1. Digital Modeling/Implementation of Valve Amplifiers
Authors: Cody Frye & Mitchell Gould
Advisor: Dr. Yufeng Lu
Department of Electrical and Computer Engineering
May 4th 2019

2. Agenda Introduction Motivation System Description Methods
Triode Valve Numerical Analysis
WDF Results
Conclusion

3. Introduction Significance of valve amplifiers Pros of valve amplifiers
Smooth clipping
Warm tone characteristics
Cons of valve amplifiers
Weight
Heat
Cost

4. Introduction

5. Motivation Affordable and Convenient
Variety of Amplifiers to choose from
Digital components reduce overall size

6. System Description

8. Pre-Amplification Stage

9. Methods Frequency Bin / Lookup Table Method
Model Individual Blocks of System
Wave Digital Filtering

10. Method 1 (Frequency Bin Method)
...

11. Method 1 (Frequency Bin Method)
Separate input signal into Multiple frequency bins
bandPass Filters
NonLinear transfer function represented by L.U.T.s
Sum all the bins together

12. WDF Method (Method 2) Wave quantities A = incident wave
B = reflected wave
A = V + RI [eq. 1]
B = V - RI [eq. 2]
V = (A+B) / 2 [eq. 3]
I = (A-B)/2R [eq. 4]

13. WDF Method (Method 2)
WDF components
WDF port adapters

14. Triode Valve Numerical Analysis
Nonlinear Triode Currents as a Function of Vgk and Vpk
Triode Amplifier
Model of Triode

15. Triode Valve Numerical Analysis
Norman Koren’s Equations
Leach’s Equations

16. Leach’s model Vgk = 2 Vgk = 1 Vgk = 0 Vgk = -1 Vgk = -2 Vgk = -3
Vpk = 350
Vgk = 2
Vpk = 300
Vpk = 250
Vgk = 1
Vpk = 200
Vpk = 150
Vgk = 0
Vgk = -1
Vpk = 100
Vpk = 50
Vpk = 0
Vgk = -2
Vgk = -3

17. Koren’s model Vgk = 1 Vgk = 0 Vgk = -1 Vgk = -2 Vgk = -3 Vpk = 300

18. Triode Valve Numerical Analysis

19. WDF 1st Order LPF
RC LPF Circuit
WDF Equivalent

20. WDF 1st Order Filter PSpice simulation results for 1st Order LPF
WDF simulation results for 1st Order LPF

21. WDF Single Triode Stage Amplifier
Single Stage Circuit
Single Stage WDF equivalent

22. WDF Single Triode Stage Amplifier
Single Stage Circuit
Single Stage WDF equivalent

23. WDF Single Triode Stage Amplifier
Single Stage Circuit
Single Stage WDF equivalent

24. WDF Single Triode Stage Amplifier
Single Stage Circuit
Single Stage WDF equivalent

25. WDF Single Triode Stage Amplifier
Single Stage Circuit
Single Stage WDF equivalent

26. WDF Single Triode Stage Amplifier
PSpice Triode Stage
WDF Triode Stage

27. WDF Single Triode Stage Amplifier
WDF G Chord results

28. Conclusion
In this project, a digital emulation of an analog valve amplifier has been designed. The non-linear characteristics of valve amplifier has been modeled. The overall response of the valve amplifier has been successfully emulated using Wave Digital Filtering technique.

29. Future Work
Model distortion characteristics of real amplifier using cascaded amplification stages and self-tuning algorithm
Implement WDF system including R-Adapter on an ARM-based embedded system

30. Questions?
Thank you!

31. [1] M. Karjalainen and J. Pakarinen, "Wave Digital Simulation of a Vacuum-Tube Amplifier," 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, Toulouse, 2006, pp. V-V. doi: /ICASSP
[2] S. D Angelo, J. Pakarinen, and V. Välimäki. New Family of Wave-Digital Triode Models. IEEE Trans. Audio, Speech, and Lang. Process., vol. 21, no. 2, pp , February 2013.
[3] Bohumil Psenicka, Francisco Garciá Ugalde, and Andrés Romero, “Design of Wave Digital Filters,” Universidad Nacional Autónoma de México, December 2009
[4] M. Antosová and V. Davídek, “Design and Implementation of Wave Digital Filters,” Department of Circuit Theory, Czech Technical University, Prague, Czech Republic September 2001
[5] Ivan Cohen, Thomas Hélie. Measures and Models of Real Triodes, for the Simulation of Guitar Amplifiers. Société Française d’Acoustique. Acoustics 2012, Apr 2012, Nantes, France
[6] Jyri Pakarinen, David T. Yeh, “A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers,” Helsinki University of Technology, Helsinki, Finland, Report, August 2009.
[7] James Siegle, “DSP Implementation of a 1961 Fender Champ Amplifier,” B.S. Thesis, Dept. Elect. Eng., Bradley University, Peoria, Illinois, U.S., 2003
[8] Marshall Leach, “SPICE Models for Vacuum-Tube Amplifiers,” Georgia Institute of Technology, Atlanta, Georgia, U.S., Report, March 1995