Overview

The Smith Chart is a graphical tool which is very useful when solving transmission line and network problems [1]. It was published in 1939 by Phillip H. Smith at the Bell Telephone Laboratories [2]. An enhanced version followed in 1944 [3], which may have become in the course of time the most widely used impedance and reflection coefficient chart. The objective of most transmission line problems is to match a line to a load [4], Although matching problems can be tackled by using current CAD software, the Smith Chart is still very useful in finding solutions step-by-step. This may lead to a deeper understanding of transmission line transformation properties. Therefore, it is also supposed that the application of the Smith Chart is of high pedagogical importance. In the context of this book, we will learn to find lumped and distributed (or mixed) elements of the matching network and to convert these elements into a microstrip circuit. The construction of the Smith Chart is based on a bilinear transformation. The z -plane is mapped onto the ?-plane due to the relation

(B.1)

where z denotes the normalized impedance and ? the reflection coefficient, z and ? are complex numbers and can be written as z = Re ( z) + jIm ( z), and ? = ? e ^{jarg ?} = Re( ?) + jIm( ?) = u + jv