Module 2 : Transmission Lines
Lecture 12 : Applications of Transmission Lines
  Use of Smith Chart for calculating and

From the impedance relation we can see that if a line of length is terminated in a short circuit or open circuit (shown in Figure below) the input impedance of the transmission line is purely reactive.
   
The input impedance of a loss-less line can be written as
Since the range of 'tan' and 'cot' functions is from to , any reactance can be realized by proper choice of . Moreover, any reactance can be realized by either open or short circuit termination. This is a very useful feature because depending upon the transmission line structure, terminating one way may be easier than other. For example, for a microstrip type line ( see in later section), realizing an open circuit is easier as short circuit would require drilling a hole in the substrate.
Now if a reactance is to be realized in a high frequency circuit one can use a short circuited line of length or an open circuited line of length given by
 
   
Smith chart can be used to find or as follows:
Choose suitable characteristics impedance of the line,
Normalize the reactance to be realized (X) by to give normalized reactance .
   
(a) Mark the reactance jx  to be realized on the Smith chart to get point 'X' in Figure.
(b)
Move in anticlockwise direction from point X to the short circuit (SC) point on the Smith chart to get (see Figure below).
(c) Move from X in the anticlockwise direction upto open circuit (OC) to get as indicated in Figure.

(d)
Note here that instead of reactance if we had to realize a normalized susceptance b, the procedure is identical except that SC and OC points are interchanged.
   
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