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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 . 714 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 713) 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 Tnetwork with purely reactive elements Z1 = Z2 = −Z3 = ±jX will provi...
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 Spring '08
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