page_title: Smith chart
section_title: 3D Smith chart
hierarchical_section_title: Smith chart / 3D Smith chart
caption_attribution_description: English: 3D Smith Chart representation generated by the non-commercial tool available at http://www.3dsmithchart.com. 3D Smith Chart
context_page_description: The Smith chart, invented by Phillip H. Smith, and T. Mizuhashi, is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio frequency engineering to assist in solving problems with transmission lines and matching circuits. The Smith chart can be used to simultaneously display multiple parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis. 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.
  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.
context_section_description: A generalized 3D Smith chart based on the extended complex plane (Riemann sphere) and inversive geometry was proposed in 2011. The chart unifies the passive and active circuit design on little and big circles on the surface of a unit sphere using the stereographic conformal map of the reflection coefficient's generalized plane. Considering the point at infinity, the space of the new chart includes all possible loads. The north pole is the perfect matching point, while the south pole is the perfect mismatch point.
caption: 3D Smith chart representation
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