The theory and design of an inexpensive rotating analyzer unit is presented, which allows a conventional null type ellipsometer to work as rotating analyzer-fixed analyzer automatic ellipsometer, without sacrificing the possibility to work in null mode. The mode switching is performed simply by adding or removing the rotating analyzer from its holder. It is shown that the rotating analyzer phase shift in rotating analyzer-fixed analyzer mode can be run-time determined from the measured Fourier coefficients. This avoids any need of recalibration procedure after mode switching and makes unnecessary plane of incidence synchronization, which further simplifies the needed hardware and reduces the errors connected with the phase shift instability of the output signal. The run-time phase shift calibration procedure and subsequent ellipsometric angles determination do not involve normalization of the output signal Fourier coefficients to the zeroth harmonic, eliminating in this way the influence of the dc component time drift.