We obtain a transfer function and a circuit model for separate absorption, grading, charge, and multiplication avalanche photodiodes (SAGCM-APD's). This model is used to calculate the frequency and time responses of the APD's, and to investigate the influence of the carrier velocities and dead-space effect on the bandwidth of the devices. It is shown that for thinner APD's, the dead-space effect can be included by considering a non-local model for carrier velocities, and a local model for impact ionization rates. The new approach is easier than the previous methods, and the calculated results are in good agreement with experimental data. (c) 2005 Elsevier Ltd. All rights reserved.