In the absence of a single module interface standard, integration of pre-designed modules in System-on-Chip design often requires the use of protocol converters. Existing approaches to automatic synthesis of protocol converters mostly lack formal foundations and either employ abstractions that ignore crucial low level behaviors, or grossly simplify the structure of the protocols considered. We present a state-machine based formal model for bus based communication protocols, and precisely define protocol compatibility, and correct protocol conversion. Our model is expressive enough to capture features of commercial protocols such as bursts, pipelined transfers, wait state insertion, and data persistence, in cycle accurate detail. We show that the most general, correct converter for a pair of protocols, can be described as the greatest fixed point of a function for updating buffer states. This characterization yields a natural algorithm for automatic synthesis of a provably correct converter by iterative computation of the fixed point. We report our experience with automatic converter synthesis between widely used commercial bus protocols, such as AMBA AHB, ASB, APB, and OCP, considering features which are beyond the scope of current techniques.