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Despite the prevalence of modern audio technology, vacuum tube amplifiers continue to play a vital role in the music industry. For this reason, over the years, many different digital techniques have been introduced for accomplishing their emulation. In this paper, we propose a novel quadric surface model for tube simulations able to overcome the Cardarilli model in terms of efficiency whilst retaining comparable accuracy when grid current is negligible. After showing the model capability to well outline tubes starting from measurement data, we perform an efficiency comparison by implementing the considered tube models as nonlinear 3-port elements in the Wave Digital domain. We do this by taking into account the typical common-cathode gain stage employed in vacuum tube guitar amplifiers. The proposed model turns out to be characterized by a speedup of 4.6× with respect to the Cardarilli model, proving thus to be promising for real-time Virtual Analog applications.

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A clipping prevention method is proposed for first- and second-order all-pass filters with time-varying coefficients. Unlike conventional anti-clipping or declipping approaches, the method operates directly on the coefficient dynamics and does not rely on assumptions about internal energy evolution, by just asking that the input signal is not already clipping. The core idea is to control the deviation between the output of the time-varying filter and that of an equivalent static all-pass structure with constant coefficients. By adaptively limiting this deviation at runtime, the output is constrained below a prescribed clipping threshold (typically unit magnitude). The method is active only during short transients where clipping would occur, after which the coefficients are released to reach their target values. This preserves the integrity of the input signal and the numerical properties of the all-pass filter. Experimental results confirm the expected behavior even in scenarios where energy-preserving all-pass structures exceed the clipping threshold, suggesting the proposed approach as a practical solution for robust dynamic filter implementations with limited additional computational cost, suitable especially for embedded digital audio processing hardware.

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