First published in Via Satellite
Antennas: The Interface with Space
by Robert A. Nelson
The antenna is the most visible part of the
satellite communicationon system. The antenna transmits and receives the modulated
carrier signal at the radio frequency (RF) portion of the electromagnetic
spectrum. For satellite communication, the frequencies range from about 0.3 GHz
(VHF) to 30 GHz (Ka-band) and beyond. These frequencies represent microwaves,
with wavelengths on the order of one meter down to below one centimeter. High
frequencies, and the corresponding small wavelengths, permit the use of antennas
having practical dimensions for commercial use. This article summarizes the
basic properties of antennas used in satellite communication and derives several
fundamental relations used in antenna design and RF link analysis.
HISTORY OF ELECTROMAGNETIC WAVES
The quantitative study of electricity and magnetism began with
the scientific research of the French physicist Charles Augustin Coulomb. In
1787 Coulomb proposed a law of force for charges that, like Sir Isaac Newton’s
law of gravitation, varied inversely as the square of the distance. Using a
sensitive torsion balance, he demonstrated its validity experimentally for
forces of both repulsion and attraction. Like the law of gravitation, Coulomb’s
law was based on the notion of "action at a distance," wherein bodies can
interact instantaneously and directly with one another without the intervention
of any intermediary.
At the beginning of the nineteenth century, the electrochemical
cell was invented by Alessandro Volta, professor of natural philosophy at the
University of Pavia in Italy. The cell created an electromotive force, which
made the production of continuous currents possible. Then in 1820 at the
University of Copenhagen, Hans Christian Oersted made the momentous discovery
that an electric current in a wire could deflect a magnetic needle. News of this
discovery was communicated to the French Academy of Sciences two months later.
The laws of force between current bearing wires were at once investigated by
Andre-Marie Ampere and by Jean-Baptiste Biot and Felix Savart. Within six years
the theory of steady currents was complete. These laws were also "action at a
distance" laws, that is, expressed directly in terms of the distances between
the current elements.
Subsequently, in 1831, the British scientist Michael Faraday
demonstrated the reciprocal effect, in which a moving magnet in the vicinity of
a coil of wire produced an electric current. This phenomenon, together with
Oersted’s experiment with the magnetic needle, led Faraday to conceive the
notion of a magnetic field. A field produced by a current in a wire interacted
with a magnet. Also, according to his law of induction, a time varying magnetic
field incident on a wire would induce a voltage, thereby creating a current.
Electric forces could similarly be expressed in terms of an electric field
created by the presence of a charge.
Faraday’s field concept implied that charges and currents
interacted directly and locally with the electromagnetic field, which although
produced by charges and currents, had an identity of its own. This view was in
contrast to the concept of "action at a distance," which assumed bodies
interacted directly with one another. Faraday, however, was a self-taught
experimentalist and did not formulate his laws mathematically.
It was left to the Scottish physicist James Clerk Maxwell to
establish the mathematical theory of electromagnetism based on the physical
concepts of Faraday. In a series of papers published between 1856 and 1865,
Maxwell restated the laws of Coulomb, Ampere, and Faraday in terms of Faraday’s
electric and magnetic fields. Maxwell thus unified the theories of electricity
and magnetism, in the same sense that two hundred years earlier Newton had
unified terrestrial and celestial mechanics through his theory of universal
As is typical of abstract mathematical reasoning, Maxwell saw
in his equations a certain symmetry that suggested the need for an additional
term, involving the time rate of change of the electric field. With this
generalization, Maxwell’s equations also became consistent with the principle of
conservation of charge.
Furthermore, Maxwell made the profound observation that his set
of equations, thus modified, predicted the existence of electromagnetic waves.
Therefore, disturbances in the electromagnetic field could propagate through
space. Using the values of known experimental constants obtained solely from
measurements of charges and currents, Maxwell deduced that the speed of
propagation was equal to speed of light. This quantity had been measured
astronomically by Olaf Romer in 1676 from the eclipses of Jupiter’s satellites
and determined experimentally from terrestrial measurements by H.L. Fizeau in
1849. He then asserted that light itself was an electromagnetic wave, thereby
unifying optics with electromagnetism as well.
Maxwell was aided by his superior knowledge of dimensional
analysis and units of measure. He was a member of the British Association
committee formed in 1861 that eventually established the centimeter-gram-second
(CGS) system of absolute electrical units.
