RESIDUAL · ADAPTIVE · MULTI-RATE · ANALOG CIRCUIT EMULATION

Residual-Driven
Adaptive
Multi-Rate
Analog Circuit Emulation

A research project on nonlinear analog circuit emulation for virtual analog audio — bridging DAE-based modeling, constraint stabilization, and residual-driven adaptive time stepping.

Read the Papers Browse Code Browse Supplementary Material Try the VST Demos

About the Project

A residual-driven adaptive solver for nonlinear analog audio circuit emulation.

RAMA explores a residual-driven adaptive multi-rate formulation for nonlinear analog circuit emulation. Starting from a DAE representation of the circuit, the method replaces nonlinear device constraints with a stabilized linear surrogate inside an equality-constrained optimization step, then uses the post-step nonlinear residual to drive adaptive internal time stepping. The result allocates computational effort proportional to local nonlinear activity — spending more steps through fast transients and recovering sample-synchronous throughput during quiescent segments.

Resources

Papers, Code & Supplementary Materials

Publications

Two peer-reviewed papers — the initial formulation presented at DAFx25, and the extended adaptive method with more complex benchmark circuits at DAFx26.

Open-Source Code

MATLAB reference implementation to reproduce the paper's results. Includes the equality-constrained solver, residual-based step controller, and reference nonlinear device models.

Browse on GitHub →

Supplementary Material

Companion documents: full circuit matrix derivations, expanded details of the proof sketch from the DAFx26 paper, etc.

Browse Material →

Listen & Experiment

VST Demos

Real-time RAMA implementations of the diode clipper and common-emitter amplifier. Listen to short loudness-matched examples below or download the VST demo packages to explore their circuit parameters directly.

Nonlinear Distortion

Diode Clipper

RAMA Diode Clipper VST plugin interface

Soft-clipping circuit using a pair of anti-parallel diodes. Emulates the characteristic asymmetric clipping and harmonic saturation of diode-based guitar pedals.

Listen

Musical example Saturation
0:00 0:22
Monophonic example Saturation
0:00 0:22
Download — .dll + PDF

Transistor Amplifier

Common-Emitter Amplifier

RAMA Common-Emitter Amplifier VST plugin interface

BJT common-emitter stage with configurable bias point. Covers the full operating range from clean boost to saturated transistor overdrive.

Listen

Musical example Distortion
0:00 0:22
Monophonic example Distortion
0:00 0:22
Download — .dll + PDF

Citation

Cite This Work

If you use RAMA in your research or build on this method, please cite the DAFx-26 paper.

Residual-Driven Adaptive Multi-Rate Quadratic Programming Framework for Nonlinear Analog Audio Circuit Emulation.
DAFx-26 Proceedings, 2026. 
@inproceedings{RAMA2026,
  author    = {Zea, M. and Rivera, L.A.},
  title     = {{Residual-Driven Adaptive Multi-Rate Quadratic 
               Programming Framework for Nonlinear Analog Audio 
               Circuit Emulation}},
  booktitle = {Proceedings of the 26th International Conference 
               on Digital Audio Effects (DAFx-26)},
  year      = {2026},
  
}
@inproceedings{RAMA2026,
  author    = {Zea, M. and Rivera, L.A.},
  title     = {{Residual-Driven Adaptive Multi-Rate Quadratic Programming Framework for Nonlinear Analog Audio Circuit Emulation}},
  booktitle = {Proceedings of the 26th International Conference on Digital Audio Effects (DAFx-26)},
  year      = {2026},
  
}