Phys 728, Spring 2005            Homework Problem Set #6

6.1  Show that the angle from the phase center at which the two ends of an observing band of bandwidth Dn are out of phase by 2p is given by q = sin-1 [c/(BDn)]. [Hint: This will occur when there are n fringes at frequency n1 at the low frequency end of the band, and n+1 fringes at frequency n2 at the high frequency end of the band.]

6.2 Given two sources of amplitude a1 = 10 and a2 = 5, and spatial position q1 = 12 arcsec and q2 = -6 arcsec, what is the resultant amplitude and phase, ar and fr measured on a baseline of fringe spacing 54 arcsec?  If measured at 5 GHz, what projected baseline length between the two antennas does this fringe spacing correspond to?  What is the corresponding value of u, in wavelengths, assuming the baseline is entirely East-West?

6.3 Given an array of (E, N, U) antenna locations (in meters) in the table below, operating at 10 GHz, construct plots of the u,v coverage (the sampling function) for (1) a source at declination d = 13o, and (2) a source at declination d = 0o. Both plots should cover an hour angle range -6h < h < +6h with 0.1 h resolution. Place your array at a latitude of 37o. In your plots, plot u on the horizontal axis, and v on the vertical axis, with (0,0) at the center of the plot, and use equal u and v scales ranging from -150 kl to 150 kl. Label the scales in kilowavelengths.
Antenna #
E (m)
N (m)
U (m)
1
0
0
0
2
700
-300
0
3
0
1000
5
4
-700
-300
0
5
1500
-700
0
6
0
2200
10
7
-1500
-700
0