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IEVref:726-19-01ID:
Language:enStatus: Standard
Term: Smith chart
Synonym1: Smith diagram
[Preferred]
Synonym2:
Synonym3:
Symbol:
Definition: 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.


Publication date:1982
Source:
Replaces:
Internal notes:2016-06-21: <i>Z</i><sub>o</sub> corrected to <i>Z</i><sub>0</sub> in equations. JGO

2017-06-02: Cleanup - Remove Attached Image 726-19-011.gif

2017-06-02: Cleanup - Remove Attached Image 726-19-012.gif

2017-06-02: Cleanup - Remove Attached Image 726-19-013.gif

2017-06-02: Cleanup - Remove Attached Image 726-19-014.gif
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