Experiment No- 8
Name –Parth Chitre
UID – 2022200022
Batch – A2
Aim: To design two single stub matching networks for the following specifications:
Characteristic impedance of transmission line and stub: 50 Ω
Load impedance: ZL= 60 – j80 Ω
Match frequency: 2 GHz
Objective:
To write a MATLAB program to determine the distance from the load end to the stub and to compute the
length of the stub in each case.
To plot the frequency response of the designed networks from 1 GHz to 3 GHz and compare the solutions
in terms of their bandwidth for 10% reflection.
To obtain an approximate solution using the Z Smith Chart.
Requirements: MATLAB software and Z Smith Chart.
Theory:
Lossless impedance matching networks using discrete components have a limitation in that they can be
used effectively for frequencies below 300 GHz. At UHF, a solution is to use open or short-circuit lossless
transmission lines called stubs. A stub may be either connected at the load or at a finite non-zero distance
from the load, limited by the length of the transmission line. The circuit can easily be fabricated using
strip lines or micro strip lines on an appropriate substrate.
Single stub tuning circuits are illustrated in Fig. 1. In single-stub tuning the two adjustable parameters are
the distance, d, from the load to the stub position, and the value of susceptance or reactance provided by
the stub. For the shunt-stub case, the basic idea is to select d so that the admittance, Y, seen looking into
the line at distance d from the load is of the form Y0 + j B. Then the stub susceptance is chosen as −jB,
resulting in a matched condition. For the series-stub case, the distance d is selected so that the impedance,
Z, seen looking into the line at a distance d from the load is of the form Z0+ jX. Then the stub reactance is
chosen as −jX, resulting in a matched condition.
For transmission line media such as micro strip or stripline, open-circuited stubs are easier to fabricate
since via hole through the substrate to the ground plane is not needed. For lines like coax or waveguide,
however, short-circuited stubs are usually preferred because the cross-sectional area of such an open-
circuited line maybe large enough (electrically) to radiate, in which case the stub is no longer purely
reactive.
The admittance at this point is Y = G+ jB= 1/Z where
The distance d can be analytically determined as
where,
The stub susceptance is then given by
The required stub lengths can be finally computed from
Procedure:
● Write a MATLAB program to determine two possible distances from the load end to the stub.
● Compute the length of the stub for each of the distances determined in Step 1.
● For each solution, plot a graph of the frequency response and compute the bandwidth for 10%
reflection.
● Solve the problem using Z Smith Chart and compare the results with the analytical approach.
MATLAB code and output:
Results Graph:
Conclusion:
● The impedance matching experiment successfully demonstrated the use of single-stub matching
networks to match a specified load impedance with a transmission line.
● By calculating the distance from the load to the stub and the stub length using MATLAB, we
could ensure minimal reflection at the designated match frequency of 2 GHz.
● Additionally, frequency response analysis over a range from 1 GHz to 3 GHz confirmed that both
designed networks achieved the desired bandwidth for a 10% reflection coefficient.
● The results from the analytical approach closely matched the graphical solution obtained with the
Smith Chart, validating the accuracy of both methods.
