# Chapter 4 MICROWAVE NETWORK ANALYSIS¶

## Example:4.1 page.no:187¶

In [1]:
#program to find the equivalent voltages and current .
from sympy import symbols,sqrt,Matrix

a,b,A,Zte,V,I,C1,C2,P=symbols('a,b,A,Zte,V,I,C1,C2,P');
P=(a*b*A**2)/(4*Zte);
c=(1/2)*V*I;
d=(1/2)*(A**2)*C1*C2;
C1=sqrt((a*b)/2); # on comparision .
C2=sqrt((a*b)/2)*Zte; # on comparision .
c=Matrix([C1,C2]);
print c;
print "which completes the transmission line equivalence for the TE10 mode "
Matrix([[sqrt(2)*sqrt(a*b)/2], [sqrt(2)*Zte*sqrt(a*b)/2]])
which completes the transmission line equivalence for the TE10 mode

## Example:4.2 page.no:188¶

In [2]:
#program to compute reflection coefficient .
from math import pi,sqrt

a=0.03485;b=0.01580;eipsilao=8.854*10**-12;muo=4*pi*10** -7;
f=4.5*10**9;
w=2*pi*f; # angular frequency .
# for z<0 region air filled.
eipsilar=2.56; # for z>0 region .
ko=w*sqrt(muo*eipsilao);
k=ko*sqrt(eipsilar);
Ba=sqrt(ko**2-(pi/a)**2); # propagation constant in air region z<0.
Bd=sqrt(k**2-(pi/a)**2); # propagation constant in dielectric region z>0.
Zoa=(ko*377)/Ba;
Zod=(ko*377)/Bd;
tao=(Zod-Zoa)/(Zod+Zoa);
print "reflection coefficient",tao
reflection coefficient -0.627245765824

## Example:4.3 page.no:195¶

In [3]:
# program to find the z parameter of the two port network .
from sympy import symbols,Matrix

Z11,Z12,Z22,Z21,Za,Zb,Zc=symbols('Z11,Z12,Z22,Z21,Za,Zb,Zc');
Z11=Za+Zc; # for I2=0.
Z12=(Zc/(Zb+Zc))*(Zb+Zc); #for I1=0.
Z21=(Zc/(Za+Zc))*(Za+Zc); # for I2=0.
Z22=Zb+Zc; #for I1=0.
Z=Matrix([[Z11,Z12],[Z21,Z22]]); # z_parameter matrix.
print "Z-parameter of two port network = ",Z
Z-parameter of two port network =  Matrix([[Za + Zc, Zc], [Zc, Zb + Zc]])

## Example:4.4 page.no:198¶

In [4]:
# program to find the s-parameter of 3-dB attenuator circuit .
from numpy import matrix

Za=8.56;Zb=8.56;Zc=141.8;Zo=50.;
S11=(((((Zo+Zb)*Zc)/(Zo+Zb+Zc))+Za)-Zo)/(((((Zo+Zb)*Zc)/(Zo+Zb+Zc))+Za)+Zo); # reflection coefficient seen at port 1.
S22=(((((Zo+Za)*Zc)/(Zo+Za+Zc))+Zb)-Zo)/(((((Zo+Za)* Zc)/(Zo+Za+Zc))+Zb)+Zo); # reflection coefficient seen at port 2.
S12=(((1/((((Zo+Za)*Zc)/(Zo+Za+Zc))+Zb))*(((Zo+Za)* Zc)/(Zo+Za+Zc)))*(Zo/(Zo+Za))); # transmission coefficient from port 2 to 1.
S21=(((1/((((Zo+Zb)*Zc)/(Zo+Zb+Zc))+Za))*(((Zo+Zb)* Zc)/(Zo+Zb+Zc)))*(Zo/(Zo+Zb))); # transmission coefficient from port 1 to 2.
S=matrix([[S11,S12],[S21,S22]]); # sparameter matrix.
print "S-parameter of 3db attenuator circuit is ="
print S
S-parameter of 3db attenuator circuit is =
[[  4.43981086e-05   7.07663252e-01]
[  7.07663252e-01   4.43981086e-05]]

## Example:4.5 page.no:202¶

In [1]:
#program to determine the reciprccity and lossless of two port network and find return loss.
from sympy import symbols,I
from numpy import matrix
from math import log10

Rl,tao=symbols('Rl,tao');
S=matrix([[0.1,0.8*I],[0.8*I,0.2]]); # s-parameter matrix.
if (S[0,1]==S[1,0]):
print "the network is reciprocal ."
else:
print "the network is not reciprocal ."
if (S[0,0]**2+S[0,1]**2==1):
print "the network is lossless ."
else:
print "the network is lossy ."
tao=S[0,0]-(S[0,1]*S[1,0])/(1+S[1,1]); #input reflection coefficient .
Rl=-20*log10(abs(tao)); # return loss in dB.
#result
print "return loss at port 1 in dB= %.3f"%Rl
the network is reciprocal .
the network is lossy .
return loss at port 1 in dB= 3.967

## Example:4.6 page.no:208¶

In [6]:
#program to find the ABCD parameter of a two-port network .
from sympy import symbols,Matrix

A,B,C,D,V1,V2,I1,I2,Z=symbols('A,B,C,D,V1,V2,I1,I2,Z');
#A=V1/V2; #for i2=0;
A=1;
B=V1/(V1/Z);
C=0;
D=I1/I1;
ABCD=Matrix([[A,B],[C,D]]);
#result
print "abcd parameter"
print ABCD
abcd parameter
Matrix([[1, Z], [0, 1]])

## Example:4.7 page.no:226¶

In [7]:
# program to find the admittance matrix for bridge-T network.
from sympy import symbols,Matrix

Za,Z1,Z2,Z3,Y,Ya,Yb,D=symbols('Za,Z1,Z2,Z3,Y,Ya,Yb,D');
Za=Matrix([[Z1+Z2,Z2],[Z2,Z1+Z2]]);
Yb=Matrix([[1/Z3,-1/Z3],[-1/Z3,1/Z3]]);
Y1=1/Z1;Y2=1/Z2;
Ya=Za**-1
Y=Ya+Yb;
D=((Z2+Z1)**2-Z2**2);
# result
print  "admittance matrix for bridge-T network="
print Y