29:106/186 RADIO ASTRONOMY
Sixth Homework Set...March 10, 2000
Due: March 29, 2000
(1) A VLBA antenna has the following characteristics: diameter = 25
meters, 
. The system temperature is 35K, and the IF bandwidth
is 50 MHz. What is the weakest source that can be detected in a 10 second
integration?
(2) You are ordering amplifiers to build a radio receiver. The first
stage amplifier has a noise temperature of 25K, and the second and
third stages a noise
temperature of 290K. What characteristic or characteristics are necessary
for the total receiver temperature to be 30K?
(3) Consider the following simple model for the radio emission from the sky. The brightness temperature depends on galactic latitude b as
This roughly characterizes the enhancement of radio emission due to the
galactic plane. You observe the sky with a radio telescope consisting of
a dipole and a receiver. You can point the dipole anywhere in the sky.
What is the maximum variation in power you can measure?
(4) The aperture excitation function of an antenna g(x,y) is uniform
inside a square and zero outside. Show that the function
maximizes for 
in the notation of the lecture
notes and the book. Note: I will not cover this material until
Wednesday, March 22. Look ahead in the book and try a crack at it.
(5) A circular loop of wire carrying the current
constitutes an oscillating magnetic dipole.
Determine the radiation fields 
and 
from this oscillator,
and the total power radiated.