The image below shows an example Smith chart used to plot the impedance Z = 1.2 - i0.7 Ohms. Suppose our unmatched load impedance is Z = 60 - i35 Ohms if the system impedance is 50 Ohms, then we divide the load and system impedances, giving a normalized impedance of Z = 1.2 - i0.7 Ohms. The system impedance might be a 50 Ohm transmission line. To start working with a Smith chart for impedance matching, we need to normalize our load component that requires impedance matching to the desired system impedance. However, some commercial applications and simulation tools will display impedance data in a Smith chart. As a graphical method for performing impedance matching, it was very useful before the time of graphical computers and simulation tools for plotting impedance. This unique type of chart was developed by Philip Smith at Bell Telephone's Radio Research Lab in the 1930s. What Is a Smith Chart?Ī Smith chart is a type of graph used to plot the normalized impedance of a circuit, a circuit element, or an interconnect.
#Smith chart matching how to#
Smith charts are a standard tool used by many RF engineers, so it pays to know how to use a Smith chart for impedance matching. Using a Smith chart might seem complicated to new designers, and one might question why it is any more or less useful than a graph in Cartesian coordinates. In some cases, such as with transmission line stub matching in RF circuits or input impedance matching to a feedline’s characteristic impedance, a graphical representation of impedance can aid impedance matching.Ī Smith chart provides just such a graphical representation of impedance, and it is a useful tool for understanding how impedance varies in different systems.
In many cases, you need to measure and carefully simulate the appropriate impedance required to ensure impedance matching and prevent power reflection. High speed and high frequency systems need impedance matching to ensure efficient power transfer and prevent reflections. Impedance matching in this PCB can be determined using a Smith chart Once impedance matching requirements are determined, the results can be simulated in a SPICE-based simulation application. One popular method for plotting impedance and determining impedance matching is to use a Smith chart. The examples provided here are solved using graphical tools and a printed Smith chart, rather than the computer program, to emphasize the techniques and approximations involved although some of the numerical results listed were obtained with a computerized Smith chart ( smith-chart.m) available with this text ( see page xi).There are many methods for impedance matching in your circuits. A computerized Smith chart can then be used to analyze conditions on lines. Naturally, any chart can also be implemented in a computer program, and the Smith chart has, but we must first understand how it works before we can use it either on paper or on the screen. Some measuring instruments such as network analyzers actually use a Smith chart to display conditions on lines and networks. Although the Smith chart is rather old, it is a common design tool in electromagnetics. As such, it allows calculations of all parameters related to transmission lines as well as impedances in open space, circuits, and the like.
The Smith chart is a chart of normalized impedances (or admittances) in the reflection coefficient plane. This has been accomplished in a rather general tool called the Smith chart. Thus, the following proposition: Build a graphical chart (or an equivalent computer program) capable of representing the reflection coefficient as well as load impedances in some general fashion and you have a simple method of designing transmission line circuits without the need to perform rather tedious calculations. You may also recall, perhaps with some fondness, the complicated calculations which required, in addition to the use of complex variables, the use of trigonometric and hyperbolic functions. The reflection coefficient, in turn, was defined in terms of the load and line impedances (or any equivalent load impedances such as at a discontinuity).
Voltage, current, and power were all related to the reflection coefficient. The reflection coefficient was used to find the conditions on the line, to calculate the line impedance, and to calculate the standing wave ratio. A look back at much of what we did with transmission lines reveals that perhaps the dominant feature in all our calculations is the use of the reflection coefficient.
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