Editing Smith chart (section)

===Working with both the ''Z'' Smith chart and the ''Y'' Smith charts===
In RF circuit and matching problems sometimes it is more convenient to work with admittances (representing [[electrical conductance|conductance]]s and [[susceptance]]s) and sometimes it is more convenient to work with impedances (representing [[electrical resistance|resistance]]s and [[reactance (electronics)|reactance]]s). Solving a typical matching problem will often require several changes between both types of Smith chart, using normalised impedance for [[series and parallel circuits|series]] elements and normalised admittances for [[series and parallel circuits|parallel]] elements. For these a dual (normalised) impedance and admittance Smith chart may be used. Alternatively, one type may be used and the scaling converted to the other when required. In order to change from normalised impedance to normalised admittance or vice versa, the point representing the value of reflection coefficient under consideration is moved through exactly 180 degrees at the same radius. For example, the point P1 in the example representing a reflection coefficient of <math>0.63\angle60^\circ\,</math> has a normalised impedance of <math> z_P = 0.80 + j1.40\,</math>. To graphically change this to the equivalent normalised admittance point, say Q1, a line is drawn with a ruler from P1 through the Smith chart centre to Q1, an equal radius in the opposite direction. This is equivalent to moving the point through a circular path of exactly 180 degrees. Reading the value from the Smith chart for Q1, remembering that the scaling is now in normalised admittance,  gives <math>y_P = 0.30 - j0.54\,</math>. Performing the calculation
:<math>y_\text{T} = \frac{1}{ z_\text{T} }\,</math>
manually will confirm this.

Once a [[transformation (mathematics)|transformation]] from impedance to admittance has been performed, the scaling changes to normalised admittance until a later transformation back to normalised impedance is performed.

The table below shows examples of normalised impedances and their equivalent normalised admittances obtained by rotation of the point through 180°. Again, these may be obtained either by calculation or using a Smith chart as shown, converting between the normalised impedance and normalised admittances planes.

{| border="1" cellpadding="2"
|+Values of reflection coefficient as normalised impedances and the equivalent normalised admittances
!width="200"|Normalised impedance plane
!width="200"|Normalised admittance plane
|-
|P<sub>1</sub> (<math>z = 0.80 + j1.40\,</math>)
|Q<sub>1</sub> (<math>y = 0.30 - j0.54\,</math>)
|-
|P<sub>10</sub> (<math>z = 0.10 + j0.22\,</math>)
|Q<sub>10</sub> (<math>y = 1.80 - j3.90\,</math>)
|}
[[Image:SmithEx3.png|thumbnail|Values of complex reflection coefficient plotted on the normalized impedance Smith chart and their equivalents on the normalized admittance Smith chart.]]