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Unformatted text preview: 37 Effective area and reciprocity Antenna response to multiple plane waves: Consider next an arbitrary antenna located at the origin with x y R z a resistive termination R , a gain function G ( , ) , and Incoherent power addition : Consider a voltage v ( t ) = V 1 cos( t ) + V 2 cos( t + ) applied across a 1 resistor where is a random phase shift param- eter. Squaring v ( t ) and taking its time-average it can be shown that the time average-power P = 1 T T v 2 ( t ) dt = 1 2 V 2 1 + 1 2 V 2 2 + V 1 V 2 cos( ) . Notice the third term in P . With random we would be unable to know P , but still its expected value is P = 1 2 V 2 1 + 1 2 V 2 2 , which is the incoherent sum of the time-average power due to signals 1 and 2 one-at-a-time . which is exposed to a spectrum of incident plane wave fields E i at a frequency f = 2 arriving from directions ( i , i ) with power densities S i , such that each E i arriving from ( i , i ) is polarized identically as the field the antenna would radiate toward direction ( i , i ) . Assume that each plane wave E i will deliver an average power P r = S i A ( i , i ) to the resistor R one-at-a-time where A ( , ) is by definition the effective area of the antenna for reception and, furthermore, the...
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- Fall '08