 Task: Given the load resistance \(R_{L}\) and source impedance \(Z_{g}\), find the characteristic impedance \(Z_{0}\) of the transmission line so that the impedance is matched. ( \(R_{L}\) is transformed to \(Z_{g}\) at the center of Smith chart. Error less than 3% is acceptable.)
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Introduction:Learn how to perform impedance matching using a quarter-wavelength transformer. Impedance matching is achieved when\(Z_{g}\)、\(Z_{0}\) and \(R_{L}\)are in geometric progression. \(\frac{Z_{0 } }{Z_{g}}=\frac{R_{L } }{Z_{0 }}\implies Z_{0 } = \sqrt {Z_{g}R_{L }}\) | Parameters:\(R_{L}\)：Load resistance\(Z_{g}\)：Source impedance, reference impedance of Smith chart \(Z_{0}\)：Characteristic impedance \(Z_{in}\)：Input Impedance |