![]() ![]() Use of the Smith chart and the interpretation of the results obtained using it requires a good understanding of AC circuit theory and transmission line theory, both of which are pre-requisites for RF engineers.Īs impedances and admittances change with frequency, problems using the Smith chart can only be solved manually using one frequency at a time, the result being represented by a point. The Smith chart may also be used for lumped element matching and analysis problems. The degrees scale represents the angle of the voltage reflection coefficient at that point. The wavelengths scale is used in distributed component problems and represents the distance measured along the transmission line connected between the generator or source and the load to the point under consideration. The Smith chart has circumferential scaling in wavelengths and degrees. Reflection coefficients can be read directly from the chart as they are unitless parameters. Once an answer is obtained through the graphical constructions described below, it is straightforward to convert between normalised impedance (or normalised admittance) and the corresponding unnormalized value by multiplying by the characteristic impedance (admittance). The most commonly used normalization impedance is 50 ohms. Normalised scaling allows the Smith chart to be used for problems involving any characteristic or system impedance which is represented by the center point of the chart. These are often known as the Z, Y and YZ Smith charts respectively. The Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance (the most common), normalised admittance or both, using different colours to distinguish between them. Ī network analyzer ( HP 8720A) showing a Smith chart. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis. The Smith chart is most frequently used at or within the unity radius region. The Smith chart can be used to represent many parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis. Use of the Smith chart utility has grown steadily over the years and it is still widely used today, not only as a problem solving aid, but as a graphical demonstrator of how many RF parameters behave at one or more frequencies, an alternative to using tabular information. Smith (1905–1987), is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits. The other overlay displays normalized polar coordinate components of impedance, i.e., magnitude and phase angle.Ī graphical method for combining two normalized polar impedance vectors in parallel, which utilizes special polar coordinates, is included.The Smith chart, invented by Phillip H. One of these coordinate overlays displays normalized input impedance components presented by the equivalent parallel-circuit (rather than the conventional series-circuit) elements, and/or normalized input admittance components - presented by the equivalent series-circuit (rather than the conventional parallel circuit) elements. Two overlays for conventional SMITH CHART coordinates which provide alternative coordinate forms, useful in specific waveguide applications, will be described. This is followed by a consideration of the input impedance (or admittance) relationships of a waveguide to those of simple series or parallel circuits which present equivalent impedance (or admittance) at a given frequency. In this chapter the concept of waveguide input impedance (and admittance) is presented first. ![]()
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