Maxwell’s theory was not accepted by scientists immediately, in
part because it had been derived from a bewildering collection of mechanical
analogies and difficult mathematical concepts. The form of Maxwell’s equations
as they are known today is due to the German physicist Heinrich Hertz. Hertz
simplified them and eliminated unnecessary assumptions.
Hertz’s interest in Maxwell’s theory was occasioned by a prize
offered by the Berlin Academy of Sciences in 1879 for research on the relation
between polarization in insulators and electromagnetic induction. By means of
his experiments, Hertz discovered how to generate high frequency electrical
oscillations. He was surprised to find that these oscillations could be detected
at large distances from the apparatus. Up to that time, it had been generally
assumed that electrical forces decreased rapidly with distance according to the
Newtonian law. He therefore sought to test Maxwell’s prediction of the existence
of electromagnetic waves.
In 1888, Hertz set up standing electromagnetic waves using an
oscillator and spark detector of his own design and made independent
measurements of their wavelength and frequency. He found that their product was
indeed the speed of light. He also verified that these waves behaved according
to all the laws of reflection, refraction, and polarization that applied to
visible light, thus demonstrating that they differed from light only in
wavelength and frequency. "Certainly it is a fascinating idea," Hertz wrote,
"that the processes in air that we have been investigating represent to us on a
million-fold larger scale the same processes which go on in the neighborhood of
a Fresnel mirror or between the glass plates used in exhibiting Newton’s
It was not long until the discovery of electromagnetic waves
was transformed from pure physics to engineering. After learning of Hertz’s
experiments through a magazine article, the young Italian engineer Guglielmo
Marconi constructed the first transmitter for wireless telegraphy in 1895.
Within two years he used this new invention to communicate with ships at sea.
Marconi’s transmission system was improved by Karl F. Braun, who increased the
power, and hence the range, by coupling the transmitter to the antenna through a
transformer instead of having the antenna in the power circuit directly.
Transmission over long distances was made possible by the reflection of radio
waves by the ionosphere. For their contributions to wireless telegraphy, Marconi
and Braun were awarded the Nobel Prize in physics in 1909.
Marconi created the American Marconi Wireless Telegraphy
Company in 1899, which competed directly with the transatlantic undersea cable
operators. On the early morning of April 15, 1912, a 21-year old Marconi
telegrapher in New York City by the name of David Sarnoff received a wireless
message from the Marconi station in Newfoundland, which had picked up faint SOS
distress signals from the steamship Titanic. Sarnoff relayed the report
of the ship’s sinking to the world. This singular event dramatized the
importance of the new means of communication.
Initially, wireless communication was synonymous with
telegraphy. For communication over long distances the wavelengths were greater
than 200 meters. The antennas were typically dipoles formed by long wires cut to
a submultiple of the wavelength.
Commercial radio emerged during the 1920s and 1930s. The
American Marconi Company evolved into the Radio Corporation of America (RCA)
with David Sarnoff as its director. Technical developments included the
invention of the triode for amplification by Lee de Forest and the perfection of
AM and FM receivers through the work of Edwin Howard Armstrong and others. In
his book Empire of the Air: The Men Who Made Radio, Tom Lewis
de Forest, Armstrong, and Sarnoff as the three
visionary pioneers most responsible for the birth of the modern communications
Stimulated by the invention of radar during World War II,
considerable research and development in radio communication at microwave
frequencies and centimeter wavelengths was conducted in the decade of the 1940s.
The MIT Radiation Laboratory was a leading center for research on microwave
antenna theory and design. The basic formulation of the radio transmission
formula was developed by Harald T. Friis at the Bell Telephone Laboratories and
published in 1946. This equation expressed the radiation from an antenna in
terms of the power flow per unit area, instead of giving the field strength in
volts per meter, and is the foundation of the RF link equation used by satellite
communication engineers today.
TYPES OF ANTENNAS
A variety of antenna types are used in satellite
communications. The most widely used narrow beam antennas are reflector
antennas. The shape is generally a paraboloid of revolution. For full earth
coverage from a geostationary satellite, a horn antenna is used. Horns are also
used as feeds for reflector antennas.
