Use the smith chart to find the normalized load impedance

#Use the smith chart to find the normalized load impedance series#

To do so, we start from the general definition of line impedance (which is equally applicable to a load impedance when d=0) ( )( ) ( )( )01( )1V d dZ d ZI d d+ = This provides the complex function ( ) ( ) ( ) Re, Im Z d f = that we want to graph.

#Use the smith chart to find the normalized load impedance series#

Im( ) Re( )1 Transmission Lines Amanogawa, 2006 - Digital Maestro Series 166The goal of the Smith chart is to identify all possible impedances on the domain of existence of the reflection coefficient. In the case of a general lossy line, the reflection coefficient might have magnitude larger than one, due to the complex characteristic impedance, requiring and extended Smith chart. This is also the domain of the Smith chart. The domain of definition of the reflection coefficient for a loss-less line is a circle of unitary radius in the complex plane. From a mathematical point of view, the Smith chart is a 4-D representation of all possible complex impedances with respect to coordinates defined by the complex reflection coefficient. The chart provides a clever way to visualize complex functions and it continues to endure popularity, decades after its original conception. Transmission Lines Amanogawa, 2006 - Digital Maestro Series 165Smith Chart The Smith chart is one of the most useful graphical tools for high frequency circuit applications.