On the Sum of the Reflection and Transmission Coefficient on the Smith Chart and 3D Smith Chart
Résumé
The paper presents in premiere a simple mapping
property of the sum of the reflection and transmission parameters
of reciprocal two port networks. It is proved that although the
reflection and transmission parameter may have very complicated
paths on the Smith chart, their sum will be always moving on the
unit circle if the circuit is symmetric and lossless. Further once
symmetrical losses at the ports occur their sum path will switch
on a family of circles through one point. Using inversive geometry
we construct a new function which maps this family of circles in
lines on the extended Smith chart. The proposed method for
checking the symmetry uses just two parameters and avoids
testing the phase of the corresponding input and output
parameters. By means of the 3D Smith chart we propose in the
end an alternative approach to visualize the parameters.