The e-model, a tool for network planning recommended by the ITU-T, suffers from the lack of predicting linear distortions as they may occur from channel filtering, codecs, and user interfaces. In order to face this deficiency, a new impairment factor is introduced in this paper which is estimated on the basis of two simple parameters from the linear portion of a system. Therewith, conventional Equipment Impairment Factors of narrowband and wideband speech codecs are decomposed into a linear and a residual part, allowing to quantify both magnitudes separately on the so-called R-scale. By extending the concept of distortion classes in the e-model, the proposed scheme provides a plausible picture of the linear effect of transmission systems. The advantage of wideband causing a 36% quality gain is well reflected. Further, the decomposition leads to a reduction of error when impairment factors are added on the R-scale. Examples for instrumentally estimating the residual impairment are given.