This paper presents a parametric study of linear induction motor for design purpose. The chosen mathematical model uses a 2D formulation with magnetic vector potential A. The implementation of the model is carried out with the finite element method on the free platform Gmsh-GetDP. Circuit model is coupled to FE model so that constant voltage supply mode can be considered. This work aims to highlight the effect of the pole pair number on the characteristics and the performances of the linear induction machine through two numerical models associated to an analytical one. Furthermore, the study shows the effect of the pole pair number on the phase imbalance and the spatial harmonic spectrum of the machine. Reducing this imbalance and higher order harmonics presence will increase machine performances.