NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 384

TABLE 9-2. Relationship Between Common Circuits and the ABCD Parameters
Circuit ABCD Matrix

Z 3 + Z 1

Z 3

Z 1 Z 2
Z 3

i 1

Z 1 + Z 2 +

i

Z 1

Z 2

v 2

1
Z 3

Z 3 + Z 2

Z 3

Z 3

v 1

R=Z 0

V

cosh γl Z 0 sinh γl Z 0 R=Z 0

1
Z 0 sinh γl

cosh γl

z=-l z =0

1 Z
01

i 1

i 2

Z

v 2

v 1

10
Y

i 1

i 2

v 2

1

v 1

Y

Y 2
Y 3

1
Y 3

i 1

i 2

1 +

Y 3

v 2

v 1

Y 1 Y 2
Y 3

Y 1
Y 3

Y 1 Y 2

Y 1 + Y 2 + 1 +

the ABCD equations reduce to

v 1 = Av 2

= Cv 2

i 1

resulting in

v 1
i 1

A
C

Z 11 = = (9-44a)

The definition of Z 12 is

i 1 = 0

v 1
i 2

Z 12 =

so the ABCD equations reduce to

v 1 = Av 2 + Bi 2

0 = Cv 2 + Di 2

Solving the equations above for v 1 / i 2 produces

v 1
i 2

BC − AD
C

=