Introduction to Electric Circuits

9.9 Characteristic impedance (Zo) 225

9.9 CHARACTERISTIC IMPEDANCE (2'0)

The characteristic impedance of a symmetrical two-port network is the
impedance which, when connected to the output port, gives rise to an input
impedance of the same value. This is illustrated in Fig. 9.18.

11 [ I2I~V~ ~

Zin = Z~ l! 2-port

V1 network Zo

o I v

Figure 9.18

Using the transmission parameters,

V 1 -'-AV2 + B12 = AV2 + BV2//Zo

and

I 1 "- CV 2 + nI 2 -- CV 2 Jr- D V2/Z o

The input impedance is

Zin = V1/I 1 -- (A V2 + B V2/Zo)/(CV2 + D V2/Zo)

Multiplying throughout the numerator and the denominator of the right-hand

side by Zo/V2 we obtain

V1/I 1 = (AZo + B)/(CZo + D)

By definition, this is equal to Zo

Zo = (AZo + B)/(CZo + A)

remembering that D = A for this symmetrical network. Thus

CZo 2 + AZo = AZo + B

SO

CZo 2= B

and

Zo = ~(B/C) (9.63)

From Equations (9.33) and (9.34) we have, with the output port open circuited

so that I2 = 0,

VI=AV2 and 11 = CV2

The open circuit input impedance Zoc = (V1/11)1,~=o = (AV2)/(CV2), so

Zor = A/C (9.64)