APPENDIX B 



CALCULATION OF THE PHASE MODULATION ^ 

 INTRODUCED BY THE SWITCHED ARRAY ANTENNA 



The UHF antenna used for SMS is switched array. As the satellite 

 spins, the transmitter and receiver are disconnected from one set 

 of antenna elements and connected to another set (one element for 

 transmit and one for receive). Since the radiating elements are 

 in separate locations about the satellite periphery, the propaga- 

 tion path length from antenna to Earth terminal suddenly changes 

 when the elements are switched. This effect causes a jump in RF 

 carrier phase. 



Also, because the phase center of the UHF satellite antenna is 

 located off the axis of spin rotation, the propagation path length 

 to the Earth terminal varies as the satellite rotates. This path 

 variation introduces a phase (frequency) modulation on the trans- 

 mitted and received carriers which may degrade link performance. 



Figure B-1 , shows the basic geometry, and Figure B-2 shows the 

 phase shift as a function of time. The step in phase occurs when 

 a new antenna is switched. The fundamental frequency of this phase 

 modulation is eight times the spin rate (13.3Hz at 100 rpm). The 

 worst case occurs on the DCP interrogation and reporting links with 

 the DCP on Earth edge at the equator (in the plane of spin motion). 



From. Figure B-1, 



AL = R - R Cos (0 - a) 

 = R (1 - Cos (0 - a) 

 = 2R sin'' e - d 



where R is the antenna radius, a is the angle from the vertical 

 to the Earth terminal (in the equatorial plane); and 6 is the 

 position of the UHF antenna element relative to the vertical. 



^^^°' A* = -^^ (360°), 



♦Obtained from the Ford Aerospace and Communications Corp. 



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