Please derive the Z- and S-matrix of the following two-port networks: (note that the component in...

Question

Please derive the Z- and S-matrix of the following two-port networks: (note
that the component in the matrix needs to be expressed using the given
variables, such as Cgs, Cgd...). No simplification of the components is
allowed. For instance, in the first question, Cgs and Cgd shall both have
contribution on the Z11.
1.
Ri
Cgs
Cgd
gm
Cds
Rds
RL vovi
+
-
+
-

2.
Ri
Cgs1
Cgd1
gm1
Cds1
Rds1
Cgs2
Cgd2
gm2
Cds2
Rds2
RL2
C1
vi
+
-
vo
+
-

3.
Ri
Cgs1
Cgd1
gm1
Cds1
Rds1
Cgs2
Cgd2
gm2
Cds2
Rds2
C1
vi
+
-
vo
+
-
Cgs3
Cgd3
gm3
Cds3
Rds3
RL3
C2

q-xgiyeuio.pdf

Vedant · Accepted Answer

1 Part1
1.1 Z-Matrix Derivation:
The Z-matrix elements can be calculated as follows:
Z11 = Ri +
1
jωCgs + jωCgd
Z12 = −
1
jωCgd
Z21 = −
1
jωCgd
Z22 = Rds +
1
jωCds +
1
RL
Where:
• ω is the angular frequency
• j is the imaginary unit
1.2 S-Matrix Derivation:
To obtain the S-matrix, we need to use the following equations:

Please derive the corresponding Z- and S-matrix for the two port networks. No simplification is allowed for the derivation.

Solution

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