In a direct feed reflector, such as on a satellite or a small
earth terminal, the feed horn is located at the focus or may be offset to one
side of the focus. Large earth station antennas have a subreflector at the
focus. In the Cassegrain design, the subreflector is convex with an
hyperboloidal surface, while in the Gregorian design it is concave with an
The subreflector permits the antenna optics to be located near
the base of the antenna. This configuration reduces losses because the length of
the waveguide between the transmitter or receiver and the antenna feed is
reduced. The system noise temperature is also reduced because the receiver looks
at the cold sky instead of the warm earth. In addition, the mechanical stability
is improved, resulting in higher pointing accuracy.
Phased array antennas may be used to produce multiple beams or
for electronic steering. Phased arrays are found on many nongeostationary
satellites, such as the Iridium, Globalstar, and ICO satellites for mobile
GAIN AND HALF POWER BEAMWIDTH
The fundamental characteristics of an antenna are its gain and
half power beamwidth. According to the reciprocity theorem, the transmitting and
receiving patterns of an antenna are identical at a given wavelength
The gain is a measure of how much of the input power is
concentrated in a particular direction. It is expressed with respect to a
hypothetical isotropic antenna, which radiates equally in all directions. Thus
in the direction (q , f ), the
G(q , f ) = (dP/dW)/(Pin
where Pin is the total input power and dP
is the increment of radiated output power in solid angle dW. The gain is maximum along the boresight
The input power is Pin =
Ea2 A / h
Z0 where Ea is the average electric field
over the area A of the aperture, Z0 is the impedance of
free space, and h is the net antenna efficiency. The
output power over solid angle dWis
dP = E2 r2 dW/ Z0, where E is the electric
field at distance r. But by the Fraunhofer theory of diffraction,
E = Ea A / r l
along the boresight direction, where l is the
wavelength. Thus the boresight gain is given in terms of the size of the antenna
by the important relation
G = h (4 p / l2)
This equation determines the required antenna area for the
specified gain at a given wavelength.
The net efficiency h is the product of
the aperture taper efficiency ha ,
which depends on the electric field distribution over the antenna aperture (it
is the square of the average divided by the average of the square), and the
total radiation efficiency h * =
P/Pin associated with various losses. These losses
include spillover, ohmic heating, phase nonuniformity, blockage, surface
roughness, and cross polarization. Thus h = ha h *. For a
typical antenna, h = 0.55.
For a reflector antenna, the area is simply the projected area.
Thus for a circular reflector of diameter D, the area is A = p D2/4 and the gain is
G = h (p D / l )2
which can also be written
G = h (p D f / c)2
since c = l f, where
c is the speed of light (3 ´ 108
m/s), l is the wavelength, and f is the
frequency. Consequently, the gain increases as the wavelength decreases or the
For example, an antenna with a diameter of 2 m and an
efficiency of 0.55 would have a gain of 8685 at the C-band uplink frequency of 6
GHz and wavelength of 0.050 m. The gain expressed in decibels (dB) is
10 log(8685) = 39.4 dB. Thus the power radiated by the antenna
is 8685 times more concentrated along the boresight direction than for an
isotropic antenna, which by definition has a gain of 1 (0 dB). At Ku-band, with
an uplink frequency of 14 GHz and wavelength 0.021 m, the gain is 49,236 or 46.9
dB. Thus at the higher frequency, the gain is higher for the same size
The boresight gain G can be expressed in terms of the
antenna beam solid angle WA that
contains the total radiated power as
G = h * (4p / WA )
which takes into account the antenna losses through the
radiation efficiency h *. The antenna beam solid angle
is the solid angle through which all the power would be concentrated if the gain
were constant and equal to its maximum value. The directivity does not include
radiation losses and is equal to G / h *.
The half power beamwidth is the angular separation between the
half power points on the antenna radiation pattern, where the gain is one half
the maximum value. For a reflector antenna it may be expressed
HPBW = a = k l / D
where k is a factor that depends on the shape of the
reflector and the method of illumination. For a typical antenna, k =
70° (1.22 if a is in radians).
Thus the half power beamwidth decreases with decreasing wavelength and
For example, in the case of the 2 meter antenna, the half power
beamwidth at 6 GHz is approximately 1.75° . At 14 GHz,
the half power beamwidth is approximately 0.75° . As an
extreme example, the half power beamwidth of the Deep Space Network 64 meter
antenna in Goldstone, California is only 0.04 ° at
X-band (8.4 GHz).
