In this section first we will describe the basic principles of antennas as applicable to radio astronomy. Next, we will discuss the antenna requirements from the point of solar observations.
11.2.1 Basic Principles for Using Antennas
The performance of a transmitting antenna is specified by the flux density of the radiated field at a distant point when a given power is supplied to the antenna terminals. If the input power W (in watts) produces a flux density F (in watts per square meters) at distance r (in meters) then,
F = ⋅ π 2 4
GW
r (11.1)
The constant of proportionality G is the gain of the antenna. G is a function of the direction of transmission and has a maximum value G0 along the axis of the main antenna beam.
In receiving antennas, including radio telescopes, it is more appropriate to specify its properties in terms of the effective area. If w is the power received by an antenna of effective area A (in square meters) when exposed to a plane wave with flux density F, then
w = A F. (11.2) The effective area is a function of direction and is proportional to the corresponding gain
G = π ⋅ λ2
4 A (11.3)
Here, λ is the wavelength.
In solar radio astronomy we are concerned with sources of wideband noise-like radiation. The received power w can be specified by equating it to the thermal noise power obtained by replacing the antenna with a resistor at the antenna temperature Ta and is expressed as,
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w = K Ta Δf. (11.4)
(K = Boltzmann’s constant and Δf = the receiving bandwidth.)
For a noise source, we may define the flux density per unit bandwidth at the receiving antenna as S (in W m–2 Hz–1), so that
F = S Δf. (11.5) It is seen from Eq. (11.2) through (11.5) that, if the receiving aperture area is A perpendicular to the direction of the source and the source is small compared to the antenna beam width, then
S A = K T. (11.6) The received power is obtained by the angular distribution of brightness in the source. For each element of the source, the brightness temperature TB is defined as the temperature of a black body for which the brightness of the thermal radiation would equal the brightness observed actually. TB may change with frequency, but, like S, it is assumed to be constant over the receiving bandwidth Δf. The power received from a source element subtending a solid angle dΩ is
dw = Δ Ω λB2 .
KT A f d (11.7)
Hence, the total received power is given by w =
These equations are used to find expressions for the signal received from a uniformly bright source of angular size considerably less than that of the antenna beam. The source is assumed to be located on the axis of the beam, where the effective area has its maximum value A0. Then
S = Ω For the special case of a circular source of angular diameter d,
S = π
Ta = π ⋅ If an antenna is surrounded by a black-body enclosure at uniform temperature TB it can be shown by a thermodynamic argument that
Ta = TB. (11.13)
Eq. (11.14) shows a relation between the antenna beam-width to the effective area (or to the gain). Therefore, for beams of circular cross-section we have,
A0 = λ
11.2.2 Antenna Requirements for Solar Observations
Antenna requirements for solar observations are summarized as follows:
(i) The antenna-receiver combination must give a high ratio of solar signal-to-noise ratio from all other sources in order to enable measurements to be made with the desired accuracy.
(ii) The response should be approximately uniform over the whole angular extent of the radio Sun.
(iii) The antenna beam must be steerable (either mechanically by turning the antenna or electrically by phase adjustments) so that it may be pointed at the Sun throughout the period of observation.
(iv) The sensitivity to the signals arriving in directions away from the Sun should be kept low to minimize interference and other spurious effects, particularly those due to reflections at the ground.
These specifications are interrelated and at the same time conflicting. The sensitivity requirement implies a wide receiving area and a narrow antenna beam.
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The need for uniform response sets a minimum beam-width and thus limits the receiving area. The absolute sensitivity of the receiving system is obtained by the relation between the wanted signal from the Sun and the unwanted statistical fluctuations owing to noise from the bright sky within the antenna beam and from the receiver itself. This noise component is expressed as an equivalent antenna temperature TN. The receiver contribution to TN at meter wavelengths is typically of the order of 300 K, since the sky brightness temperature TSK is usually uniform over a solid angle greater than the antenna beam. The effect of the sky radiation is to increase the antenna temperature by an amount TSK. Sky temperatures are shown in Fig. 11.1. The figure shows the following: (a) upper limit and (b) lower limit of sky noise component; (c) typical receiver noise, expressed as an equivalent antenna temperature; (d) and antenna temperature corresponding to quiet Sun at sunspot minimum, for an antenna with an effective area of 20 m.
Figure 11.1: The antenna temperature in a solar radiometer.
In wideband antennas for radio-spectrographs there is an unavoidable compromise between uniformity of response at the shortest wavelength and sensitivity at the longest wavelength.
The ground-reflection problem is common to all mechanically steerable radio telescopes. This can be minimized by careful design (e.g., paraboloid reflectors should be designed to minimize side-lobe responses, even at some sacrifice of efficiency). A substantial improvement can also be obtained by using vertical rather than horizontal polarization. The reflectance of the ground at large incident angles (i.e., at low solar elevation) is smaller for vertically than for horizontally polarized
waves. At elevation angles less than about 40° the vertically polarized ground reflection is from 3 to 20 dB weaker than the horizontally polarized component.