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In this paper, we propose an architecture for FPGA emulation of mixed-signal systems that achieves high accuracy at a high throughput. We represent the analog output of a block as a superposition of step responses to changes in its analog input, and the output is evaluated only when needed by the digital subsystem. Our architecture is therefore intended for digitally-driven systems; that is, those in which the inputs of analog dynamical blocks change only on digital clock edges. We implemented a high-speed link transceiver design using the proposed architecture on a Xilinx FPGA. This design demonstrates how our approach breaks the link between simulation rate and time resolution that is characteristic of prior approaches. The emulator is flexible, allowing for the real-time adjustment of analog dynamics, clock jitter, and various design parameters. We demonstrate that our architecture achieves 1% accuracy while running 3 orders of magnitude faster than a comparable high-performance CPU simulation.