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

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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
Answered 2 days After Apr 09, 2024

## Solution

Vedant answered on Apr 12 2024
1 Part1
1.1 Z-Matrix Derivation:
The Z-matrix elements can be calculated as follows:
Z11 = Ri +
1
jÏ‰Cgs + jÏ‰Cgd
Z12 = âˆ’
1
jÏ‰Cgd
Z21 = âˆ’
1
jÏ‰Cgd
Z22 = Rds +
1
jÏ‰Cds +
1
RL
Where:
â€¢ Ï‰ is the angular frequency
â€¢ j is the imaginary unit
1.2 S-Matrix Derivation:
To obtain the S-matrix, we need to use the following equations:
S11 =
Z11 âˆ’ Z0
Z11 + Z0
S12 =
2
âˆš
Z0
Z22
Z11 + Z0
S21 =
2
âˆš
Z0
Z11
Z11 + Z0
S22 =
Z22 âˆ’...
SOLUTION.PDF

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