# Single stub matching

Stub matching in Transmission lines:-

A section of Transmission line can be inserted between Load and source besides it is also possible to connect sections of open (or) short circuited lines as stub (or) tuning stubs in shunt with the main Transmission lines at a certain point to effect the matching.

Matching with the help of tuning stub (or) stub is called as stub matching and has the following advantages

1. Length  $l,\&space;Z_{o}$ are  unchanged.
2. It is possible to add adjustable susceptance in shunt with the line.

Stub matching can be possible by

1. Single stub matching.
2. Double stub matching.

Single stub matching:-

A type of transmission line frequently used in single stub matching is a short circuited section of transmission line , which is connected in parallel to the main transmission line at a particular distance from the load. By using such stub anti resonance is achieved providing impedance at resonance equal to  $R_{o}$ .

The conductance at that point is equal to   $Y_{o}$  and the stub length is adjusted to provide a susceptance which is equal in value but opposite in sign to the input susceptance of the main line at that point so that the total susceptance at that point is zero.

The combination of stub and line will thus represent a conductance which is equal to $Y_{o}$ of the line.

We are connecting the stub in parallel to the main Tx line , we will work out with admittance’s instead of impedance’s.

$Y_{s}=G_{o}\pm&space;jB$

This is the admittance at a point A before stub was connected. The point A is now connected to a stub which provides a susceptance of  $\mp&space;jB$.

$Y_{s}=G_{o}\pm&space;jB\mp&space;jB$.

$Y_{s}=G_{o}$.

$Y_{s}=\frac{1}{R_{o}}$.

$Z_{s}=R_{o}$.

Thus the input impedance of the line is  $R_{o}$ itself up to the point A, after A to load the reflection and hence standing waves occurs but by making this distance less than the wave length the losses can be minimized.

For the single stub, it is important to know where the stub is to be connected exactly and the length of the stub for these two measurements must be made on the line it is easy to measure S and  $V_{min}$  nearest to load.

The measurement is accurate in case of    $V_{min}$  rather than   $V_{max}$

From the expression of  $Z_{s}$ in terms of reflection coefficient

$Z_{s}=Z_{o}(\frac{e^{\gamma&space;l}+ke^{-\gamma&space;l}}{e^{\gamma&space;l}-ke^{-\gamma&space;l}})$ .

$Z_{s}=Z_{o}(\frac{1+ke^{-2\gamma&space;l}}{1-ke^{-2\gamma&space;l}})$ .

Thus at point from load, input impedance is resistive and its value is minimum equal to this is point from the load

At distance