# 350lect38 - 38 Equivalent circuit models of coupled anten...

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Unformatted text preview: 38 Equivalent circuit models of coupled anten- nas • Since Maxwell’s equations and the associated boundary conditions which govern the interaction of a pair of antennas with input currents I 1 , 2 and response voltages V 1 , 2 are linear , the equivalent circuit model describ- ing the relationships of I 1 , 2 and V 1 , 2 is also linear and obeys a set of equations +- +- I 1 I 2 V 1 V 2 r +- +- I 1 I 2 V 1 V 2 Linear 2-Port V 1 = Z 1 I 1 + Z 12 I 2 V 2 = Z 21 I 1 + Z 2 I 2 Ant.1 Ant.2 V 1 = Z 1 I 1 + Z 12 I 2 V 2 = Z 21 I 1 + Z 2 I 2 . – With I 2 set to zero, we recognize Z 1 above as the input impedance of ant.-1, while Z 21 is a coupling impedance connecting the open circuit response voltage of ant.2 to the driver current of ant.1. – Likewise, Z 2 is the input impedance of ant.2 and Z 12 is a coupling impedance from ant.2 to ant.1. • The reciprocal behaviour of a pair of antennas separated in free space restricts the coupling impedances in the model circuit to satisfy Z 21 ≡ V 2 I 1 | I 2 =0 = Z 12 ≡ V 1 I 2 | I 1 =0 ≡ Z c so that transmission gain P t /P r is independent of the transmission and reception roles assigned to the antennas (as verified below). 1 With that restriction the equivalent circuit model of the coupling sim- plifies as (see margin) Reciprocal circuit model for antenna coupling: +- +- V 1 V 2 I 1 I 2 Z c Z...
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350lect38 - 38 Equivalent circuit models of coupled anten...

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