Abaque de Smith – Download as PDF File .pdf), Text File .txt) or read online. EXERCICE ABAQUE DE – Download as PDF File .pdf), Text File .txt) or read online. fr. abaque de Smith, m diagramme de Smith, m diagramme polaire d’impédance, m. représentation graphique en coordonnées polaires du facteur de réflexion.

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The complex reflection coefficient is generally simply referred to as reflection coefficient. In fact this value is not actually used. Solving a typical matching problem will often require several changes between both types of Smith chart, using normalised impedance for series elements and normalised admittances for parallel elements. Dealing with the reciprocals smiyh, especially in complex numbers, is more time consuming and error-prone than using linear addition.

A point with a reflection coefficient magnitude 0.

A suitable inductive shunt matching would therefore be a 6. This occurs in microwave circuits and when high power requires large components in shortwave, FM and TV Broadcasting. From the table it can be seen that a negative admittance would require an inductor, connected in parallel with the transmission line. The analysis of lumped element components assumes that the wavelength at the frequency of operation is much greater than the dimensions of the components themselves.

The Y Smith chart is constructed in a similar way to the Z Smith chart case but by expressing values of voltage reflection coefficient in terms of normalised admittance instead of normalised impedance.

## File:Smith chart bmd.gif

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.

As the transmission line is loss free, a circle centred at the centre of the Smith chart is drawn through the point P 20 to represent the path of the constant magnitude reflection coefficient due to the termination. The choice of whether to use the Z Smith chart or the Y Smith chart for any particular calculation depends on which is more convenient. A generalized 3D Smith chart based on the extended complex plane Riemann sphere and inversive geometry was proposed in Alternatively, one type may be used and the scaling converted to the other when required.

For example, the point P1 in the example representing a reflection coefficient of 0. 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: 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.

In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. The outer circumferential scale of the Smith chart represents the distance from the generator to the load scaled in wavelengths and is therefore scaled from zero to 0. Using just the characteristic impedance or characteristic admittance and test frequency an equivalent circuit can be found and vice versa.

The Smith chart is actually constructed on such a polar diagram. As 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 snith by a point.

The length of the line would then be scaled to P 1 assuming the Smith chart radius to be unity.

### Smith chart – Wikipedia

If the termination was a perfect open circuit or short circuit the magnitude of the reflection coefficient would be unity, all power would be reflected and the point would lie at some point on the unity circumference circle.

These are the equations which are used to construct the Z Smith chart. The Smith chart may also be used for lumped element matching and analysis problems. Views Read Edit Smithh history.

### File:Smith chart – Wikimedia Commons

In other projects Wikimedia Commons. Ssmith both change with frequency so for any particular measurement, the frequency at which it was performed must be stated together with the characteristic impedance. This is plotted on the Z Smith chart at point P The region above the x-axis represents inductive impedances positive imaginary parts abaquee the region below the x -axis represents capacitive impedances negative imaginary parts. The component dimensions themselves will be in the order of millimetres so the assumption of lumped components will be valid.

Points with suffix P are in the Z plane and points with suffix Q are in the Y plane. Thus most RF circuit analysis software includes a Smith chart option for the display of results and all but the simplest impedance measuring instruments can display measured results on a Smith chart display.

The Smith chart scaling is designed in such a way that reflection coefficient can be converted abaqke normalised impedance or vice versa. This page was last edited on 15 Augustat For each, the reflection coefficient is abaqeu in polar form together with the corresponding normalised impedance in rectangular form. The analysis starts with a Z Smith chart looking into R 1 only with no other components present. The normalised admittance y T is the reciprocal of the normalised impedance z Tso.

The region above the x -axis represents capacitive admittances and the region below the x -axis represents inductive admittances. Using the Smith chart, the normalised impedance amith be obtained with ce accuracy by plotting the point representing the reflection coefficient treating the Smith chart as a polar diagram and then reading its value directly using the characteristic Smith chart scaling.

In general therefore, most RF engineers work in the plane where the circuit topography supports linear addition.

This is the equation which describes how the complex reflection coefficient changes with the normalised impedance and may be used to construct both families of circles. Once the result is obtained it may be de-normalised to obtain the actual result.

Again, if the termination is perfectly matched the reflection coefficient will be zero, represented by a ‘circle’ of zero radius or in fact a point at the centre of the Smith chart.