Editing Smith chart (section)

===Choice of Smith chart type and component type===
The choice of whether to use the ''Z'' Smith chart or the ''Y'' Smith chart for any particular calculation depends on which is more convenient. Impedances in series and admittances in parallel add while impedances in parallel and admittances in series are related by a reciprocal equation. If <math>Z_\text{TS} </math> is the equivalent impedance of series impedances and <math>Z_\text{TP} </math> is the equivalent impedance of parallel impedances, then
:<math>Z_\text{TS} = Z_1 + Z_2 + Z_3 + ... \,</math>
:<math>\frac{1}{Z_\text{TP}} = \frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3} + ... \,</math>
For admittances the reverse is true, that is
:<math>Y_\text{TP} = Y_1 + Y_2 + Y_3 + ... \,</math>
:<math>\frac{1}{Y_\text{TS}} = \frac{1}{Y_1} + \frac{1}{Y_2} + \frac{1}{Y_3} + ... \,</math>
Dealing with the [[multiplicative inverse|reciprocal]]s, especially in complex numbers, is more time-consuming and error-prone than using linear addition. In general therefore, most [[radio frequency|RF]] engineers work in the plane where the circuit topography supports linear addition. The following table gives the complex expressions for impedance (real and normalised) and admittance (real and normalised) for each of the three basic [[passive components|passive circuit elements]]: resistance, inductance and capacitance. Using just the characteristic impedance (or characteristic admittance) and test frequency an [[equivalent circuit]] can be found and vice versa.

{| border="1" cellpadding="1"
|+ <big>'''Expressions for impedance and admittance'''</big> <br/>normalised by impedance {{mvar|Z}}{{sub|0}} or admittance {{mvar|Y}}{{sub|0}} 
!rowspan="2" width="100" style="text-align:center;"| '''Element type'''
|colspan="2" width="180" style="text-align:center;"| '''Impedance''' ({{mvar|Z}} or {{mvar|z}}) or '''Reactance''' ({{mvar|X}} or {{mvar|x}})
|colspan="2" width="180" style="text-align:center;"| '''Admittance''' ({{mvar|Y}} or {{mvar|y}}) or '''Susceptance''' ({{mvar|B}} or {{mvar|b}})
|-
|style="text-align:center;"| '''Actual''' <br/>([[Ohm (unit)|&Omega;]])
|style="text-align:center;"| '''Normalised''' <br/>(no units)
|style="text-align:center;"| '''Actual''' <br/>([[Siemens (unit)|S]])
|style="text-align:center;"| '''Normalised''' <br/>(no units)
|-
|style="text-align:center;"| '''Resistance''' ({{mvar|R}})
| <math>\; Z = R \;</math>
| <math>\; z = \frac{R}{Z_0} = R Y_0 \;</math>
| <math>\; Y = G = \frac{1}{R} \;</math>
| <math>\; y = g = \frac{1}{R Y_0} = \frac{Z_0}{R} \;</math>
|-
|style="text-align:center;"| '''Inductance''' ({{mvar|L}})
| <math>\; Z = j X_\text{L} = j \omega L \;</math>
| <math>\; z = j x_\text{L} = j \frac{\omega L}{Z_0} = j \omega L Y_0 \;</math>
| <math>\; Y = -jB_\text{L} = \frac{-j}{\omega L} \;</math>
| <math>\; y = -jb_\text{L} = \frac{-j}{\omega L Y_0} = \frac{-j Z_0}{\omega L} \;</math>
|-
|style="text-align:center;"| '''Capacitance''' ({{mvar|C}})
| <math>\; Z = -j X_\text{C} = \frac{-j}{\omega C} \;</math>
| <math>\; z = -j x_\text{C} = \frac{-j}{\omega C Z_0} = \frac{-j Y_0}{\omega C} \;</math>
| <math>\; Y = j B_\text{C} = j \omega C \;</math>
| <math>\; y = j b_\text{C} = j\frac{\omega C}{Y_0} = j \omega C Z_0 \;</math>
|}