Introduced by Prof. Alfred Fettweis in 1971, Wave Digital Filters (WDF) mimics classical filter structures by utilizing wave variable representation. Digital modeling using WDF is able to deal with series and parallel circuits containing a single-port nonlinearity.
In 2015, Dr. Kurt Werner et al. in CCRMA introduced a novel WDF adaptor - R(Rigid)-Adaptor, which enables us to model circuits with arbitrary topologies and multiple/multiport nonlinearities, such as tube amplifier circuits.
For this project, a new C++ WDF library is implemented under the adjustable discretization of α-transform to avoid oscillations in systems with highly-damped poles.
For multi-stage tube amplifiers, simulating the behavior of all tubes together is too slow, which means we must find a way to divide the circuit and lower the computational load to achieve real-time simulation. Because of the interstage loading effect, we cannot simply divide the circuit stage by stage.
According to Dr. Jaromir Macak's study in 2010, the loading effects between multiple cascaded tube amplifiers are mainly affected by the adjacent amplifier. Therefore, he introduced the Modified Block-Wise Method to resolve interstage loading effects.
Combining R-Adaptor with Modified Block-Wise Method, here we present the system diagram of our WDF multi-stage vacuum tube amplifier model.