The Smith Chart is a mapping between reflection coefficient and normalized
impedance characterized by a pair of equations:

      z - 1
Gamma = -----
      z + 1

   Gamma + 1
z = --------
   1 - Gamma

The impedance matching problem is mainly finding the

z

that having reflection coefficient

Gamma  = ℜ  + jℑ
   z    z      z

satisfies:

           2    2        2
          ℜ  + ℑ   = Gamma
           z    z
       1   2    2    1
( ℜ  - - )   + ℑ   = -
   z   2        z    4

Using some algebra it is easy to find out

        2
ℜ  = Gamma
z

,

       _____________
    _ |    2       4
ℑ  =  \|Gamma  - Gamma
z

Now, we already know that the real component of

z

is

1

Then the imaginary part of the two matching impedance would be:

           2ℑ
             z
+/- -----------------
     2          2
    ℜ  - 2ℜ  + ℑ  + 1
     z     z    z

You are viewing proxied material from sdf.org. The copyright of proxied material belongs to its original authors. Any comments or complaints in relation to proxied material should be directed to the original authors of the content concerned. Please see the disclaimer for more details.