The gain may be expressed directly in terms of the half power
beamwidth by eliminating the factor D/l .
G = h (p k / a
Inserting the typical values h = 0.55
and k = 70° , one obtains
G = 27,000/ (a°
where a° is expressed in degrees. This
is a well known engineering approximation for the gain (expressed as a numeric).
It shows directly how the size of the beam automatically determines the gain.
Although this relation was derived specifically for a reflector antenna with a
circular beam, similar relations can be obtained for other antenna types and
beam shapes. The value of the numerator will be somewhat different in each
For example, for a satellite antenna with a circular spot beam
of diameter 1° , the gain is 27,000 or 44.3 dB. For a
Ku-band downlink at 12 GHz, the required antenna diameter determined from either
the gain or the half power beamwidth is 1.75 m.
A horn antenna would be used to provide full earth coverage
from geostationary orbit, where the angular diameter of the earth is 17.4° . Thus, the required gain is 89.2 or 19.5 dB. Assuming an
efficiency of 0.70, the horn diameter for a C-band downlink frequency of 4 GHz
would be 27 cm.
EIRP AND G/T
For the RF link budget, the two required antenna properties are
the equivalent isotropic radiated power (EIRP) and the "figure of merit"
G/T. These quantities are the properties of the transmit antenna
and receive antenna that appear in the RF link equation and are calculated at
the transmit and receive frequencies, respectively.
The equivalent isotropic radiated power (EIRP) is the power
radiated equally in all directions that would produce a power flux density
equivalent to the power flux density of the actual antenna. The power flux
density F is defined as the radiated power P per
unit area S, or F = P/S. But P
= h * Pin , where
Pin is the input power and h * is the
radiation efficiency, and
d2 WA ,where
d is the slant range to the center of coverage and WA is the solid angle containing the total
power. Thus with some algebraic manipulation,
F = h *
(4p / WA
)( Pin / 4p d2) =
G Pin / 4p
Since the surface area of a sphere of radius d is 4p d2, the flux density in terms of the EIRP
F = EIRP / 4p
Equating these two expressions, one obtains
EIRP = G Pin
Therefore, the equivalent isotropic radiated power is the
product of the antenna gain of the transmitter and the power applied to the
input terminals of the antenna. The antenna efficiency is absorbed in the
definition of gain.
The "figure of merit" is the ratio of the antenna gain of the
receiver G and the system temperature T. The system temperature is
a measure of the total noise power and includes contributions from the antenna
and the receiver. Both the gain and the system temperature must be referenced to
the same point in the chain of components in the receiver system. The ratio
G/T is important because it is an invariant that is independent of
the reference point where it is calculated, even though the gain and the system
temperature individually are different at different points.
Since electromagnetic energy propagates in the form of waves,
it spreads out through space due to the phenomenon of diffraction. Individual
waves combine both constructively and destructively to form a diffraction
pattern that manifests itself in the main lobe and side lobes of the
The antenna pattern is analogous to the "Airy rings" produced
by visible light when passing through a circular aperture. These diffraction
patterns were studied by Sir George Biddell Airy, Astronomer Royal of England
during the nineteenth century, to investigate the resolving power of a
telescope. The diffraction pattern consists of a central bright spot surrounded
by concentric bright rings with decreasing intensity.
The central spot is produced by waves that combine
constructively and is analogous to the main lobe of the antenna. The spot is
bordered by a dark ring, where waves combine destructively, that is analogous to
the first null. The surrounding bright rings are analogous to the side lobes of
the antenna pattern. As noted by Hertz, the only difference in this behavior is
the size of the pattern and the difference in wavelength.
Within the main lobe of an axisymmetric antenna, the gain
G(q ) in a direction q
with respect to the boresight direction may be approximated by the
G(q ) = G - 12 (q / a
where G is the boresight gain. Here the gains are
expressed in dB. Thus at the half power points to either side of the boresight
direction, where q = a /2, the
gain is reduced by a factor of 2, or 3 dB. The details of the antenna, including
its shape and illumination, are contained in the value of the half power
beamwidth a . This equation would typically be used to
estimate the antenna loss due to a small pointing error.
The gain of the side lobes can be approximated by an envelope.
