Generalized network equations of the non-uniform transmission lines solved using amplitude/phase representation

For the generalized network equations of the nonuniform transmission line with harmonic excitation, linear second order and non-linear first order equations are derived by purely algebraic modification or by applying well-known transformations for ordinary differential equations. These serve to get solutions in terms of the primary voltage and current. Introducing auxiliary quantities leads to other differential equations which exhibit further insight into the solution. The Prüfer transformation for example provides differential equations for the amplitude and phase. This enables insight into the oscillation which is not immediately available from the network equations.