# What is the 3D Smith Chart?

#### ANDREI MULLER - 3D Smith Chart Tools S.R.L.

May 23, 2017

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. 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.

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. East inductive, West capacitive.

Construction : 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 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.

Fig 1. a                                                               Fig 1.  b

Fig 1. 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. When they reach the contour of the Smith chart ( reflection coefficient magnitude=1) they waste their energy and can't continue  thus they just long to meet again following the path chosen and just dream to see each other again at infinity in different directions of the horizon.

Fig 1. b) On the 3D Smith chart they start at the North pole (perfect match corresponding to origin in 2D) with their back to each other. The girl goes again inductive (East) while the boy capacitive (West). When their reflection coefficients magnitude reaches 1 they get energy-less at Equator. The idea of crossing the South hemisphere to meet at infinity in the South pole refreshes them and they become energized again continuing renewed and awaken their journey to a refashioned reality while meeting happy at infinity in the South pole young again.

( drawing Dolores Gonzalez Demchenko based on a dual vision of infinity on 2D and 3D Smith charts- Andrei Muller)

3D Smith chart tool

The 3D Smith chart tool produced by Andrei Muller (telecommunications engineering), Alin Moldoveanu (virtual reality prof.), Victor Asavei (computer graphics prof) with the web&deployment lead of Cristian Fleischer (software engineering) uses in a unique interactive way the compact capabilities of the 3D Smith chart.

It is an ideal educational tool for the fast and simple understanding and matching use of both 2D and 3D smith charts in both Z/Y configurations when using resistances, capacitors, inductors, in series or shunt configuration, transmission lines or stubs.

It is also and advanced analysis mode for S parameters, stability circles, power levels , group delays and quality factors making it a new software for the measuring stage or design stage of microwave devices. The simultaneous display of a variety of parameters form imported touchstone files speeds up the analysis phase and helps in the optimizations of the high frequency devices.

Educational design mode, moving on r,x,g,b,constant magnitude of the reflection coefficient, stubs in 2D and 3D Smith chart, interactive highly reconfigurable interface which can ease the teaching and the understanding of both Smith and 3D Smith chart

Simple L,C matching on 2D and 3D Smith charts

Fritz Caspers  Aug 11, 2017

This is an interesting alternative/extension for those who are already familiar with the conventional Smith Chart in electronic format