Enhanced Wave Digital Triode Model for Real-Time Tube Amplifier Emulation

Electric circuits containing vacuum tubes form an integral part of various audio equipment, such as guitar amplifiers, certain equalizers, microphone preamplifiers, and dynamic range compressors. Although most audio signal processing operations are straightforward to implement with modern computers, real-time digital simulation of vacuum tubes poses a significant challenge due to the dynamic nonlinearities of the tube circuits. Most of the current vacuum-tube emulators model the unidirectional signal path of the circuit using linear filters and nonlinear waveshapers, possibly with signal-dependent parameters. This paper introduces a physical model of a tube stage circuit using wave digital filters. In contrast to previous unidirectional signal models, the wave digital model implements bidirectional signal propagation. This allows realistic simulation of interesting dynamical nonlinearities, such as the bias variation under reactive load. The new model is an extension of the wave digital tube presented in ??Wave digital simulation of a vacuum-tube amplifier?? (M. Karjalainen and J. Pakarinen Proc. Int. Conf. Acoustics, Speech, Signal Processing, 2006, vol. V, pp. 153-156). In particular, the enhanced model for the tube grid-to-cathode connection enables the simulation of interstage coupling and blocking distortion.