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...)
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-3o2efxki.pdf

Bhaumik · Accepted Answer

Assignment
Ri	Cgd+
vi
-
Rds
Cgs
gm
+
RL	vo
-
Cds
1. To derive the Z- and S-matrices of the given two-port network, we'll express the components using the given variables:
a) : Input resistance.
b) : Gate-to-source capacitance.
c) : Gate-to-drain capacitance.
d) : Transconductance
e) : Drain-to-source capacitance.
f) : Load Resistance.
Now, let's derive the Z-matrix and S-matrix:
For the Z-matrix:
: represents the input impedance seen from port 1 when port 2 is terminated with its characteristic impedance.
It includes  and  in parallel:
represents the impedance between port 1 and port 2 when port 2 is terminated with its characteristic impedance.
It includes  and in series:
 represents the impedance between port 2 and port 1 when port 1 is terminated with its characteristic impedance.
It includes  and in series:
 represents the input impedance seen from port 2 when port 1 is terminated with its characteristic impedance. 
It includes and  in parallel:
For the S-matrix: 
The S-matrix elements can be calculated using the Z-matrix elements according to the relations:

Please provide a clear derivation of the problems

Solution

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