Once the boundary and initial conditions for the transmission line problem have been introduced, the simultaneous solution of this set of equations is required in order to completely, specify the system. Due to their complexity, however, these fundamental relations are too difficult to solve analytically and it is necessary to make simplifying assumptions which have the effect of reducing the equations to a set of linear relations for which analytic solutions can be found.
Each of the models considered was derived from the fundamental equations of fluid dynamics and from general considerations of the boundary and flow conditions. The higher order models are those which most closely resemble the fundamental equations, having had the least number of terms removed. Subsequent models containing either fewer terms or approximate representations of terms are of lower order and are generally less accurate. The hierarchical structure of the models is shown in Fig. 1. The detailed discussion of models, their underlying assumptions and their solutions is presented in ref. [54] and their experimental verification is presented in [55].
Fig. 1 Long transmission
line models - classification