5.18 Calculate and plot the percent bandwidth for an N = 1-, 2-, and 4-section binomial
matching transformer versus ZL /Z0 = 1.5 to 6 for _m = 0.2.
Solution
A Code was written on MATLAB to calculate the desired values of bandwidth vs given values of Zl/Zo
The code is as under
MATLAB Code
clc
clear all
impedenceratio= [1.5 2 2.5 3 3.5 4 4.5 5 5.5 6];
N1=1
N2=2
N3=4
gamma_m=0.2
%for N1
A_N1= 2^(-N1).*((impedenceratio-1)./(impedenceratio+1))
A_N1=abs(A_N1)
theta_m_N1= acosd((1./2).*(gamma_m./A_N1).^(1/N1))
bandwidth_N1= (2- ((4.*theta_m_N1)./180)).*100
%for N2
A_N2= 2^(-N2).*((impedenceratio-1)./(impedenceratio+1))
A_N2=abs(A_N2)
theta_m_N2= acosd((1./2).*(gamma_m./A_N2).^(1/N2))
bandwidth_N2= (2-((4.*theta_m_N2)./180)).*100
% for N3
A_N3= 2^(-N3).*((impedenceratio-1)./(impedenceratio+1))
A_N3=abs(A_N3)
theta_m_N3= acosd((1./2).*(gamma_m./A_N3).^(1/N3))
bandwidth_N3= (2- ((4.*theta_m_N3)./180)).*100
%Plotting N1,N2 and N3 vs Zl/Zo
x = impedenceratio;
y1 = bandwidth_N1;
a1= plot(x,y1); M1 = "N1";
xlabel('Zl/Zo')
ylabel('% bandwidth')
title('Percent Bandwidth vs Zl/Zo Plot')
hold on
y2 = bandwidth_N2;
a2= plot(x,y2); M2 = "N2";
y3 = bandwidth_N3;
a3= plot(x,y3) ; M3 = "N3";
legend([a1,a2,a3], [M1, M2, M3])
hold off
The values found from code are tabulated below
Zl/Zo
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
For N=1
A
0.1
0.16667
0.21429
0.25
0.27778
0.3
0.31818
0.33333
0.34615
0.35714
For N=2
Bandwidth A
200
0.05
81.933106 0.08333
61.818087 0.10714
52.395952 0.125
46.889324 0.13889
43.269379 0.15
40.705996 0.15909
38.794674 0.16667
37.314327 0.17308
36.133788 0.17857
Plot of Percent Bandwidth vs Zl/Zo
For N=3
Bandwidth A
200
0.0125
112.81884 0.02083
95.752718 0.02679
87.181157 0.03125
81.933106 0.03472
78.36531
0.0375
75.773613 0.03977
73.802024 0.04167
72.250038 0.04327
70.995688 0.04464
Bandwidth
200
137.0129891
123.8723913
117.0685203
112.8188434
109.8882543
107.7363756
106.0854883
104.7770738
103.7136324
Images of solved questions are appended below