
Two-Port Networks
181
Summarizing,
Z
y
z
y
z
y
z
y
z
[]
=
−
−
22 12
21
11
EXERCISE 4
H
to Z
conversion. Determine the Z
matrix in terms of H
matrix
elements.
ANSWER
Let’s recall the
H
matrix expression
v
i
hh
hh
i
v
1
2
11 12
21 22
1
2
=
and rewrite the second equation as
v
h
h
i
h
izizi
2
21
22
1
22
2211 22 2
1
=−
def
while from the rst equation we can write
vhihvhih
h
h
i
h
i
h
h
i
h
1111 12 2111 12
21
22
1
22
2
22
1
12
1
=+ =+−+
=+
∆
hh
izizi
22
2111 12 2
def
+
with
hhhhh
11 22 12 21
.
Finally,
Z
h
h
h
h
h
[]
=
−
∆
22
12
22
21
22 22
1
EXERCISE 5
Z
to Y
conversion. Determine the
Y
matrix in terms of Z
matrix
elements.
ANSWER
Let’s start from the denition of ...