An Offset-Cancelling Discrete-Time Analog Computer for Solving 1-D Wave Equations

This article describes a single-chip analog computer for solving 1-D wave equations. The chip uses switched-capacitor (SC)-based fully differential analog circuits to build a discrete-time but continuous-valued finite difference solver with spatially programmable wave velocity, selectable boundary conditions, and arbitrary input excitation waveforms. Correlated double sampling (CDS) and auto-zero techniques are utilized to minimize the offset and low-frequency noise of the op-amps. Built-in third-order \Delta - \Sigma modulators allow the analog solution to be easily read out by a digital processor. The design was realized in TSMC 180-nm CMOS and has an active area of 3.596 mm \times3.131 mm. The solver consumes 560 mW while providing a dynamic range (DR) of 41 dB and a computational bandwidth of either 2.5 MHz (if limited by the analog core) or 0.25 MHz (if limited by the on-chip modulators). Normalized mean squared solution errors for a typical problem (uniform medium with radiation boundary condition) range from 0.3% to 2% (−25 to −17 dB). Measured simulation times are 21\times , 5\times , and 1.3\times faster than CUDA-C code running on a modern GPU (NVIDIA GTX 1080 Ti) and MATLAB or C code running on an 8-core CPU (Intel Xeon Silver 4110 at 2.10 GHz), respectively.