A data-efficient PINN-Bayesian optimization framework for state variable active filter design

Designing an analog active filter is rarely a single-target exercise: cutoff frequency, quality factor, gain, power draw, total harmonic distortion (THD), and sensitivity to component spread all have to be pulled into line at once. In practice, this still means loop after loop of SPICE runs and manual tweaking, which eats up design time and computing budget alike. This paper instead builds a Bayesian Optimization loop around a Physics-Informed Neural Network (PINN) surrogate to automate the synthesis of State Variable Filters (SVFs). Adaptive sampling of the design space, LTspice-based circuit simulation, PINN surrogate modeling, and Bayesian Optimization are brought together so that optimal component values can be located with far fewer costly simulation runs. By incorporating the governing circuit relationships, analytical transfer function, frequency–response characteristics, and stability constraints into PINN training, the proposed surrogate captures the nonlinear relationship between component values and filter performance while maintaining physical consistency. That trained surrogate then drives the Bayesian search, quickly narrowing in on Pareto-optimal filter configurations across cutoff frequency accuracy, passband gain, quality factor, power consumption, THD, and sensitivity. The resulting design reached a cutoff frequency of 10.01 kHz, a gain of 0.998, a quality factor of 0.709, an estimated active-filter power of 12.4 mW, THD of 0.32%, and a sensitivity index of 0.048, with Bayesian Optimization converging in 37 iterations and an average run time of 42.8 s. Benchmarked against Random Search, Particle Swarm Optimization, Genetic Algorithm, and Differential Evolution, the proposed framework consistently reached lower objective values than any of them. A TL084-based hardware prototype backed up the simulation results as well: measured cutoff frequency, gain, and phase response tracked the LTspice predictions closely, and the absolute THD deviation came in at just 0.04%. Taken together, these results point to a PINN-assisted Bayesian Optimization framework that is efficient, scalable, and well suited to next-generation computer-aided design of analog and mixed-signal circuits.