# 3d Smith Chart Demo

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**Please use for the 3D Smith chart demo the latest available Java version- if not possible errors may occur**

The 3D Smith chart demo version has 3 planes : normalized impedance plane, reflection plane and 3D Smith chart. One may draw the impedance and get the image of it on the reflection coefficient's plane or on the 3D Smith chart. On the 3D Smith chart one can rotate it and play with the constant r,x, and abs(z) circles. The 3D Smith chart includes both extended reflection and impedance planes. One may get used with the geometrical meaning of the reflection coefficient: it maps line-like shapes into circles on the 3D Smith chart.Circle like shapes are mapped into circles. The 3D Smith chart becomes a generalized Smith and dual Smith chart that includes all possible loads .Note : **The Smith chart i**s not a conformal mapping of the complex impedance plane (as it is mostly seen), it is a conformal mapping **of the extended impedance plane** and thus the 3D Smith chart based on the Riemann sphere should be seen as the natural generalization of the Smith chart, that unifies the active and passive microwave circuit design**.**More: The user can see an inductor, a capactior and a R,L,C circuit S parameters on the 3D Smith diagram. One may change the complex ports impedances and see how the S parameters move on the 3D Smith chart.

Copyright Andrei Muller, registered with Iulia Burbea Intellectual Property Law and protected by the copyright law

Program when runned should plot a similar window to the one below ( in the demo version for the 3 circuits ( inductor, capacitor and r,l,c, circuit)

**Load and source instability circles at a specific frequency for an amplifer with the following S parameters:**

0.69 146 1.3 31 0.07 55 0.53 -49 (S11, S12,S21,S22) in Magnitude angle format Green circle is in the south (since it lied outside of the smith chart) and in the West since it was in the capacitve region, the Orange circle lies in the south ( since it was outside of the Smith chart) and in the East since it was in the Inductive part. Pls note that on a 2D Smith chart becomes very un-handy to see the possible unstable regions and scaling problems can occur, these things are avoided on a 3D Smith chart since any circle in the reflection plane is mapped somewhere to a different circle on the 3D Smith chart

A simple capacitor on the 3D Smith chart seeing impedances of 50 Ohms at the two ports. It lies west of Greenwich and in the north hemisphere. The circle arc form is explained by the fact the the capacitor represents a simple line in the complex plane as one changes the frequency, thus the reflection coefficient which is an inversive transformation will map that line into a circle arc. The position into the north hemisphere is a consequence of the reflection coefficient's magnitude which is smaller than one ( a passive circuit) thus will be mapped into the north