A Smith chart is a type of nomogram used in electrical engineering that shows how the complex impedance of a transmission line varies along its length. It is often used to simplify the impedance matching of a transmission line with its load.

Origin

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It was invented by Phillip Smith in 1939 while he was working for RCA (although the Japanese engineer Kurakawa invented a similar device one year earlier). When asked why he invented this chart, Smith explained:

"From the time I could operate a slide rule, I've been interested in graphical representations of mathematical relationships."

Mathematical basis

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The basis for all Smith charts is the following equation:

$\backslash rho\; =\; \backslash frac\{Z\_L\; -\; Z\_0\}\{Z\_L\; +\; Z\_0\}\; =\; \backslash frac\{z\_L\; -\; 1\}\{z\_L\; +\; 1\}$

$\backslash rho$ is the complex reflection coefficient (also called the one-port scattering parameter s or $s\_\{11\}$). $z\_L$ is the normalized impedance of the load of the line, and is equal to $Z\_L/Z\_0$, where:

• $Z\_L$ is the load impedance and
• $Z\_0$ is the characteristic impedance of the transmission line

The chart itself occurs in the complex plane, representing the reflection coefficient, which is expressed in polar coordinates. The center of the chart corresponds to the case when the line and the load are matched, and the reflection coefficient is therefore zero. The perimeter of the chart corresponds to 100% reflection, and the angles printed around the perimeter indicate the phase of the reflection coefficient from zero to 180°, or half a wavelength. The impedance of the load and at other points along the line are indicated by circular coordinates. The full circles represent the resistive component of the impedance and the crossing partial circles the reactive component.

Some Smith charts graph the admittance rather than the impedance. An admittance Smith chart is created by rotating an impedance Smith chart 180°. Another commonly used variant is the ZY Smith chart. It is constructed by overlaying the impedance and admittance chart, and useful if admittances and impedances are needed at the same time.

Although, in the age of computers, the paper Smith chart is used less frequently to solve problems, it is still a very useful way of displaying data. Students studying electromagnetism (RF engineering in particular) are usually assigned problem-solving exercises using the chart, which remains an important teaching tool.

Measuring instruments often display their results in the form of a Smith chart, as do studies in academic journals.

External links

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• A Collection of Smith Chart Resources Tutorials, graphics and other info on Smith Chart
• linSmith Smith charting program for Linux.
• Smith Chart Print free Smith Charts from your computer.
• Black Magic Smith Chart - Vector-graphic (infinitely scalable) Smith Chart for practical use.
• The Java Smith-Chart-Tool - A free Java-Tool to paint s-parameters in a Smith-Chart.
• Smith Excel Graph plots reflection coefficient data in real and imaginary formats on a customizable Smith Chart (Microsoft Excel Spreadsheet 53K)
• PostScript functions Functions to plot dots, lines, gamma circle, constant real and imaginary path in PostScript format to make vectorial images.
• An online educational interactive Smith chart. A choice of impedance and admittance charts with a chart marker.

Electrical engineering | Diagrams

Smith-Diagramm | Carta de Smith | Abaque de Smith | Carta di Smith | スミスチャート | Carta de Smith | 史密夫圖表