A system-on-chip (SoC) contains numerous intellectual property blocks, or IPs. Protocol mismatches between IPs may affect the system-level functionality of the SoC. Mismatches are addressed by introducing converters to control inter-IP interactions. Current approaches towards converter generation find limited practical application as they use restrictive models, lack formal rigour, handle a small subset of commonly encountered mismatches, and/or are not scalable. We propose a formal technique for SoC design using incremental converter synthesis. The proposed formulation provides precise models for protocols and requirements, and provides a scalable algorithm that allows adding multiple components and requirements to an SoC incrementally. We prove that the technique is sound and complete. Experimental results obtained using real-life AMBA benchmarks show the scalability and wide range of mismatches handled by our approach.