a) On a 2D Smith chart two persons start on the center of the chart and propose each other to meet at infinity, the girl taking the inductive route, while the boy the capacitive route going always on the same line with the back to each other.
The construction is presented by the authors of the 3D Smith chart tool in Microwave Journal, IEEE Transactions n Microwave and Techniques, IEEE Microwave and Wireless Letters or Electronics Letters.įig 1. East inductive, West capacitive.Ĭonstruction : it uses an ingenious trick of group theory of "inversive geometry" which treats Mobius transformations as (z-1)/(z+1) just as a subclass of the inversive transformations-all together these transformations long for a mapping on a sphere in order to map always circles into circles, in 2D they always fail to form a group, thus need a compact surface to live on in order that circles should be mapped to circles, so that they should all together form a single family -infinite lines are just circles too when mapped on the sphere. The 3D Smith chart generalizes the 2D Smith chart in the sense that all circles which never met in 2D meet in the South hemisphere which becomes the "home" of active circuits (exhibiting negative resistance) while the North hemisphere the one of passive circuits.
The circuits which are mapped out of the unit circle Smith chart represent circuits with negative resistance which occur in active circuits design( amplifiers, transistors, oscillators) or in circuits using complex characteristic impedances.
On a 2D Smith chart one is bounded by the unit circle, all the circles which never get together on a 2D Smith chart "long" to meet again but never do since the points are thrown at infinity in all directions.
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