We outline a linearized analysis of pulsed-source time-of-flight crystal analyzer spectrometers (CAS) based on scattered neutron analysis by crystal monochromators and intended for use in high-resolution quasielastic scattering and Brillouin scattering measurements. Spectrometers of this kind, often called "backscattering spectrometers," provide for high resolution measurements of excitations with typical energies in the range 1-100 microeV in both steady source and pulsed source applications. The analysis is fully general, treating three-dimensionally the geometric conditions for time focusing of the orientations of the source (moderator), sample, monochromator crystal and detector, considered as thin elements having large areas, and allows for the use of mosaic crystal monochromators. We report the results of VITESS Monte Carlo simulations, which verify the analytical focusing conditions for dispersionless excitations, reveal higher-order (than linear) contributions to the resolution widths, and provide absolute intensity estimates.