Module 6.1 Smith Chart
refernce impedance \(Z_{0}\) : \(\Omega\)
refernce admittance \(Y_{0}\) : \(mS\)
Load impedance ( \(Z_{L}\) ) = + j \(\Omega\)
=>Normalized impedance z: + j
Load admittance ( \(Y_{L}\) ) = + j \(mS\)
=> Normalized admittance y: + j
Reflection coefficient ( \(\Gamma_{L}\) ): \(\angle\) °
( Show \(\left|\Gamma\right|\) )  
(reflection coefficient) ( \(\Gamma_{L} = \left|\Gamma\right|\ * \angle \theta_{\Gamma}\) )

Voltage standing wave ratio ( \(VSWR\) ):
(voltage standing wave ratio)

Introduction:

Select one type of the Smith charts to observe the locations of load impedance
\(Z_{L}\), load admittance \(Y_{L}\), and reflection coefficient \(\Gamma_{L}\).
Furthermore, find the relationship between \(Z_{L}\), \(Y_{L}\), \(\Gamma_{L}\), and \(VSWR\) on the chart.

Parameters:

Load impedance： \(Z_{L} = R_{L} + jX_{L}\)
Normalized impedance： \(z = Z_{L} / Z_{0} = r + jx\)
Load admittance： \(Y_{L} = G_{L} + jB_{L}\)
Normalized admittance： \(y =Y_{L} / Y_{0} = g + jb\)
Reflection coefficient ： \(\Gamma_{L} = \left|\Gamma\right|\ \angle \theta_{\Gamma}\)
  a. \(\left|\Gamma\right|\)：magnitude of  \( \Gamma_{L}, 0 \leqq \left|\Gamma\right|\ \leqq 1 \)
  b. \(\theta_{\Gamma}\)：phase of \(\Gamma_{L}\)