3.8 Two-Port Networks and S-parameters
149
Figure 3.8-3 Two-port network setup to measure and . Input and output transmission lines have electrical
lengths which cannot be neglected
As we saw in section 3.2, eq. (3.2-3), adding a length of line means that the phase of the
reflection coefficient changes according to the electrical length of such a line. This case is no
different, we just have two ports instead of one. The spatial coordinate (or position along the line) at
which the S-parameters are measured, is called a reference plane. Two reference planes are shown
for both input (port 1', port 1) and output (port 2', port 2) in Figure 3.8-3.
Suppose that we are characterising a transistor or a filter and that we are measuring the S-
parameters at x
1
=0 and x
2
=0. We would like to make our measurement independent of the lengths
of line that we have use to characterise our network so that, if we sell our product, in the datasheet
we will be able to specify the S-parameters right at the input and output ports!
This transformation may be achieved as shown below.
At the reference planes x
1
= and x
2
= (port 1 and port 2) we may write
[
( )
( )
] [
][
( )
( )
]
At the reference planes x
1
=0 and x
2
=0, (port 1' and port 2')
[
( )
( )
] [
][
( )
( )
]
Now we can relate waves at port 1 and port 1' by means of the electrical length that separates them.
( )
( )
( )
( )
Z
S
= Z
0
Z
TLin
= Z
0
Z
TLout
= Z
0
Two-port
Network
b
1
(l
ͳ
)
Z
L
INPUT
OUTPUT
a
1
(l
ͳ
)
b
1
(0)
a
1
(0)
b
2
(l
ʹ
)
a
2
(l
ʹ
)
b
2
(0)
a
2
(0)
θ
ͳ
ൌβl
ͳ
θ
ʹ
ൌβl
ʹ
V
S
Port 1'
x
1
= 0
Port 1
x
1
=l
ͳ
Port 2 '
x
2
= 0
Port 2
x
2
=l
ʹ
Conquer Radio Frequency
149 www.cadence.com/go/awr
