A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart

This work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry and basic non-Euclidean geometry. The beaut...

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Bibliographic Details
Main Authors: María Jose Pérez-Peñalver, Esther Sanabria-Codesal, Florica Moldoveanu, Alin Moldoveanu, Victor Asavei, Andrei A. Muller, Adrian Ionescu
Format: Article
Language:English
Published: MDPI AG 2018-10-01
Series:Symmetry
Subjects:
hyperbolic geometry
Möbius transformation
Smith chart
Online Access:http://www.mdpi.com/2073-8994/10/10/458
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spelling doaj-904ba127ebbe439fa81d687b638503ea2020-11-24T20:41:46ZengMDPI AGSymmetry2073-89942018-10-01101045810.3390/sym10100458sym10100458A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith ChartMaría Jose Pérez-Peñalver0Esther Sanabria-Codesal1Florica Moldoveanu2Alin Moldoveanu3Victor Asavei4Andrei A. Muller5Adrian Ionescu6Universitat Politècnica de València, Matemática Aplicada, 46022 Valencia, SpainUniversitat Politècnica de València, Matemática Aplicada, 46022 Valencia, SpainDepartment of Computer Science and Engineering, Faculty of Automatic Control and Computers, University POLITEHNICA of Bucharest, 060042 Bucharest, RomaniaDepartment of Computer Science and Engineering, Faculty of Automatic Control and Computers, University POLITEHNICA of Bucharest, 060042 Bucharest, RomaniaDepartment of Computer Science and Engineering, Faculty of Automatic Control and Computers, University POLITEHNICA of Bucharest, 060042 Bucharest, RomaniaEcole Polytechnique Federale de Lausanne, Nanoelectronic Devices Laboratory, 1015 Lausanne, SwitzerlandEcole Polytechnique Federale de Lausanne, Nanoelectronic Devices Laboratory, 1015 Lausanne, SwitzerlandThis work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry and basic non-Euclidean geometry. The beauty and simplicity of this perspective are complementary to the classical way in which the Smith chart is taught in the electrical engineering community by providing a visual insight that can lead to new developments. Further we extend our previous work where we have just drawn the conceptual hyperbolic Smith chart by providing the equations for its generation and introducing additional properties.http://www.mdpi.com/2073-8994/10/10/458hyperbolic geometryMöbius transformationSmith chart
collection DOAJ
language English
format Article
sources DOAJ
author María Jose Pérez-Peñalver
Esther Sanabria-Codesal
Florica Moldoveanu
Alin Moldoveanu
Victor Asavei
Andrei A. Muller
Adrian Ionescu
spellingShingle María Jose Pérez-Peñalver
Esther Sanabria-Codesal
Florica Moldoveanu
Alin Moldoveanu
Victor Asavei
Andrei A. Muller
Adrian Ionescu
A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
Symmetry
hyperbolic geometry
Möbius transformation
Smith chart
author_facet María Jose Pérez-Peñalver
Esther Sanabria-Codesal
Florica Moldoveanu
Alin Moldoveanu
Victor Asavei
Andrei A. Muller
Adrian Ionescu
author_sort María Jose Pérez-Peñalver
title A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
title_short A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
title_full A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
title_fullStr A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
title_full_unstemmed A Review and Mathematical Treatment of Infinity on the Smith Chart, 3D Smith Chart and Hyperbolic Smith Chart
title_sort review and mathematical treatment of infinity on the smith chart, 3d smith chart and hyperbolic smith chart
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2018-10-01
description This work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry and basic non-Euclidean geometry. The beauty and simplicity of this perspective are complementary to the classical way in which the Smith chart is taught in the electrical engineering community by providing a visual insight that can lead to new developments. Further we extend our previous work where we have just drawn the conceptual hyperbolic Smith chart by providing the equations for its generation and introducing additional properties.
topic hyperbolic geometry
Möbius transformation
Smith chart
url http://www.mdpi.com/2073-8994/10/10/458
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