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Lecture 8 - Antenna Theorum (Convolution (Translation invarient processes,…
Lecture 8 - Antenna Theorum
Black-body cavity
The part of the antenna beam solid angle Omega radiates towards antenna but only part will b absorbed
antenna is not fully efficient and its effective aperture is Ae
The receiver radiates power back into the cavity via the antenna - cavity absorbs it
Antenna is essentially a matched load resistance, also at temperature T, which produces transferable power maths
Antenna can only collect power from one polarisation (lose factor of 2)
Directivity and Gain of antenas
concentration enabled by the antenna beam, compared with a system radiating/recieving isotropically
maths
Antenna Temperature in practice
the power collected by the antenna per unit bandwidth is its effective area multiplied by the sky brightness temperature
weighted by the antenna beam pattern, integrated over the whole sphere, halved for single polarisation
LOTS OF EXAMPLES
Effect of the Beam
Asymmetric beam pattern gets traced out as the antenna moves in theta, a convolution
Flipped around in angle/time
say that the sky has been convolved with the beam pattern, similar to correlation, but different because one function is flipped
beam can also be called point spread function PSF or impulse response
Convolution
Flip through one function
move through first function
point by point multiplication
integration
Is a smoothing
Sky brightness is smoothed by the telescope beam
linear
Output amplitudes are simple linear multiples of the input amplitudes rather than some non linear relation ship
Translation invarient processes
output variation does not depend on the absolute arrival time (or equivalently the absolute and or location)
the same relative input changes produce the same output variations regardless of where they start
preserves the relative positions of temporal spatial or angular features of the input and hence the phases
Maths