Passive networks and reciprocity theorem

The ABCD parameters for a 2-port network are:

V1 = AV2 −BI2                   (28)

I1 = CV2 −DI2                    (29)

Figure shown below shows a two-port network whose terminals RS are short-circuited with an input voltage V across terminals PQ. Then V2 in the above equations is 0 and the equations become:

V =−BI2                    (31)

and    I1 =−DI2                  (32)

 DIA  41.49

 

This is a theorem called the reciprocity theorem, amd this states that if a voltage is supplied to a linear passive network at its 1 terminal & produces a current at another terminal,then the same voltage applied to a 2nd terminal will generate the same amount of current at the 1st terminal. Since the same voltage has been supplied at each of the 2 terminals, then I1=I2
 

Thus, AD−BC=1 (35)
 

This condition must be satisfied by any linear passive network.