This paper shows the development of transmission line model, based on lumped element circuit that provides answers directly in the time and phase domain. This model is valid to represent the ideally transposed line, the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal domain. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the line modal domain.