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Area Transmission lines and waveguides / Standing-wave and impedance measurements

IEV ref 726-19-01

en
Smith chart
Smith diagram
graphical representation in polar coordinates of the amplitude reflection factor r for a lossless uniform transmission line with characteristic impedance Z0:

r _ = Z _ Z 0 Z _ + Z 0 = Z _ / Z 0 1 Z _ / Z 0 +1 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiqadkhagaqhaiabg2da9maalaaabaGabmOwayaaDaGaeyOeI0IaamOwamaaBaaaleaacaqGVbaabeaaaOqaaiqadQfagaqhaiabgUcaRiaadQfadaWgaaWcbaGaae4BaaqabaaaaOGaeyypa0ZaaSaaaeaadaWcgaqaaiqadQfagaqhaaqaaiaadQfadaWgaaWcbaGaae4BaaqabaGccqGHsislcaaIXaaaaaqaamaalyaabaGabmOwayaaDaaabaGaamOwamaaBaaaleaacaqGVbaabeaakiabgUcaRiaaigdaaaaaaaaa@49FC@

in terms of the complex impedance Z by two families of orthogonal circles on each of which either the resistance R or the reactance X has a constant value, where Z = R + jX is the complex impedance in the direction of propagation of the incident wave at the point at which the amplitude reflection factor is evaluated

Note 1 – The Smith chart may be used with impedances Z, admittances Y _ = 1 Z _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiqadMfagaqhaiabg2da9maalaaabaGaaGymaaqaaiqadQfagaqhaaaaaaa@3923@ , normalized impedances Z _ Z 0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaamaalaaabaGabmOwayaaDaaabaGaamOwamaaBaaaleaacaqGVbaabeaaaaaaaa@385D@ or normalized admittances Y _ Y 0 = Z 0 Z _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaamaalaaabaGabmywayaaDaaabaGaamywamaaBaaaleaacaqGVbaabeaaaaGccqGH9aqpdaWcaaqaaiaadQfadaWgaaWcbaGaae4BaaqabaaakeaaceWGAbGba0baaaaaaa@3C85@

Note 2 – The Smith chart is usually restricted to positive values of R, in which case it is bounded by an outer circle where the magnitude of the amplitude reflection factor is unity.

Note 3 – The Smith chart allows the conversion by direct reading of the amplitude reflection factor into the real and imaginary parts of the impedance or admittance and vice versa; the representation also simplifies the transformation of impedance or admittance from one point to another on the same transmission line.


fr
abaque de Smith, m
diagramme de Smith, m
diagramme polaire d'impédance, m
représentation graphique en coordonnées polaires du facteur de réflexion complexe r, pour une ligne de transmission uniforme sans pertes, d'impédance caractéristique Z0:

r _ = Z _ Z 0 Z _ + Z 0 = Z _ / Z 0 1 Z _ / Z 0 +1 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiqadkhagaqhaiabg2da9maalaaabaGabmOwayaaDaGaeyOeI0IaamOwamaaBaaaleaacaqGVbaabeaaaOqaaiqadQfagaqhaiabgUcaRiaadQfadaWgaaWcbaGaae4BaaqabaaaaOGaeyypa0ZaaSaaaeaadaWcgaqaaiqadQfagaqhaaqaaiaadQfadaWgaaWcbaGaae4BaaqabaGccqGHsislcaaIXaaaaaqaamaalyaabaGabmOwayaaDaaabaGaamOwamaaBaaaleaacaqGVbaabeaakiabgUcaRiaaigdaaaaaaaaa@49FC@

en fonction de l'impédance complexe Z à l'aide de deux familles de cercles orthogonaux sur chacun desquels soit la résistance R, soit la réactance X a une valeur constante, Z = R + jX étant l'impédance complexe dans la direction de propagation de l'onde incidente au point de détermination du facteur de réflexion complexe

Note 1 – L'abaque de Smith peut être employé avec des impédances Z, des admittances Y _ = 1 Z _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiqadMfagaqhaiabg2da9maalaaabaGaaGymaaqaaiqadQfagaqhaaaaaaa@3923@ , des impédances normées Z _ Z 0 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaamaalaaabaGabmOwayaaDaaabaGaamOwamaaBaaaleaacaqGVbaabeaaaaaaaa@385D@ ou des admittances normées Y _ Y 0 = Z 0 Z _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaamaalaaabaGabmywayaaDaaabaGaamywamaaBaaaleaacaqGVbaabeaaaaGccqGH9aqpdaWcaaqaaiaadQfadaWgaaWcbaGaae4BaaqabaaakeaaceWGAbGba0baaaaaaa@3C85@

Note 2 – L'abaque de Smith est habituellement limité aux valeurs positives de R ; tout l'abaque est alors compris à l'intérieur d'un cercle où le module du facteur de réflexion est égal à l'unité.

Note 3 – L'abaque de Smith permet, par lecture directe, de convertir le facteur de réflexion complexe en parties réelle et imaginaire de l'impédance ou de l'admittance et inversement; cette représentation simplifie aussi la transformation des impédances ou des admittances d'un point à un autre d'une ligne radioélectrique.


ar
مخطط سميث

de
Smith-Diagramm, n

es
diagrama de Smith

fi
Smithin diagrammi

it
carta di Smith

ko
스미스 선도

ja
スミス図表

pl
wykres Smitha
wykres kołowy (impedancji lub admitancji)

pt
diagrama de Smith
ábaco de Smith

sv
Smith-diagram

Publication date: 1982
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