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| Smith chart | |
|---|---|
| Name | Smith chart |
| Invented | 1930s |
| Inventor | Phillip H. Smith |
| Field | Radio frequency engineering |
Smith chart.
The Smith chart is a graphical aid for solving problems involving complex impedances and reflection coefficients in transmission line and microwave engineering, developed to visualize relationships among impedance, admittance, reflection, standing wave ratio, and network parameters; it links practical measurement techniques used at facilities such as Bell Labs, Massachusetts Institute of Technology, Iowa State University, Harvard University and Stanford University with theoretical frameworks from Oliver Heaviside, Guglielmo Marconi, James Clerk Maxwell, Heinrich Hertz and Nikola Tesla, and it remains fundamental in curricula at institutions like California Institute of Technology, Imperial College London, University of Cambridge, ETH Zurich and Tsinghua University.
Phillip H. Smith introduced the chart in the 1930s while working with industrial and academic engineers at Bell Labs, drawing on prior work by mathematicians and physicists such as Lord Kelvin, Hermann von Helmholtz, Augustin-Jean Fresnel and Oliver Heaviside; contemporaneous applications during the interwar and wartime periods connected the chart to projects at Bell Labs, RCA, BAE Systems predecessors, General Electric and Westinghouse Electric Corporation, and it was disseminated through texts from publishers associated with McGraw-Hill and Wiley and via standards bodies including IEEE and IEC.
The chart maps the complex reflection coefficient plane onto normalized impedance and admittance parameters using conformal transformation techniques rooted in complex analysis developed by figures such as Bernhard Riemann, Augustin-Louis Cauchy, Carl Friedrich Gauss, Jean le Rond d'Alembert and Pierre-Simon Laplace; the construction employs circles of constant resistance and reactance derived from bilinear transformations related to Möbius transforms studied by August Ferdinand Möbius and Évariste Galois, and it encodes relationships between voltage standing wave ratio (VSWR), reflection coefficient magnitude, and complex impedance used by engineers referencing methods from John Vincent Atanasoff and Claude Shannon.
Engineers apply the chart to impedance matching, network synthesis, scattering-parameter interpretation and antenna feed design in systems developed at organizations and projects like NASA, European Space Agency, CERN, AT&T, F-16 avionics programs, GPS infrastructure and satellite projects by Intelsat and Iridium Communications; it is used alongside measurement equipment from Keysight Technologies, Rohde & Schwarz, Tektronix, Anritsu and Agilent Technologies in design efforts at Lockheed Martin, Raytheon Technologies, Northrop Grumman and startups incubated at MIT Lincoln Laboratory.
Practitioners normalize impedances to system characteristic impedances such as 50 Ω or 75 Ω (standards promulgated by entities like IEEE and Telecommunications Industry Association) and use the chart to perform tasks including single-stub matching, double-stub tuning, quarter-wave transformer design and visualization of S-parameters; typical workflows integrate data from vector network analyzers produced by Rohde & Schwarz and Keysight Technologies, circuit simulations from tools by Cadence Design Systems and Mentor Graphics and lab courses at universities such as Pennsylvania State University and University of Michigan.
Extensions include admittance Smith charts, reflection-coefficient-only plots, log-magnitude overlays, constant-Q circles, multi-frequency overlays and polar-format adaptations used in conjunction with techniques from Claude Shannon information theory, Harry Nyquist sampling concepts, and modal analysis applied in research at Bell Labs, MITRE Corporation and Sandia National Laboratories; academic work has linked the chart to network parameter generalizations for multiport systems as studied by H. W. Bode, Rudolf E. Kalman, W. J. R. Firth and contributors to ITU recommendations.
Modern implementations appear in commercial and open-source software such as Keysight Technologies's PathWave, National Instruments LabVIEW toolkits, MATLAB toolboxes, Python-based packages maintained by communities around SciPy and NumPy, and EDA suites from Cadence Design Systems, ANSYS, COMSOL Multiphysics and CST Studio Suite; these integrate with measurement automation using instruments from Rohde & Schwarz, Tektronix and Anritsu and are taught in courses at Massachusetts Institute of Technology, Stanford University, University of California, Berkeley and Imperial College London.