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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.

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This work extends our previously proposed Quadratic Programming (QP) approach for the emulation of nonlinear analog audio circuits by formalizing its main numerical ingredients and introducing a residual-driven adaptive multi-rate scheme. Starting from a state-space Differential Algebraic System of Equations (DAE) formulation, the nonlinear algebraic circuit device relations are replaced inside the QP by a first-order surrogate linear constraint, and the post-step nonlinear residual is shown to act as a valid defect indicator for adaptive step-size control. This yields a single-step simulation procedure that avoids the usual combination of nonlinear iterative solves and separate integration updates. The method is evaluated on a diode clipper, a BJT common-emitter amplifier, and a Colpitts oscillator, using SPICE as a baseline reference. The results show that adaptive step sizing considerably improves agreement with the reference solution, that the pseudo-inverse implementation is essentially equivalent to the full equality-constrained QP in the tested cases, and that the proposed formulation remains effective beyond the baseline clipper example, including for a self-oscillating circuit. These results position the proposed method as a promising bridge between SPICE-like interpretability and the efficiency demands of virtual analog (VA) audio applications.

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