near or on tion to the net power accepted by the anten- Techniques, McGraw-Hill Book Co., an antenna, on which it is convenient to na from the connected transmitter. New York, 1947. (Derivation of the make assumptions regarding the field values Notes: (1) When the direction is not stated, equation for beamwidth in Chapter 1.) for the purpose of computing fields at exter- the power gain is usually taken to 6. Silver, S. (ed.), Microwave Antenna nal points. be the power gain in the direction Theory and Design, Boston Technical Note: The aperture Is often taken as that of its maximum value. Publishing, Inc., 1964. (Discussion of portion of a plane surface near the (2) Power gain does not include gain and absorption cross section.) antenna, perpendicular to the direc- reflection losses arising from mis- tion of maximum radiation, through match of impedance. 7. Southworth, G. C., Principles and which the major part of the radiation Applications of Waveguide Transmission passes. Power gain in physical media. In a given D. Van Nostrand Co., 1950. (Discussion direction and at a given point in the far of gain from effective aperture area point Aperture illumination. The field over the field, the ratio of the power flux per unit of view.) aperture as described by amplitude, phase, area from an antenna to the power flux per and polarization distributions. unit area from an isotropic radiator at a 8. Weeks, W. L., Antenna Engineering, specified location with the same power input McGraw-Hill Book Co., New York. Aperture illumination efficiency. For a planar as the subject antenna. (Discussion of gain with respect to radia- antenna aperture, the ratio of its directivity tion resistance.) to the directivity obtained when the aperture Note: The isotropic radiator must he within illumination is uniform. the smallest sphere containing the 9. Wolff, E. A., Antenna Analysis, John antenna. Suggested locations are Beam. The major lobe of the radiation pattern. Wiley & Sons, Inc., New York. antenna terminals and points of sym- (Discussion of gain in terms of admit- Directive gain. In a given direction, 4π times metry, if such exist. tance, current and effective aperture area.) the ratio of the radiation intensity in that Power gain referred to a specified polarization. direction to the total power radiated by the The power gain of an antenna, reduced by antenna. the ratio of that portion of the radiation Directivity. The value of the directive gain in intensity corresponding to the specified the direction of its maximum value. polarization to the radiation intensity. Effective area of an antenna. In a given direc- Radiation efficiency. The ratio of the total tion, the ratio of power available at the ter- power radiated by an antenna to the net

power accepted by the antenna from the space coordinates. impedance to a specified impedance. connected transmitter. Notes: (1) In the usual case the radiation Realized radiation efficiency. The efficiency of Radiation, electromagnetic. The emission of pattern is determined in the far- an antenna in its environment reduced by all field region and is represented as energy in the form of electromagnetic waves. losses suffered by it, including: ohmic losses, a function of directional coordi- mismatch losses, feedline transmission losses, Radiation intensity. In a given direction, the nates. and radome losses. (This term is not defined power radiated from an antenna per unit (2) Radiation properties include in the IEEE STD 145). solid angle. power flux density, field strength, Relative power gain. The ratio of the power phase, and polarization. Radiation lobe. A portion of the radiation gain in a given direction to the power gain of pattern bounded by regions of relatively Radiator. Any antenna or radiating element a reference antenna in its reference direction. weak radiation intensity. that is a discrete physical and functional entity. Note: Common reference antennas are half- Radiation pattern (antenna pattern). A Realized gain. The power gain of an antenna wave dipoles, electric dipoles, mag- graphical representation of the radiation in its environment, reduced by the losses due netic dipoles, monopoles, and cali- properties at the antenna as a function of to the mismatch of the antenna input brated horn antennas.

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