## The Smith Chart

Here is another one. It is essentially a graphic technique to add and subtract vectors. Calculating the impedance of transmission line.

https://en.wikipedia.org/wiki/Smith_chart

The Smith chart, invented by Phillip H. Smith (1905–1987),[1][2] is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits.[3] The Smith chart can be used to simultaneously display multiple parameters including impedances, admittances, reflection coefficients, S n n {\displaystyle S_{nn}\,} S_{{nn}}\, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis.[4][5] The Smith chart is most frequently used at or within the unity radius region. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis.[6]

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 charts display is still the preferred method of displaying how RF parameters behave at one or more frequencies, an alternative to using tabular 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 display measured results on a Smith chart display.