CHAPTER 3 - Foundations of RF & Microwave Circuit Characterisation
148
Figure 3.8-2 Two-port network with setup to measure and . Input and output transmission lines have negligible
electrical lengths
We have effectively switched our source to port 2 and terminated port 1 with a matched
termination i.e. Z
L
=Z
0
.
represents the reflection coefficient at port 2 (eq.(3.8-9)) and measures the power
transmitted to port 1 from port 2 (eq.(3.8-8)).
A note on the indexing of S-parameters. The first index represents the port which the power is
travelling to, the second index represents the port which the power is originating from.
S-parameters are effectively ratios of normalised voltage waves (eq. (3.8-2),(3.8-6) and
(3.8-7)) and if we square their magnitudes we obtain the normalised power. In the case of a lossless
two-port passive network, since power can only be transmitted or reflected we can say
|
|
|
|
So far we have assumed that the input and output transmission lines (Z
TLin
and Z
TLout
) which
we have used to connect to our network and measure incident and reflected powers (Figure 3.8-1
and Figure 3.8-2), are very small and that their electrical length is negligible. This however is not
often the case and we need to "calibrate out" such lengths if what we want is the S-parameters right
at the network ports. This process is called de-embedding or shifting the reference planes. Figure
3.8-3 illustrates this.
Z
S
= Z
0
Z
TLin
=
Z
0
Two-port
Network
a
1
b
1
a
2
b
2
INPUT
OUTPUT
Z
TLout
=
Z
0
V
S
Z
L
(3.8-8)
(3.8-9)
(3.8-10)
Conquer Radio Frequency
148 www.cadence.com/go/awr
