Iconic: A Real-Time Tube Guitar Amplifier Modeler

OVERVIEW

What it does

The Iconic modeler is a set of DSP algorithms that simulate the sound of a vacuum-tube guitar amplifier by a processing a mathematical model which characterizes the amplifier’s electronic circuit.

The entire Iconic modeler was developed in-house.

How it works

An amplifier’s circuit is divided into smaller circuits called stages. A set of simultaneous equations is used to represent the circuit of an amplifier stage. All the sets of circuit equations representing each stage constitute the mathematical model of the amplifier. Iconic employs an efficient quasi-Newton algorithm which solves all sets of simultaneous equations that represent a non-linear dynamical system; in this case, a vacuum-tube guitar amplifier. Here, the dynamical parts of the amplifier are the energy-storage components such as capacitors and inductors, while its non-linear parts are the vacuum tubes and the magnetization saturation of the transformer core

The circuit equations are derived beforehand using Modified Nodal Analysis and organized into a vector. This vector, along with its Jacobian matrix and the circuit’s nodal voltages (also a vector) are passed to the Newton solver which, calculates a new set of nodal voltages. This occurs at every sample of the input signal from the guitar. One of the nodal voltages represents the amplifier’s input. Another one of the nodal voltages represents the amplifier’s output. The input and output voltage signals are connected to the host’s respective sound device ports

Innovations

While algorithms based on Newton’s method are nothing new (it’s a 300-year old method), Iconic does incorporate the following in-house technologies which increase processing efficiency and which make real-time operation possible:

 A new algorithm for directly evaluating multivariate non-linear functions.
 A new look-up table algorithm for evaluating multivariate non-linear functions.
An approximation of the long-tail pair phase inverter circuit which results in the reduction of its associated circuit matrix.

Prototypes

Using the Iconic modeler, amplifier models based on the following circuits were created and tested:
Marshall® 2204, a.k.a the “Master Volume”, a.k.a. the JCM 800
Fender® AB763, a.k.a. the Blackface circuit
Soldano® SLO100 with modified interstage coupling capacitances

For each amplifier, the following were modeled:
Triode preamp stages
Phase inverter
Tone stack
Power Amp (two pentodes)
Preamp tube Miller capacitances
Preamp interstage capacitor coupling
Power amp sag
Negative feedback loop between power amp and phase inverter stages (enables the use of Presence control)
Power amp output transformer based on the linear Gyrator-Capacitor model (a non-linear model is available, but it is not used in the prototypes)

The Marshall-based and Soldano-based Iconic models use an approximated phase-inverter circuit which, behaves similarly to a long-tail phase inverter (single-ended input, differential output) but results in a faster run time. The Fender-based Iconic model uses the full long-tail phase inverter circuit.

The prototypes of the three above-mentioned amplifier models consist of single-threaded, 32-bit VST plugins. They were created using the Audio Plugin Generator (APG) application from dlab®.

The above image shows the Iconic Marshall-based amplifier model VST plugin embedded in its standalone host. The plugin .DLL files can be used in any VST host or DAW.

Real-Time Performance

The performance and quality of the amplifier models were evaluated by examining the direct output from each amplifier stage and by convolving the power amp output signal with 3rd-party guitar speaker cabinet IR’s. The evaluations included signal analysis and playing guitar through the Iconic amplifier models.

The Iconic amp models were run on a laptop with a 4th-generation Intel® i7 processor (4 physical cores, 2 threads/core, 2.4 GHz).

As a Matlab® function in Simulink®, each entire Iconic amplifier model runs in real time at 2x the input sampling frequency of 44.1 kHz with a buffer latency of 0.7 ms (32 samples).

As a single-threaded, 32-bit VST plugin, each entire Iconic amplifier model runs in real time at 1x the input sampling frequency of 44.1 kHz with a buffer latency of 0.7 ms (32 samples).

If implemented for multi-core processing, therefore, the Iconic algorithm has the potential to run in real time at higher multiples of the sampling frequency. Running at higher multiples of the sampling frequency reduces aliasing caused by high-gain distortion, thus resulting in higher sound quality. Also, a multi-core implementation of Iconic can enable the use of the non-linear output transformer model and the full phase inverter circuit in the amplifier models currently using its approximation circuit.

LISTEN TO THE RESULTS

MUSIC PRODUCED WITH ICONIC

The above-mentioned Iconic amplifier models were used in all rhythm and lead guitar tracks on three songs from the Agan Rock EP. (See the EP’s Track Credits for song details and listen to each one on the web page). Iconic amplifier models were also used in the rhythm guitar tracks on one song from the Electric Fez: Project A’ EP. (See also the EP’s Track Credits.) In these songs, the guitar parts were processed in real time at 2x the input sampling frequency.

No distortion or overdrive effects of any kind were used in creating the sound of the guitar tracks processed with Iconic. The distortion and overdrive sounds in these tracks were derived solely from the Iconic amplifier models. All tracks were processed in real time.

Applications

The technologies developed for Iconic are not limited to just guitar amplifier modeling. They can be easily adapted to model any linear or non-linear dynamical system – some of them also in real time. Some applications include the following:

 In-Car Entertainment (In-Vehicle Infotainment): hi-fi amplifier simulation, sound enhancement and effects
 Mechanical systems: vehicles, guidance and control systems, machines, engines
 Structures: bridges, towers, skyscrapers, castles made of sand
 Medicine: neuron clusters, vascular fluid flow, biological processes
 Econometrics: currency, stock and commodities markets, trading patterns, trends

The call

We are currently seeking interested parties for collaboration and funding in order to develop, market and sell software and hardware products that will implement the Iconic modeler. Those interested can refer to the Contact page.