A 3D Smith Chart based on the Riemann Sphere for Active and Passive Microwave Circuits

“© © 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”This letter proposes a spherical 3-D Smith Chart suitable for representing both active and passive microwave circuits. Using the mathematical concept of the Riemann sphere, the extended reflection coefficient plane is transformed into the surface of the unit sphere. Since the proposed Smith Chart compiles the whole complex plane, all possible loads are included. A simple graphic tool is thus obtained that successfully unifies active and passive circuits. In addition, lossy lines with complex characteristic impedances can also be represented. The letter presents the 3-D Smith Chart, provides its main governing equations, and also enumerates its more important properties. © 2011 IEEE.This work was supported in part by the POSDRU ID 7713 European Project and by the Ministerio de Ciencia e Innovacion, Spanish Government under Research Project TEC2010-21520-C04-01.Muller, AA.; Soto Pacheco, P.; Dascalu, D.; Neculoiu, D.; Boria Esbert, VE. (2011). A 3D Smith Chart based on the Riemann Sphere for Active and Passive Microwave Circuits. IEEE Microwave and Wireless Components Letters. 21(6):286-288. https://doi.org/10.1109/LMWC.2011.2132697S28628821

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