For new earth station antennas with
D/l > 100, the side lobes must fall within the envelope 29 - 25 log q by international
regulation. This envelope is determined by the requirement of minimizing
interference between neighboring satellites in the geostationary arc with a
nominal 2° spacing.
The gain pattern of a reflector antenna depends on how the
antenna is illuminated by the feed. The variation in electric field across the
antenna diameter is called the antenna taper.
The total antenna solid angle containing all of the radiated
power, including side lobes, is
WA = h * (4p / G) = (1/ha) (l2
where ha is the
aperture taper efficiency and h * is the radiation
efficiency associated with losses. The beam efficiency is defined as
e = WM / WA
where WM is thesolid angle for the main lobe. The values of ha and are e
calculated from the electric field distribution in the aperture plane and the
antenna radiation pattern, respectively.
For a theoretically uniform illumination, the electric field is
constant and the aperture taper efficiency is 1. If the feed is designed to
cause the electric field to decrease with distance from the center, then the
aperture taper efficiency decreases but the proportion of power in the main lobe
increases. In general, maximum aperture taper efficiency occurs for a uniform
distribution, but maximum beam efficiency occurs for a highly tapered
For uniform illumination, the half power beamwidth is 58.4° l /D and the first side
lobe is 17.6 dB below the peak intensity in the boresight direction. In this
case, the main lobe contains about 84 percent of the total radiated power and
the first side lobe contains about 7 percent.
If the electric field amplitude has a simple parabolic
distribution, falling to zero at the reflector edge, then the aperture taper
efficiency becomes 0.75 but the fraction of power in the main lobe increases to
98 percent. The half power beamwidth is now 72.8° l /D and the first side lobe is 24.6 dB below peak
intensity. Thus, although the aperture taper efficiency is less, more power is
contained in the main lobe, as indicated by the larger half power beamwidth and
lower side lobe intensity.
If the electric field decreases to a fraction C of its
maximum value, called the edge taper, the reflector will not intercept all the
radiation from the feed. There will be energy spillover with a corresponding
efficiency of approximately 1 - C2.
However, as the spillover efficiency decreases, the aperture taper efficiency
increases. The taper is chosen to maximize the illumination efficiency, defined
as the product of aperture taper efficiency and spillover efficiency.
The illumination efficiency reaches a maximum value for an
optimum combination of taper and spillover. For a typical antenna, the optimum
edge taper C is about 0.316, or - 10 dB (20 log
C). With this edge taper and a parabolic illumination, the aperture taper
efficiency is 0.92, the spillover efficiency is 0.90, the half power beamwidth
is 65.3° l /D, and the
first side lobe is 22.3 dB below peak. Thus the overall illumination efficiency
is 0.83 instead of 0.75. The beam efficiency is about 95 percent.
The gain of a satellite antenna is designed to provide a
specified area of coverage on the earth. The area of coverage within the half
power beamwidth is
S = d2 W
where d is the slant range to the center of the
footprint and W is the solid angle of a cone that
intercepts the half power points, which may be expressed in terms of the angular
dimensions of the antenna beam. Thus
where a and b are the principal plane half
power beamwidths in radians and K is a factor that depends on the shape
of the coverage area. For a square or rectangular area of coverage, K =
1, while for a circular or elliptical area of coverage, K = p /4.
The boresight gain may be approximated in terms of this solid
angle by the relation
G = h¢ (4p / W ) = (h¢ / K)(41,253 / a° b° )
where a° and b° are in degrees and h¢ is an
efficiency factor that depends on the the half power beamwidth. Although h¢ is conceptually distinct from the net efficiency h , in practice these two efficiencies are roughly equal for
a typical antenna taper. In particular, for a circular beam this equation is
equivalent to the earlier expression in terms of a if
h¢ = (p k /
4)2 h .
If the area of the footprint S is specified, then the
size of a satellite antenna increases in proportion to the altitude. For
example, the altitude of Low Earth Orbit is about 1000 km and the altitude of
Medium Earth Orbit is about 10,000 km. Thus to cover the same area on the earth,
the antenna diameter of a MEO satellite must be about 10 times that of a LEO
satellite and the gain must be 100 times, or 20 dB, as great.
