Smith chart

The Smith chart (sometimes also called Smith diagram, Mizuhashi chart (水橋チャート), Mizuhashi–Smith chart (水橋スミスチャート), Volpert–Smith chart (Диаграмма Вольперта—Смита) or Mizuhashi–Volpert–Smith chart) is a graphical calculator or <a href="/facts/Nomogram/ysXLNuVY">nomogram</a> designed for <a href="/facts/Electrical_engineering/YYXW1KLW">electrical and electronics engineers</a> specializing in <a href="/facts/Radio_frequency/aWku7h4R">radio frequency</a> (RF) engineering to assist in solving problems with <a href="/facts/Transmission_line/cYlqaPo3">transmission lines</a> and <a href="/facts/Impedance_matching/0mdy9TAp">matching</a> circuits.
It was <a href="/facts/Simultaneous_invention/8ISpCxDv">independently</a> proposed by Tōsaku Mizuhashi (水橋東作) in 1937, and by Amiel R. Volpert [ru] (Амиэ́ль Р. Во́льперт) and <a href="/facts/Phillip_Hagar_Smith/MfRgdYke">Phillip H. Smith</a> in 1939. Starting with a rectangular diagram, Smith had developed a special <a href="/facts/Polar_coordinate/HBko4YoN">polar coordinate</a> chart by 1936, which, with the input of his colleagues Enoch B. Ferrell and <a href="/facts/James_W._McRae/QLn804nT">James W. McRae</a>, who were familiar with <a href="/facts/Conformal_mapping/cEpQnMad">conformal mappings</a>, was reworked into the final form in early 1937, which was eventually published in January 1939. While Smith had originally called it a "transmission line chart" and other authors first used names like "reflection chart", "circle diagram of impedance", "immittance chart" or "Z-plane chart", early adopters at <a href="/facts/MIT/Xk49vNA8">MIT</a>'s <a href="/facts/MIT_Radiation_Laboratory/hYcQJtxR">Radiation Laboratory</a> started to refer to it simply as "Smith chart" in the 1940s, a name generally accepted in the Western world by 1950.
The Smith chart can be used to simultaneously display multiple parameters including <a href="/facts/Electrical_impedance/I06NSXtN">impedances</a>, <a href="/facts/Admittance/EVdb3QT2">admittances</a>, <a href="/facts/Reflection_coefficient/se689p3C">reflection coefficients</a>, 
 
 
 
 
 S
 
 n
 n
 
 
 
 
 
 {\displaystyle S_{nn}\,}
 
 <a href="/facts/Scattering_parameters/z6ffeKh6">scattering parameters</a>, <a href="/facts/Noise_figure/XUtUWKDL">noise figure</a> circles, constant gain contours and regions for <a href="/facts/Stability_theory/Su5sHnxs">unconditional stability</a>.: 93–103  The Smith chart is most frequently used at or within the <a href="/facts/Unity_radius/VsTffjPK">unity radius</a> region. However, the remainder is still mathematically relevant, being used, for example, in <a href="/facts/Electronic_oscillator/6NaXsSzJ">oscillator</a> design and <a href="/facts/Stability_theory/Su5sHnxs">stability</a> analysis.: 98–101  While the use of paper Smith charts for solving the complex mathematics involved in matching problems has been largely replaced by software based methods, the Smith chart is still a very useful method of showing how RF parameters behave at one or more frequencies, an alternative to using <a href="/facts/Table_(information)/vQcp2QSb">tabular</a> information. Thus most RF circuit analysis software includes a Smith chart option for the display of results and all but the simplest impedance measuring instruments can plot measured results on a Smith chart display.

Smith chart open-in-new

Smith chart