Smith chart

The Smith chart is a circular nomogram used in radio frequency (RF) engineering to solve transmission line and impedance-matching problems. It plots a complex reflection coefficient (

Γ

{\displaystyle \Gamma }

) on a grid of normalized electrical impedance (

z

{\displaystyle z}

). Depending on the region, it is also known as the Smith diagram, Volpert–Smith chart, or Mizuhashi chart.

Because normalized impedance is complex, the chart maps two families of curves: circles of constant resistance (

Re

⁡

(

z

)

{\displaystyle \operatorname {Re} (z)}

) and arcs of constant reactance (

Im

⁡

(

z

)

{\displaystyle \operatorname {Im} (z)}

). Standard charts focus on passive circuits where resistance is non-negative (

Re

⁡

(

z

)

≥

0

{\displaystyle \operatorname {Re} (z)\geq 0}

). Regions outside the unit circle (

Re

⁡

(

z

)

<

0

{\displaystyle \operatorname {Re} (z)<0}

) correspond to negative resistance, which is used for oscillator design and stability analysis.

The display allows engineers to evaluate multiple RF parameters at once, including admittance,

S

n

n

{\displaystyle S_{nn}}

scattering parameters, noise figures, and stability boundaries.

Although paper charts have mostly been replaced by software for calculations, the display format remains standard across RF simulation software and vector network analyzers to visualize how parameters change with frequency.

History

The Smith chart emerged in the late 1930s through the independent work of Tōsaku Mizuhashi, Amiel R. Volpert, and Phillip H. Smith. It was initially known by several names before Smith chart became the standard name in the Western world by 1950.