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Waveguide photodetectors are considered leading candidates to overcome the bandwidth efficiency tradeoff of conventional photodetectors. In this paper, a theoretical physics-based model of the waveguide separated absorption charge multiplication avalanche photodetector (WG-SACM-APD) is presented. Both time and frequency modeling for this photodetector are developed and simulated results for different thicknesses of the absorption and multiplication layers and for different areas of the photodetector are presented. These simulations provide guidelines for the design of these high-performance photodiodes. In addition, a circuit model of the photodetector is presented in which the photodetector is a lumped circuit element so that circuit simulation of the entire photoreceiver is now feasible. The parasitics of the photodetector are included in the circuit model and it is shown how these parasitics degrade the photodetectors performance and how they can be partially compensated by an external inductor in series with the load resistor. The results obtained from the circuit model of the WG-SACM-APD are compared with published experimental results and good agreement is obtained. This circuit modeling can easily be applied to any WG-APD structure. The gain-bandwidth characteristic of WG-SACM-APD is studied for different areas and thicknesses of both the absorption and the multiplication layers. The dependence of the performance of the photodetector on the dimensions, the material parameters and the multiplication gain are also investigated.