Let us discuss today discuss what is impedance matching and what is stub:

IMPEDANCE MATCHING

A transmission line is matched when the load impedance ,Z_ris equal to the characteristic impedance ,Z₀ of the line that is

Z_R=Z₀

As                                     p= Z_R-Z₀/ Z_R+Z₀

If                                                Z_R=Z₀

Then,reflection coefficient,

P=0

Thus, there is no reflected wave so the incident power is fully absorbed by the load. Therefore ,the maximum power transfer is possible.

So in communication networks, the elements of network should be designed such that maximum power transfer takes place between the source (or transmitter)and load (or antenna) .This means that if maximum power transfer has to take place between the source and the load,the resistance of the load should be equal to that of the source and the reactance of the load should be equal to that of the source but opposite in sign. That is if the source is inductive ,the load should be capacitance and vice-versa. When this condition is achieved,it is referred to as impedance matching , and the methods employed to achieve this are termed as impedance matching devices.

Stub

A stub is a piece of transmission line.

It is possible to connect sections of open or short circuited line called stub in shunt with the main line at some point or ponts to effect impedance matching. This is called stub matching.

It has two advantages:

(a)    The length and characteristic impedance of the line remains unchanged.

(b)   Adjustable susceptance can be added in shunt with the transmission line.

Stub matching is of two types:

(i)                 Single stub matching

(ii)               Double stub matching

(i) Single stub matching:-

(a) Connection of stub in parallel with transmission line

It consists of an open or short circuited section of transmission line of length l_t,connected in parallel with the main line at distance l_s from the load Z_R.Stub has the same characteristic impedance as the main line.

Generally short circuited stubs are preferred comparable to open circuited stub as open circuited stub radiates some energy at high frequencies.

Use of a single stub to provide impedance matching. It is shown that a transmission line having characteristic impedance of ‘Z₀’ is terminated in a complex load admittance of (g_R+jb_R)

First step:-

Locate a point nearest to the load on the transmission line where the normalized admittance is (1+jb_R)

Second step:

A stub (short or open circuited transmission line) is added in parallel across the transmission line at a point so as to offer a suscetpance of –jb_R. Thus the transmission line with a characteristic impedance of ‘Z₀’ gets matched to a complex load upto that point.

We connect the stub in parallel with the main line as it is easier to deal with the admittance as they can be added up.

(b) Connection of stub in series with transmission line

Here also the first step is to locate a point on the transmission line where the normalized impedance looking towards the load end is(1+j X) .At that point,a stub is added with the stub offering a normalised reactance of (-j X). The feed line needs to be cut for insertion of series stub. This technique is therefore not commonly used as it is difficult to fabricate in co-axial and striplines.

(ii) Double stub matching

In single stub matching, the stub is placed on the line at a specified point.Its location varies with Z_R and frequency. This creates some difficulties as the specified point may occur at an undesirable location. In such cases, double stubs are used. Here the distance between the two stubs is fixed such as λ/16,λ/8,3λ/16,3λ/8 or even closer and the lengths of the two stubs are adjusted to match the load.