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We briefly review the electrical-optical response of materials to radiative forcing within the formalism of the Kramers-Kronig relations. A commensurate set of criteria is described that must be met by any frequency-domain model representing the time-domain response of a real (i.e., physically possible) material. The criteria are applied to the Brendel-Bormann (BB) oscillator, a model that was originally introduced for its fidelity at reproducing the non-Lorentzian peak broadening experimentally observed in the infrared absorption by thin amorphous films but has since been used for many other common materials. We show that the BB model fails to satisfy the established physical criteria. Taking an alternative approach to the model derivation, a physically consistent model is proposed. This model provides the appropriate line-shape broadening for modeling the infrared optical response of thin amorphous films while adhering strictly to the Kramers-Kronig criteria. Experimental data for amorphous alumina (${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$) and amorphous quartz silica (${\mathrm{SiO}}_{2}$) are used to obtain model parametrizations for both the noncausal BB model and the proposed causal model. The proposed model satisfies consistency criteria required by the underlying physics and reproduces the experimental data with better fidelity (and often with fewer parameters) than previously proposed permittivity models.