1
Chapter
1
Fundamental Parameters
1.1 Overview
Communication satellite systems depend significantly on both space segment and user segment antenna designs. Space segment antennas must meet their performance requirements over their specified coverage areas with allowance for satellite attitude variations. User segment antennas likewise must meet their performance requirements while tracking the satellite in orbit. Antenna requirements depend on specific program needs, and a significant diversity of technology has been developed to accommodate the diverse objectives of individual programs. As a result, space segment antennas are the most diverse technology in the space segment, and specific designs for one application cannot be applied to other applications. User segment antenna hardware likewise exhibits a wide variety of antenna hardware ranging from small handheld technologies to much larger ground terminal antennas, which are often associated in the public’s mind with communication satellite antenna systems. A review of the system parameters used to quantify antenna performance is presented as a basis for subsequent chapters.
1.2 Antenna Parameters
Antenna parameters must describe both the spatial characteristics and terminal interfaces with system electronics. The spatial characteristics specify the twodimensional description of the antenna’s sensitivity variations in a coordinate system embedded in the antenna. These spatial characteristics must also indicate the antenna’s polarization properties that define the orientation of the electric field during one RF (radio frequency) cycle. The antenna’s terminal impedance quantifies the interface relations
1
2 Chapter One
with system electronics. Satellite system antennas are commonly in the class of aperture antennas. The relationship between the aperture size and spatial characteristics is a most important issue in system sizing. This relationship dictates the antenna’s gain levels and beamwidth requirements. Perhaps the most commonly asked question regarding antennas is the size required to meet system requirements. This question is typically followed by a request to explain why the size must be that large. Noise in receiving systems is an important system parameter and is characterized by the antenna noise temperature at the antenna’s terminal. The antenna noise temperature added to the receiver noise temperature equals the total system noise temperature, an important factor in the performance of receiving antennas.
1.2.1 Spatial Characteristics
The spatial characteristics describe the spatial variation of the antenna’s sensitivity. They also describe the vector nature of the antenna’s field distribution in a coordinate system referenced to the antenna’s structure. Commonly, satellite systems use aperture antennas that have a distribution of fields in the aperture and a corresponding distribution of fields in space. The coordinate system used for this specification generally places the aperture plane with the XY plane as indicated in Fig. 11. At a sufficient distance from the aperture (referred to as the antenna’s far field), the variation of the fields becomes invariant with the range from the antenna’s aperture. The electric field quantities,
E
q
and
E
j
, are orthogonal to one another as specified and vary with separation R from the aperture as 1/R. The power density in the far field is proportional to (
E
q

2
+

E
j

2
)/
Z
o
, where
Z
o
equals 120
p
and is the free space impedance.
Figure 11
Coordinate system for aperture antennas
yE
θ
E
ϕ
ϕ
xz
θ
Fundamental Parameters 3
The relationship between the fields in an antenna’s aperture to the spatial distribution is the radiation integral [1]
g
(
k
x
,
k
y
)
=
∫∫
F
(
x
,
y
) exp(
j
(
k
x
x
+
k
y
y
) dx dywhere
g
(
k
x
,
k
y
) is the pattern (voltage),
F
(
x
,
y
) is the field distribution in the aperture having coordinates
x
and
y
, the integration limits are the physical extent of the aperture, and
k
x
=
k
sin
q
cos
j
k
y
=
k
sin
q
sin
j
where
k
is the free space wavenumber equal to 2
p
/
l
,
l
is the wavelength equal to
c
/
f
where
c
is the speed of light, and
f
is the RF frequency. The aperture fields are vector functions representing the polarization properties of the aperture fields. The variation of the antenna’s sensitivity with direction is referred to as its pattern, and
g
(
k
x
,
k
y
) is proportional to the electric field variation. This relation assumes the spatial fields are sufficiently separated from the aperture that the fields are independent of the range, a condition referred to as the far field. Commonly, the required far field separation for aperture antennas is taken as 2
D
2
/
l
, where
D
is the aperture width. It should also be noted that antennas generally satisfy reciprocity relations so that at the same frequency, the characteristics are identical independent of whether the antenna is transmitting or receiving. The exception is when the antenna incorporates nonreciprocal devices such as active amplifiers.The relation between the aperture fields and the far field pattern is a twodimensional Fourier transform. Similarly, the aperture field is the inverse twodimensional Fourier transform of the far field pattern. The antenna size is thus related to the beamwidth in the far field, and likewise the beamwidth in the far field is related to the antenna size through the transform. The familiar properties of Fourier transforms are inherent in antenna design. If the aperture fields have an amplitude taper, the far field beamwidth broadens and the sidelobes surrounding the main beam are reduced. If the aperture fields are in phase over the extent of the aperture, the beam maximum is normal to the aperture plane. If the aperture fields have a linear phase gradient over the extent of the aperture, the beam maximum is normal to the phase gradient, a consequence of the familiar shifting theorem of Fourier transforms.
Antenna gain
measures the antenna’s ability to transfer or receive signals in a particular direction. It is referenced to an idealized lossless antenna having uniform sensitivity in all directions. In a sense, this reference for antenna gain follows the definition of electronics gain that is referenced to the transfer response of an idealized,
4 Chapter One
lossless “straight wire.” The maximum value of antenna gain for aperture designs equals
G
=
h
(4
p
A/
l
2
)where
h
is the antenna efficiency (
<
1), A is the physical area of the antenna’s aperture, and
l
is again the free space wavenumber. Ideally, an antenna having 100% efficiency is lossless and has an aperture distribution uniform in both amplitude and phase. Practically, this ideal antenna efficiency can only be approached, and the antenna efficiency of practical antenna designs falls short of the ideal value because of ohmic and impedance mismatch losses, the aperture amplitude and phase deviations from the ideal, and scattering and blockage from the antenna’s structure. In determining the required antenna size or aperture area, an estimated value of the antenna’s efficiency is required. The efficiency value depends on the specific antenna design. Another term defined for receiving antennas is effective aperture, which equals
A
e
=
(
l
2
/4
p
) GThe received power equals the product of the incident power density and the effective aperture.The far field parameters implicitly assume the antenna responds to an incident plane wave or a wave that approximates a plane wave. The far field criteria 2
D
2
/
l
is derived based on the required range from the point of srcin of a spherical wave such that the phase deviation over a planar surface of dimension
D
has a maximum value of 22.5
ο
relative to an ideal inphase plane wave.
Directivity
or
directive gain
is another term that characterizes an antenna’s directional properties. Directivity is a function of the antenna pattern or the variation of the antenna’s sensitivity to different signal directions. Directivity differs from antenna gain because ohmic and mismatch losses are not included in directivity. Thus, antenna gain has a lower value than directivity. Directivity is defined by
D
(
q
,
j
)
=
4
p
P
(
q
,
j
)/
∫∫
(
P
(
q
,
j
) sin
q
d
q
d
j
The integral in the denominator is total power radiated or received from all directions. The fields of an antenna are vector quantities and (as will be discussed) have a principal polarized component with the design polarization state and, unavoidably, a crosspolarized component that is orthogonal to the principal polarization. Directivity is generally computed with the power pattern in the numerator limited to principal polarized fields and the total power in the denominator comprised of