Electromagnetics Engineering Lab
EXPERIMENT 8
Name- Sudhanshu Pandey UID- 2022200112
Batch – B3
AIM:- To design two single stub matching networks for the following specifications:
1. Characteristic impedance of transmission line and stub: 50 Ω
2. Load impedance: ZL= 60 – j80 Ω
3. Match frequency: 2 GHz
THEORY :
Single-stub matching minimizes reflection and maximizes power transfer in transmission lines by
using a short-circuited or open-circuited stub to cancel load reactance.
Key Parameters:
1. Stub Position (d): Distance from the load for impedance adjustment.
2. Stub Length (l): Length providing the required reactance or susceptance.
Tuning Types:
1. Shunt-Stub: Neutralizes admittance's reactive part.
2. Series-Stub: Adds reactance for matching.
Applications:
1. Common at UHF (between 300 MHz and 3 GHz) and higher frequencies. 2. Open
stubs for microstrip; short stubs for coaxial/waveguides to avoid losses.
1
clear all; Z0 = input("Enter the characteristic impedance of the
transmission line(Ω):" ); real_ZL = input("Enter the real part of the
load impedance ZL (Ω):" ); imag_ZL = input("Enter the imaginary part of
the load impedance ZL (Ω):" ); ZL = complex(real_ZL, imag_ZL); % Create
complex load impedance freq = input("Enter the match frequency in GHz:")
* 1e9; %
Convert GHz to Hz % Constants and derived parameters lambda = 3e8 / freq;
% Wavelength (m) beta = 2 * pi / lambda; % Phase constant (rad/m) %
Extract real and imaginary parts of ZL RL = real(ZL);
XL = imag(ZL); % Calculate parameter 't1' and 't2'
using Equation (4) if RL ~= Z0 t1 = (XL + sqrt(RL * ((Z0 - RL)^2 +
XL^2) / Z0)) / (RL - Z0); t2 = (XL - sqrt(RL * ((Z0 - RL)^2 + XL^2)
/ Z0)) / (RL - Z0); else t1 = XL / (2 * Z0); t2 = t1; % Both values
are the same if RL = Z0 end fprintf("Calculated parameter t1:
%.4f\n", t1); % Print the value of t1
Calculated parameter t1: 0.8318
fprintf("Calculated parameter t2: %.4f\n", t2); % Print the value of t2
Calculated parameter t2: -16.8318
% Calculate distance 'd' using Equation (3) for both t1 and t2
if t1==0 d1 = (lambda / (2 * pi)) * atan(t1); else d1 = (lambda / (2 *
pi)) * (pi + atan(t1)); end if t2 == 0 d2 = (lambda / (2 * pi)) *
atan(t2); else d2 = (lambda / (2 * pi)) * (pi + atan(t2)); end
fprintf("Calculated distance d1: %.4f m\n", d1); % Print the value of d1
Calculated distance d1: 0.0916 m
fprintf("Calculated distance d2: %.4f m\n", d2); % Print the value of d2
Calculated distance d2: 0.0389 m
2
% Calculate G and B using Equations (2a) and (2b)
G = RL * (1 + t1^2) / (RL^2 + (XL + Z0 * t1)^2);
B = (RL^2 * t1 - (Z0 - XL * t1) * (XL + Z0 * t1)) / (Z0 * (RL^2 + (XL + Z0
*t1)^2)); fprintf("Calculated conductance G: %.4f\n", G); % Print the value
of G
Calculated conductance G: 0.0200
fprintf("Calculated susceptance B: %.4f\n", B); % Print the value of B
Calculated susceptance B: 0.0294
% Stub susceptance Bs for open-circuited stub
Bs = -B; % Calculate stub length 'l' using Equations (5a) and (5b)
l_open = (lambda / (2 * pi)) * atan(Bs / Z0); % for open-circuited stub l_short
= -(lambda / (2 * pi)) * atan(Z0 / Bs); % for short-circuited stub %
Adjust stub length if negative if l_open < 0 l_open = l_open + lambda / 2;
end
Error using < Not enough
input arguments.
if l_short < 0 l_short = l_short + lambda / 2; end % Output
results fprintf("Calculated distance from load to stub (d1): %.4f
m\n", d1); fprintf("Calculated distance from load to stub (d2): %.4f
m\n", d2); fprintf("Open-circuited stub length (l_open): %.4f m\n",
l_open); fprintf("Short-circuited stub length (l_short): %.4f m\n",
l_short); d1_lambda = d1 / lambda; d2_lambda = d2 / lambda;
fprintf("Calculated distance d1 in terms of wavelength: %.4f λ\n", d1_lambda);
3
Conclusion:
The impedance matching experiment effectively showcased the application of single stub matching
networks to align a given load impedance with a transmission line. Using MATLAB, the distance from
the load to the stub and the stub length were calculated, ensuring minimal signal reflection at the
target frequency of 2 GHz.
