The cutoff filter and circular window are critically important elements of circular waveguide TE11 mode transmission systems, but no detailed analysis of their characteristics has yet been undertaken. In order to gain a detailed understanding of return loss and other frequency characteristics, one must analyze the electromagnetic (E-M) fields in the waveguide cavity to the cutoff domain and higher mode oscillations. In this work we present a theoretical analysis employing a method in which E-M fields are represented in the form of transmission equations, and show that the results are in remarkably close agreement with experimental results obtained from a prototype device. It is also demonstrated that the results obtained by the proposed method are far more accurate than those obtained using conventional approximation theory.