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 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. In this case the wavelength scaling on the Smith chart circumference is not used.
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. At point P 21 the circle intersects with the unity circle of constant normalised resistance at. The following table gives some similar examples of points which are plotted on the Z Smith chart. Impedances in series and admittances in parallel add while impedances in parallel and admittances in series are related by a reciprocal equation.
These are the equations which are used to construct the Z Smith chart. 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: This page was last edited on 15 Augustat 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.
Once the result is obtained it may be de-normalised to obtain the actual result. Provided the frequencies are sufficiently close, the resulting Smith chart points may be joined by straight lines to create a locus. 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.
Again, if the termination is perfectly abaquw 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. 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.
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They both change with frequency so for any particular measurement, the frequency at which it was performed must smih stated together with the characteristic impedance. 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 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. Dealing with the reciprocalsespecially in complex numbers, is more time consuming and error-prone than using linear addition. The length of the line would then be scaled to P 1 assuming the Smith abxque radius to be unity.
In other projects Wikimedia Commons. All terms are actually multiplied by this to obtain the instantaneous phasebut it is conventional and understood to omit it.
Once a transformation from impedance to admittance has been performed, the scaling changes to normalised admittance until a later transformation back to normalised impedance is performed. The north pole is the perfect matching point, while the south pole is the perfect mismatch point. For these a dual normalised impedance and admittance Smith chart may be used. 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.
Using complex exponential notation:. From the table it can be seen that a negative admittance would require an inductor, connected in parallel with the transmission line.
This is plotted on the Z Smith chart at point P The magnitude of a complex number is the length of a straight line drawn from the origin to the point representing it. Versions of the transmission line equation may be similarly derived for the admittance loss free case and for the impedance and admittance lossy cases.
To graphically change this to the equivalent normalised admittance point, say Q1, a line is drawn with a ruler from P1 through the Smith chart centre to Q1, an equal radius in the opposite direction. A generalized 3D Smith chart based on the extended complex plane Riemann sphere and inversive geometry was proposed abaue The region above the x -axis represents capacitive admittances and the region smifh the x -axis represents inductive admittances. The conversion may be read directly from the Smith chart or by substitution into the equation.
How may the line be matched? Points with suffix P are in the Z plane and points with suffix Q are in the Y plane.
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. In this case the circumferential wavelength abaqque must be used, remembering that this is the wavelength within the transmission line and may differ from the free space wavelength.