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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Smith —[1] [2] 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. 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.

In sbaque to change from normalised impedance to normalised admittance or vice versa, the point representing the value of reflection coefficient under consideration is moved through exactly degrees at the same radius. If there were very different values of resistance present a value closer to these might be a better choice.

Interactive online Smith chart

Using the Smith chart, the normalised impedance may be ds with appreciable 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. Points with suffix P are in the Z plane and points with suffix Q are in the Y plane.

By using this site, you agree to the Terms of Use and Privacy Policy. The component dimensions themselves will be in the order of millimetres so the assumption of lumped components will be valid. The north pole is the perfect matching point, while the south pole is the perfect mismatch point.

The most commonly used normalization impedance is 50 ohms. At this frequency the free space wavelength is 3 m. Provided the frequencies are sufficiently close, the resulting Smith chart points may be joined by straight lines to create a locus.

The degrees scale represents the angle of the voltage reflection coefficient at that point. This smjth shows that, for a standing wave, the complex reflection coefficient and impedance repeats every half wavelength along the transmission line. In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. This technique is a graphical alternative to substituting the values in the equations.


At point P 21 the circle intersects with the unity circle of constant normalised resistance at. The path along the arc of the circle represents how the impedance changes whilst moving along the transmission line. 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.


Point Q 20 is the equivalent of P 20 but expressed as a normalised admittance. In RF circuit and matching problems sometimes it is more convenient to work with admittances representing conductances and susceptances and sometimes it is more convenient to work with impedances representing resistances and reactances.

This occurs in microwave circuits and when high power requires large components in shortwave, FM and TV Broadcasting. For example, the point P1 in the example representing a reflection coefficient of 0.

Smith chart – Wikipedia

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.

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. These are the equations which are used to construct the Z Smith chart.

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

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 represented by a point. From Wikipedia, the free encyclopedia. If the termination was a perfect open or short circuit the magnitude of the voltage reflection coefficient would be unity, all power would be reflected and the point would lie at some point on the unity circumference circle of the Smith chart. 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 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.

The Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance the most commonnormalised admittance or both, using different colours to distinguish between them.

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Again, these may be obtained either by calculation or using a Smith chart as shown, converting between the normalised impedance and normalised admittances planes.

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.

The Smith chart may also be used for lumped element matching and analysis problems.

Smith chart

ds The first transformation is OP 1 along the line of constant normalized resistance in this case the addition of a normalized reactance of – j 0. Retrieved from ” https: A locus of points on a Smith chart covering a range of frequencies can be used to visually represent:.

The normalised admittance y T is the reciprocal of the normalised impedance aaque Tso. A point with a reflection coefficient magnitude 0. 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.

The Smith chart has circumferential scaling in wavelengths and degrees. 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.

Considering the point at infinity, the space of the new chart includes all possible loads.

The earliest point at which a shunt conjugate match could be introduced, moving towards the generator, would be at Q 21the same position as the previous P 21but this time representing a normalised admittance given by. Using complex exponential notation:. The analysis starts with a Z Smith chart looking into R 1 only with no other components present.

Any actual reflection coefficient must abaqe a magnitude of less than or equal to unity so, at the test frequency, this may be expressed by a point inside a circle of unity radius.

The normalised impedance Smith smirh is composed of two families of circles: In fact this value is not actually used. Versions of the transmission line equation may be similarly derived for the admittance loss free case and for the impedance and admittance lossy cases. Here the electrical behaviour of many lumped df becomes rather unpredictable.