Single Stub Matching

 Editor:張宏彬

Advisor:江簡富

(I) Analytic Approach

 

 

 

where n is an integer (positive or negative). The amplitude and phase of  are

 

 

The parameter and can be expressed in terms of and  as

 (1)

  (2)

Two possible solutions for b and ds are given in (1) and (2) respectively, where the integer value for n is chosen such that .

 

(II) Smith Chart Approach

(a)  => point A

(b) Drawing constant SWR circle passing through A, go around the constant SWR circle by half a revolution to B which corresponds to

(c) The constant SWR is also the locus of

   . Draw r = 1 circle and find C and F which correspond to two solutions of . The distance moved from B to C is the location of stub.

  

(d) Since the short circuit corresponds to a susceptance of infinity, we start at point D

(the outmost circle) to reach E which is the input admittance of the stub normalized with. The distance moved from D to E is the length of the stub.

(e) The second solution of can be obtained from (c), which is the distance moved

from B to F.

(f) The second solution of  can be obtained from (d).where is the distance from D to G.

 

 

 

Parameter in DEMO

=>

 

The general expressions for the line voltage and line current are

the waves satisfy the boundary condition given by

(1)   at =0 ,

(2)   at =0 ,

(3)   at =0 ,

(4)   (5) at =0, =,=,

(6)

Form above , we can obtain voltage and current in which region as follows

Region 1

Region 2

Region 3