On the Iridium satellite there are three main mission L-band
phased array antennas. Each antenna has 106 elements, distributed into 8 rows
with element separations of 11.5 cm and row separations of 9.4 cm over an
antenna area of 188 cm ´ 86 cm. The pattern produced by
each antenna is divided into 16 cells by a two-dimensional Butler matrix power
divider, resulting in a total of 48 cells over the satellite coverage area. The
maximum gain for a cell at the perimeter of the coverage area is 24.3 dB.
From geostationary orbit the antenna size for a small spot beam
can be considerable. For example, the spacecraft for the Asia Cellular Satellite
System (ACeS), being built by Lockheed Martin for mobile telephony in Southeast
Asia, has two unfurlable mesh antenna reflectors at L-band that are 12 meters
across and have an offset feed. Having different transmit and receive antennas
minimizes passive intermodulation (PIM) interference that in the past has been a
serious problem for high power L-band satellites using a single reflector. The
antenna separation attenuates the PIM products by from 50 to 70 dB.
Often the area of coverage has an irregular shape, such as one
defined by a country or continent. Until recently, the usual practice has been
to create the desired coverage pattern by means of a beam forming network. Each
beam has its own feed and illuminates the full reflector area. The superposition
of all the individual circular beams produces the specified shaped beam.
For example, the C-band transmit hemi/zone antenna on the
Intelsat 6 satellite is 3.2 meters in diameter. This is the largest diameter
solid circular aperture that fits within an Ariane 4 launch vehicle fairing
envelope. The antenna is illuminated by an array of 146 Potter horns. The beam
diameter a for each feed is 1.6° at 3.7 GHz. By appropriately exciting the beam forming
network, the specified areas of coverage are illuminated. For 27 dB spatial
isolation between zones reusing the same spectrum, the minimum spacing s is given by the rule of thumb s
³ 1.4 a , so that s ³ 2.2° .
This meets the specification of s = 2.5° for Intelsat 6.
Another example is provided by the HS-376
dual-spin stabilized Galaxy 5 satellite, operated by PanAmSat. The
reflector diameter is 1.80 m. There are two linear polarizations, horizontal and
vertical. In a given polarization, the contiguous United States (CONUS) might be
covered by four beams, each with a half power beamwidth of 3° at the C-band downlink frequency of 4 GHz. From
geostationary orbit, the angular dimensions of CONUS are approximately
6° ´ 3° . For this rectangular beam pattern, the maximum gain is
about 31 dB. At edge of coverage, the gain is 3 dB less. With a TWTA ouput power
of 16 W (12 dBW), a waveguide loss of 1.5 dB, and an assumed beam-forming
network loss of 1 dB, the maximum EIRP is 40.5 dBW.
The shaped reflector represents a new technology. Instead of
illuminating a conventional parabolic reflector with multiple feeds in a
beam-forming network, there is a single feed that illuminates a reflector with
an undulating shape that provides the required region of coverage. The
advantages are lower spillover loss, a significant reduction in mass, lower
signal losses, and lower cost. By using large antenna diameters, the rolloff
along the perimeter of the coverage area can be made sharp. The practical
application of shaped reflector technology has been made possible by the
development of composite materials with extremely low coefficients of thermal
distortion and by the availability of sophisticated computer software programs
necessary to analyze the antenna. One widely used antenna software package is
called GRASP, produced by TICRA of Copenhagen, Denmark. This program calculates
the gain from first principles using the theory of physical optics.
The gain of an antenna is determined by the intended area of
coverage. The gain at a given wavelength is achieved by appropriately choosing
the size of the antenna. The gain may also be expressed in terms of the half
Reflector antennas are generally used to produce narrow beams
for geostationary satellites and earth stations. The efficiency of the antenna
is optimized by the method of illumination and choice of edge taper. Phased
array antennas are used on many LEO and MEO satellites. New technologies include
large, unfurlable antennas for producing small spot beams from geostationary
orbit and shaped reflectors for creating a shaped beam with only a single
Dr. Robert A. Nelson, P.E. is president of Satellite
Engineering Research Corporation, a satellite engineering consulting firm in
Bethesda, Maryland, a Lecturer in the Department of Aerospace Engineering at the University of
Maryland and Technical Editor of Via Satellite magazine. Dr. Nelson is the instructor for the ATI course Satellite
Communications Systems Engineering. Please see our Schedule for dates and