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# C zl if we want the proportionality constant to be

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Unformatted text preview: impedance will be equal to a (possibly complex) constant times the inverse of the output impedance if A = 0, D = 0, in which case B1 ZIN = . C ZL If, we want the proportionality constant to be positive and real, then it is necessary to have B = kC , where − k is a real constant, in which case ZIN = kZL 1 . 7-14 Solution The ABCD parameters are deﬁned as follows: V1 = AV2 − BI2 (6) I1 = CV2 − DI2 (7) ￿ ￿−1 V2 Z1 A= =1+ V1 I2 =0 Z3 ￿ ￿−1 I2 Z1 Z2 B=− = Z1 + Z2 + V1 V2 =0 Z3 ￿ ￿−1 V2 1 C= = I1 I2 =0 Z3 ￿ ￿−1 I2 Z2 D=− = (1 + ) I1 V2 =0 Z3 To satisfy the impedance inverter conditions (see problem 7-13) we require: A = 0 → Z1 = −Z3 D = 0 → Z2 = −Z3 Taken together, these conditions imply Z1 = Z2 = −Z3 which leads to B = −Z3 Enforcing the ﬁnal impedance inverter equation, B√ kC (with k a positive real constant), yields −Z3 = = √ k/Z3 , or Z3 = ±j k . It follows that Z1 = Z2 = ∓j k . 2 Thus, a T-network with purely reactive elements Z1 = Z2 = −Z3 = ±jX will provi...
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