The trochoidal electron monochromator employs an axial magnetic field and a transverse electric field. Many aspects of its performance can be described by electron trajectory equations which include the voltage drop across the entrance aperture. A beam shear is predicted, which is a function of a parameter tan&Vthgr;. Optimum performance is achieved by matching the exit aperture to the sheared beam. tan&Vthgr; establishes a relationship between the field magnitudes and the dimensions of the monochromator. Estimates of appropriate values for these parameters can be made, with the final optimum values being determined by a combination of practical and empirical considerations. Finally, the use of the instrument as an energy analyzer is described.