Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 22

In the derivation of the approximate formulas of and Z 0 for low-loss lines in Subsection 9- 3.1, all terms containing the second and higher powers o f (R/ L ) and (G/ C ) were neglected in comparison with unity. At lower frequencies, better approximations than those given in Eqs. (9- 54) and (9- 58) may be required. Find new formulas for and Z 0 for low-loss lines that retain terms containing ( R/ L ) 2 and ( G/ C ) 2 Obtain the corresponding expression for phase velocity.