Using a Landau-de-Gennes-type free-energy density expansion, we have analyzed the effect of high pressure on the smectic A-isotropic (S A I) phase transition temperature and nonlinear dielectric effect (NDE) of a homologous series 5-n-alkyl-2(4'-isothiocyanatophenyl)-1,3-dioxanes (nDBT). The pressure dependence of (S A I) transition temperature (T SAI ) is explained in terms of the pressure-dependent Landau coefficients associated with the order parameter coupling terms of the free-energy density expansion. We have shown that the S A I transition remains first order even at the elevated pressures. We have investigated the temperature and pressure dependence of the NDE in the isotropic phase of IS A transition. The role of alkyl chain length of the homologous series on the IS A transition and NDE has been studied and has been found to be substantial. A close agreement between the theoretical and experimental results has been found.