Guitar Tube Simulation

Proc. of the 13th Int. Conference on Digital Audio Effects (DAFx-10), Graz, Austria , September 6-10, 2010

REAL-TIME GUITAR TUBE AMPLIFIER SIMULATION USING AN APPROXIMATION OF
DIFFERENTIAL EQUATIONS
Jaromir Macak

Jiri Schimmel

Dept. of Telecommunications,
FEEC, Brno University of Technology
Brno, Czech Republic
jaromir.macak@phd.feec.vutbr.cz

Dept. of Telecommunications,
FEEC,Brno University of Technology
Brno, Czech Republic
schimmel@feec.vutbr.cz

ABSTRACT
Digital simulation of guitar tube amplifiers is still an opened topic.
The efficient implementation of several parts of the guitar amplifier is presented in this paper. This implementation is based on
the pre-computation of the solution of the nonlinear differential
system and further approximation of thesolution. It reduces the
computational complexity while the accuracy is comparable with
the numerical solution. The method is used for simulation of different parts of the guitar amplifier, namely a triode preamp stage,
a phase splitter and a push-pull amplifier. Finally, the results and
comparison with other methods are discussed.

the ODEs depends on an input signal voltage and on a circuit state(capacitor voltages). Therefore, the described system is considered
to have more inputs. To reduce the computational complexity, the
solution of the ODEs is pre-computed and approximated for the
combination of different inputs (the input signal and the capacitor voltages). The approximated values can be used for one iteration of the Newton-Rapson method as an estimation or directly as
outputsignal values if the step of input voltages is small enough.
Furthermore, the stability of the solution is guaranteed if the input
voltages are within the approximated range.
2. BLOCK DIAGRAM OF THE GUITAR TUBE
AMPLIFIER

1. INTRODUCTION
Recently, there has been extensive research in the field of digital
simulation of analog guitar effects and amplifiers and several algorithms for real-timesimulation has been proposed [1]. Fundamentally, all circuit simulation-based algorithms use a block decomposition, which allows description of each block more precisely. The
static waveshaping and linear filtration algorithm presented in [2]
provides good results for stationary signals but fails on transients
because of the dynamic bias changes that appear in analog circuits.
The majoradvantage of this algorithm is its speed if a nonlinearity
is implemented as the look-up table or approximated via linear or
spline interpolation.
Nonlinear wave digital filters (WDF) offer efficient and dynamic simulation of circuits with one nonlinear function (more
nonlinearities typically decrements efficiency). The diode limiter
unit is simulated in [3] and the simulation of common-cathode triodeamplifier with no grid current is presented in [4]. The WDF
are very efficient if the circuit is linear or if there are one [4] or two
[5] nonlinear functions. However, the guitar amplifier circuits can
contain more nonlinear functions.
Numerical methods for simulation of the nonlinear diode limiter unit are described in [6]. They are based on a numerical solution of the nonlinear differentialequations (ODE) and it is possible to use this method for simulation of more complicated circuits with more nonlinear functions. A similar approach is used in
professional circuit schematic simulators (e.g., SPICE) where the
nonlinear circuit equations are in matrix form and LU decomposition is used for solving the system. The major disadvantage is its
computational complexity.
A common-cathodetriode amplifier with a nonlinear grid and
plate currents, a triode phase splitter and a pentode push-pull amplifier are described using nonlinear ODEs in this paper. Subsequently, the Euler method is applied for the ODEs. The solution of

A typical guitar tube amplifier is shown in Figure 1. The preamp
consists of several common-cathode triode amplifiers with different values of circuit...