![]() The Smith Chart is a polar plot of the complex reflection coefficient, Γ, for a normalized complex load impedance Zn = R + jX, where R is the resistance and X the reactance. There is some algebra involved in understanding the basic transmission line equations, but - once you understand how to move on the graph - you can forget the math and just read the chart. What Is a Smith Chart?Īlthough there are many computer programs 2, 3 and network analyzers that can solve impedance matching problems for you, a complete understanding of the Smith Chart is highly beneficial in understanding the nature of transmission lines. This chart closely resembles the chart we see today. According to his biography, his impedance coordinates were not orthogonal - which means perpendicular - and there were no true circles, but the standing wave ratio was linear. The first graphical chart was limited by the range of data so he came up with a polar plot that was a scaled version of the first plot. He used a thermocouple bridge and voltmeter to make the measurements. Smith developed the first graphical solution in the form of a rectangular plot from his measurements of the maxima and minima voltages along the transmission line. Phillip Smith - Inventor of the Smith Chart. He relished the problem of matching the transmission line to the antenna a component he considered matched the line to space. Although Smith did a great deal of work with antennas, his expertise and passion focused on transmission lines. In 1928, he joined Bell Labs, where he became involved in the design of antennas for commercial AM broadcasting. Smith attended Tufts College and was an active amateur radio operator with the callsign 1ANB. The Smith Chart was invented by Phillip Smith, who was born in Lexington, MA on April 29, 1905. ![]() After reading this, you will have a better understanding of impedance matching and VSWR - common parameters in a radio station. The purpose of this article is to introduce you to the basics of the Smith Chart. 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.The Smith Chart is one of the most useful tools in radio communications, but it is often misunderstood. 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. 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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