213 in addition to not dissipating power a lossless line has two 17059

Question

2.13 In addition to not dissipating power, a lossless line has two important features: (1) it is dispersionless (u, is independent of frequency), and (2) its characteristic impedance Zo is purely real. Sometimes, it is not possible to design a transmission line such that R' <<WL' and G<<WC', but it is possible to choose the dimensions of the line and its material properties to satisfy the condition Such a line is called a distortionless line, because despite the fact that it is not lossless, it nonetheless possesses the previously mentioned features of the lossless line. Show that for a distortionless line, R'C' = L'G(distortionless line) \alpha=R^{\prime} \sqrt{\frac{C^{\prime}}{L^{\prime}}}=\sqrt{R^{\prime} G^{\prime}} \beta=\omega \sqrt{L^{\prime} C^{\prime}} Z_{0}=\sqrt{\frac{L^{\prime}}{C^{\prime}}}