The process of plotting admittance is essentially reversed - where adding an inductor to a series circuit would move the impedance value clockwise along a constant resistance circle, a shunt inductor would move it counter-clockwise along a constant admittance circle shunt capacitors similarly move your values clockwise on an admittance chart, where a series capacitor would be counter-clockwise.
This is an important step too, as by flipping it over, you now have a chart that will assist you in dealing with shunt components rather than those in series. It is actually surprisingly easy to plot the equivalent chart for admittance - all you have to do is mirror the Chart horizontally. The terms corresponding to resistance and reactance are called conductance and susceptance, respectively. Let's get started by writing the equation for the reflection coefficient of a load impedance, given a source impedance: Once we get past the derivation, there will be a few simplified images showing how those equations can be used and combined to get the final product. That's all the Smith Chart really is: a collection of circles, each one centered in a different place in (or outside) the plot, and each one representing either constant resistance or constant r eactance. By taking the standard reflection coefficient formula and manipulating it so that it provides us with the equations for circles of various radii, we'll be able to construct the basic Smith Chart. That said, even if you don't fully understand the derivation below, you can still use the chart to help you with your own design.
In order to understand the construction of the chart, you'll need to understand high school algebra and the basics of complex numbers, as well as have a basic understanding of impedance in electronic circuits. The Smith Chart has been in use since the 1930s as a method to solve various RF design problems - notably impedance matching with series and shunt components - and it provides a convenient way to find these solutions without the use of a calculator. The Smith Chart is a clever way of graphically solving impedance matching problemsit is still useful today despite the availability of computer based solutions. This article covers the mathematics behind creating the chart and its physical interpretation. Smith Charts are an extremely useful tool for engineers and designers concerned with RF circuits.
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