The conditions under which a composite retarder consisting of two different retardation plates can be operated as a tunable quarter-wave plate are derived. The explicit expressions for the azimuthal angle of a linear polarizer and those of two retardation plates to generate circularly polarized light are presented as a function of retardation angles. Those expressions for the azimuthal angles derived using the Jones matrix formalism are verified as identical to the expressions derived from the analysis of the trajectory on a Poincar$acute{e}$ sphere. A couple of examples are presented for generating circularly polarized light when two identical retardation plates are used.