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Sensitivity of antenna amplitude gain determination:
Assume we have an interferometer with N antennas. We want to determine the power gain  of antenna i, by observing a point source of flux density S.
The quantities we measure are the baseline amplitudes: Let us note  the amplitude of the correlation product of the outputs of antennas i and j.
One has:  which may be written, since the power gains are positive:
 where  , and  . We thus have N (N-1) linear equations to solve for the N unknowns  . Such a system is usually solved using the method of least squares. One minimizes:
for which the N conditions are:
which may be rewritten as:
Adding these equations one obtains:
It is then straightforward to substitute this back and get:
Here the second term contains all the baseline amplitudes. This formula is derived in a much more elegant way (and in French) by E. Anterrieu ([1992]). Let's rewrite it in a slightly different way:
Now the first term contains all baselines connected to antenna i, the second one contains all the other baselines; for instance for 3 antennas, one obtains the well-known formula:
Now all the  contain noise terms which are uncorrelated. Then for the corresponding r.m.s. fluctuations we get:
In the large signal-to-noise limit:  ,  . Let us assume further that all antennas have the same gain  and sensitivity:  :
The rms of the power gain is thus behaving like  in the large N limit. This is because in Eq.1 the first (N-1) terms are going to dominate the summation when N is large, since the other (N-1)(N-2)/2 are multiplied by a  factor. The rms gain also diverges for N <3: it is well-known that it is not possible to measure the gain of a single antenna in a two-element interferometer. This formula slightly differs from that of Cornwell and Fomalont ([1989]); the asymptotic behaviour is the same ( for the amplitude gains) but their result diverges for N=3.
In the case of heterogeneous arrays the previous analysis has to be refined; We do this in Appendix A. The result for a large number of antennas is simply:
 where  is the gain of kind 1 ,  the rms in one baseline connecting two antennas of kind 1, and A is the total collecting area of the array.
Formulae by Prof. Syed Idris Syed Hassan,
Universiti Sains Malaysia, Serak
Misc. Formulae
wavelength = 11803 / frequency
i.e.:
11803 / 107.9 = 109.38832 (spacing of antennas)
107.9 / 4 = 27.34708 (quater-wave spacing)
directivity = max. power radiated / unit solid angle / tl. power radiated / 4 pi
gain = max. power radiated / unit solid angle / tl power delivered to antenna / 4 pi
(waveguide)
Determination of half-power beamwidth:
.707 = cosn dia.
where:
dia. = half-power beam width
n = cos # for either h or e plane
AMPS * VOLTS = WATTS
WATTS / 746 = HORSEPOWER
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