3.8 Two-Port Networks and S-parameters
147
Figure 3.8-1 Two-port network with setup to measure and . Input and output transmission lines have negligible
electrical lengths.
But how do we work out these coefficients? Let us start with and . To measure these two we
keep the voltage source on port 1 as shown in Figure 3.8-1 and then set Z
L
to Z
0
.
Depending on what's in our network, we may get some power reflected back out of port one, and
the ratio between reflected and incident power at port 1 is our
as shown in eq. (3.8-6). Note that
is the same as for a single port network!
28
The parameter
measures the ratio between the power that comes out of port 2, in response to a
stimulus on port 1 (eq. (3.8-7)). This is not power reflected from an input at port 2 because we have
set
by terminating the port in its characteristic impedance Z
0
. We can therefore see it as
power transmitted through the network, from port 1 to port 2 when port 2 is terminated with an
impedance Z
L
equal to Z
0
. If the two-port network was an amplifier, it would tell us the gain. If it was
a filter, it would tell us the insertion loss and allow us to profile the passband.
Now for
and , we rejig things around a bit as shown in Figure 3.8-2.
28
Note that, in MWO, even for a single port network, an measurement is what must be set up to obtain !
Z
S
= Z
0
Z
TLin
=
Z
0
Two-port
Network
a
1
b
1
a
2
b
2
Z
L
INPUT
OUTPUT
Z
TLout
=
Z
0
V
S
(3.8-6)
(3.8-7)
Conquer Radio Frequency
147 www.cadence.com/go/awr
