Editing Smith chart (section)

===The {{math|Y}} Smith chart===
The {{math|Y}} Smith chart is constructed in a similar way to the {{math|Z}} Smith chart case but by expressing values of voltage reflection coefficient in terms of normalised admittance instead of normalised impedance. The normalised admittance {{mvar|y}}{{sub|T}} is the reciprocal of the normalised impedance {{mvar|z}}{{sub|T}}, so
:<math> y_\mathsf{T} = \frac{1}{z_\mathsf{T}} \,</math>
Therefore:
:<math> y_\mathsf{T} = \frac{1-\Gamma}{\, 1 + \Gamma \,} \,</math>
and
:<math> \Gamma = \frac{ 1 - y_\mathsf{T} }{\, 1 + y_\mathsf{T} \,} \,</math>
The {{math|Y}} Smith chart appears like the normalised impedance, type but with the graphic nested circles rotated through 180°, but the numeric scale remaining in its same position (not rotated) as the {{math|Z}} chart.

Similarly taking
:<math> y_\mathsf{T} = \tilde{o} + j\,\tilde{p} \,</math>
for [[real number|real]] <math>\,\tilde{o}\,</math> and <math>\,\tilde{p}\,</math> gives an analogous result, although with more and different minus signs:
:<math>\Gamma = c + j d = \left[\frac{1 - \tilde{o}^2 - \tilde{p}^2}{\,(\tilde{o} + 1)^2 + \tilde{p}^2\,}\right] + j \left[\frac{ -2\tilde{p} }{\,(\tilde{o} + 1)^2 + \tilde{p}^2\,}\right]  = \left[ \frac{ 2(\tilde{o} + 1) }{\,(\tilde{o} + 1)^2 + \tilde{p}^2\,}- 1 \right] + j \left[\frac{ - 2 \tilde{p} }{\,(\tilde{o} + 1)^2 + \tilde{p}^2\,}\right] \,.</math>

The region above the {{mvar|x}}-axis represents capacitive admittances and the region below the {{mvar|x}}-axis represents inductive admittances. Capacitive admittances have positive [[Imaginary number|imaginary]] parts and inductive admittances have negative imaginary parts.

Again, if the termination is perfectly matched the reflection coefficient will be zero, represented by a 'circle' of zero radius or in fact a point at the centre of the Smith chart. If the termination was a perfect open or short circuit the magnitude of the voltage reflection coefficient would be unity, all power would be reflected and the point would lie at some point on the unity circumference circle of the Smith chart.