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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If a polar diagram is mapped on to a cartesian coordinate system it is conventional to measure angles relative to the positive x -axis using a counterclockwise direction for positive angles.

The Smith chart abaqu circumferential scaling in wavelengths and degrees. Provided the frequencies are sufficiently close, the resulting Smith chart points may be joined by straight lines to create a locus. By substituting the expression for how reflection coefficient changes along an unmatched loss free transmission line.

Retrieved from ” https: 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. Reading from the Smith chart scaling, remembering that this is now a normalised admittance gives.

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

The Smith chart scaling is designed in such a way that reflection coefficient can be converted to normalised impedance or vice versa. 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. The north pole is the perfect matching point, while the south pole is the perfect mismatch point.


File:Smith chart – Wikimedia Commons

Once the result is obtained it may be de-normalised to obtain the actual result. In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius xe at the origin.

In this case the circumferential wavelength scaling must be used, remembering that this is the wavelength within the transmission line and may differ from the free space wavelength. 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 as a qbaque diagram and then reading its value directly using the characteristic Smith chart scaling.

File:Smith chart bmd.gif

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. How ed the line be matched?

The wavelengths scale is used in distributed component problems and represents the distance measured along the transmission line connected between the generator or source smitth the smlth to the point under consideration. The most commonly used normalization impedance is 50 ohms. For each, the reflection coefficient is given in polar form together with the corresponding normalised dr in rectangular form. This occurs in microwave circuits and when high power requires large components in shortwave, FM and TV Broadcasting.

Here the electrical behaviour of many lumped components becomes rather unpredictable. They both change with frequency so for smitth particular measurement, the frequency at which it was performed must be stated together with the characteristic impedance. The degrees scale represents the angle of the voltage reflection coefficient at that point.

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.


The analysis starts with a Z Smith chart looking into R 1 only with no other components present.


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.

Normalised impedance and normalised admittance are dimensionless. A point with a reflection coefficient magnitude 0. The accuracy of the Smith chart is reduced for problems involving a large locus of impedances or admittances, although the scaling can be magnified for individual areas to accommodate these. The normalised impedance Smith chart is composed of two families of circles: 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: 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 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. Considering the point at infinity, the space of the new chart includes all possible loads.

The following table gives some similar examples of points which are plotted on the Z Smith chart.

Capacitive admittances have positive imaginary parts and inductive admittances have negative imaginary parts. Again, if the termination is perfectly matched the reflection coefficient will be zero, represented by a ‘circle’ of zero radius or in smitth a point at the centre of the Smith chart.