Towards Efficient Emulation of Nonlinear Analog Circuits for Audio Using Constraint Stabilization and Convex Quadratic Programming
This paper introduces a computationally efficient method for
the emulation of nonlinear analog audio circuits by combining state-space representations, constraint stabilization, and convex quadratic programming (QP). Unlike traditional virtual analog (VA) modeling approaches or computationally demanding
SPICE-based simulations, our approach reformulates the nonlinear
differential-algebraic (DAE) systems that arise from analog circuit
analysis into numerically stable optimization problems. The proposed method efficiently addresses the numerical challenges posed
by nonlinear algebraic constraints via constraint stabilization techniques, significantly enhancing robustness and stability, suitable
for real-time simulations. A canonical diode clipper circuit is presented as a test case, demonstrating that our method achieves accurate and faster emulations compared to conventional state-space
methods. Furthermore, our method performs very well even at
substantially lower sampling rates. Preliminary numerical experiments confirm that the proposed approach offers improved numerical stability and real-time feasibility, positioning it as a practical
solution for high-fidelity audio applications.