a Matlab package for phased array beam shape inspection

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A +
Z 2
I A Z 1
B +
Z 3
V
V (B)
A
A −
B −
(a)
A +
V (A)
B
V Z 1
Z 2
B +
Z 3
I B
A −
B −
(b)
Figure 7: Reciprocity in electronic circuitry. Assume that in panel (a), a current I A =
I 0 is applied to port A of a two-port circuit, and that it causes the voltage
V (B)
A
= U 0 in port B. Then assume that the current generator and the voltmeter
are interchanged, to get the situation shown in panel (b). Assume that the
generator is adjusted so that it produces the same current I 0 to port B, I B = I 0 .
Then the statement of reciprocity is that the voltage meter at port A will read
U 0 , V (A)
B
= U 0 . For the specific circuitry shown here, this can be verified
by direct computation of the voltage, which in both cases gives U 0 = Z AB I 0 ,
where Z AB = Z 1 Z 3 /(Z 1 + Z 2 + Z 3 ). The internal currents and voltages in
cases (a) and (b) are different—for instance, the currents through Z 2 and Z 3
are equal in case (a) and non-equal in case (b)—but the coupling between the
ports is the same; in both cases, it is quantified by the same linear relationship
involving the impedance Z AB .