The compact free electron maser (FEM), with the advantages of small size and low cost, is important for realistic applications in medicine and industry. In order to utilize the planar wiggler to the best advantage and simultaneously to reduce the necessary electron beam voltage and the size of FEM device, we propose to utilize an elliptical waveguide as the high frequency structure of planar wiggler FEM. A set of universal operating equations suitable for elliptical waveguide and rectangular waveguide FEMs is derived by using the nonlinear theory. The characteristics of the FEMs are numerically analyzed, comparatively.