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An exact solution is developed for the frequency response of photodiodes composed of multiple spatially uniform layers. Each layer is analyzed separately to obtain a set of linear response coefficients. The response of the multilayer diodes is calculated using matrix algebra. Effects of carrier transit, electron and hole trapping, avalanche decay, and finite absorption length are included in the analysis. The results of R.B. Emmons (1967) and G. Lucovsky et al. (1958) for avalanche photodiodes (APDs) and p-i-n's, respectively, are obtained as special cases. The theory is illustrated by applying it to the separated absorption and multiplication