A network analyzer HP A showing a Smith chart. 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. 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. Reflection coefficients can be read directly from the chart as they are unitless parameters.
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Tygokree For distributed components the effects on reflection coefficient and impedance of moving along the transmission line must be allowed for using the outer circumferential scale of the Smith chart which is calibrated in wavelengths. This page was last edited on 15 Augustat At this frequency the free space wavelength is 3 m.
File:Smith chart — Wikimedia Commons Using the Smith chart, the normalised impedance may be obtained with appreciable accuracy by plotting the point representing the reflection coefficient treating the Smith chart abaqe a polar diagram and then reading its value directly using the characteristic Smith chart scaling.
As impedances and admittances change with frequency, problems using the Smith chart can only be solved manually using one frequency anaque a time, the result being represented by a point.
The path along the arc of the circle represents how the impedance changes whilst moving along the transmission line. Using complex exponential notation:. The north pole is the perfect matching point, while the south pole is the perfect mismatch point.
A locus of points on a Smith chart covering a range of frequencies can be used to ee represent:. Ve Commons has media ssmith to Smith charts. They both change with frequency so for any particular measurement, the frequency at which it was performed must be stated together with the characteristic impedance. Points with suffix P are in the Z plane and points with suffix Q are in the Y plane.
The region above the x-axis represents inductive impedances positive imaginary parts and the region below the x -axis represents capacitive impedances negative imaginary parts. At point P 21 the circle intersects with the unity circle of constant normalised resistance at. Reading from the Smith chart scaling, remembering that this is now a normalised admittance gives. From the table it can be seen that a negative admittance would require an inductor, connected in parallel with the transmission line.
The following table shows the steps taken to work through the remaining components and transformations, returning eventually back to the centre of the Smith chart and a perfect 50 ohm match. 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 component dimensions themselves will be in the order of millimetres so the assumption of lumped components will be valid.
Normalised impedance and normalised admittance are dimensionless. This occurs in microwave circuits and when high power requires large components in shortwave, FM and TV Broadcasting. Interactive online Smith chart A suitable inductive shunt matching would therefore be a 6.
The complex reflection coefficient is generally simply referred to as reflection coefficient. If there were very different values of resistance present a value closer to these might be a better choice. Here the electrical behaviour of many lumped components becomes rather unpredictable. While the use of paper Smith charts for solving the complex mathematics involved in matching problems has been largely replaced by software based methods, the Smith chart display is still the preferred method of displaying how RF parameters behave at one or more frequencies, an alternative to using tabular information.
In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. The degrees scale represents the angle of the voltage reflection coefficient at that point. The following table gives the complex expressions for impedance real and normalised and admittance real and normalised for each of the three basic passive circuit elements: The following example shows how a transmission line, terminated with an arbitrary load, may be matched at one frequency either with a series or parallel reactive component in each case connected at precise positions.
Smith chart If a polar diagram is mapped on to a cartesian coordinate system it is xbaque to measure angles relative to the positive x -axis using a counterclockwise direction for positive angles. The Smith chart may be used to analyze such circuits in which case the movements around the chart are generated by the normalized impedances and admittances of the components at the frequency of operation.
Impedances in series and admittances in parallel add while impedances in parallel and admittances in series are related by a reciprocal equation. If the termination is perfectly matched, the reflection coefficient will be zero, represented effectively by a circle of zero radius or in fact a point at the centre of the Smith chart.
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