# Smith chart

A **Smith chart** is a type of graph used in electrical engineering that shows how the complex impedance of a transmission line varies along its length, and simplifies the design of matching networks to match the line to its load. 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). The reason for its invention, Smith explained - *"From the time I could operate a slide rule, IÒve been interested in graphical representations of mathematical relationships."*

The basis for all Smith charts is the following equation:

is the complex reflection coefficient (also called the one-port scattering parameter

*s*or ).is the normalized impedance of the load of the line, and is equal to , where:

is the load impedance and- is the characteristic impedance of the transmission line

Some Smith charts graph the admittance rather than the impedance. An admittance Smith chart is created by rotating an impedance Smith chart 180°.

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.