Digital ModelingImplementation of Valve Amplifiers Authors Cody Frye

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Digital Modeling/Implementation of Valve Amplifiers Authors: Cody Frye & Mitchell Gould Advisor: Dr. Yufeng

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

Agenda 1. 2. 3. 4. 5. 6. 7. Introduction Motivation System Description Methods Triode

Agenda 1. 2. 3. 4. 5. 6. 7. Introduction Motivation System Description Methods Triode Valve Numerical Analysis WDF Results Conclusion 2

Introduction ● Significance of valve amplifiers ● Pros of valve amplifiers ○ Smooth clipping

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

Introduction 4

Introduction 4

Motivation ● Affordable and Convenient ● Variety of Amplifiers to choose from ● Digital

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

System Description 6

System Description 6

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Pre-Amplification Stage 8

Pre-Amplification Stage 8

Methods ● Frequency Bin / Lookup Table Method ● Model Individual Blocks of System

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

Method 1 (Frequency Bin Method) . . . 10

Method 1 (Frequency Bin Method) . . . 10

Method 1 (Frequency Bin Method) ● Separate input signal into Multiple frequency bins ○

Method 1 (Frequency Bin Method) ● Separate input signal into Multiple frequency bins ○ band. Pass Filters ● Non. Linear transfer function represented by L. U. T. s ● Sum all the bins together 11

WDF Method (Method 2) ● Wave quantities ● A = incident wave ● B

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 I = (A-B)/2 R [eq. 4] [eq. 3] 12

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

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

Triode Valve Numerical Analysis Nonlinear Triode Currents as a Function of Vgk and Vpk

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

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

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

Leach’s model V gk = 350 k= Vp 00 =3 250 Vpk k= p

Leach’s model V gk = 350 k= Vp 00 =3 250 Vpk k= p V 200 k= Vp 150 k= Vp 00 =1 Vpk = 50 Vpk =0 Vpk 2 k Vg = 1 k Vg =0 = gk V k Vg -1 2 =- k= Vg -3 16

Koren’s model 0 30 0 k = = 25 0 p V pk 20

Koren’s model 0 30 0 k = = 25 0 p V pk 20 0 V k = = 15 00 p V pk 1 V pk = 50 V k= 0 Vp k= Vp = gk 1 V =0 k Vg = gk -1 V k= Vg Vgk -2 = -3 17

Triode Valve Numerical Analysis 18

Triode Valve Numerical Analysis 18

WDF 1 st Order LPF RC LPF Circuit WDF Equivalent 19

WDF 1 st Order LPF RC LPF Circuit WDF Equivalent 19

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

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

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

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

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

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

WDF Single Triode Stage Amplifier WDF G Chord results 27

WDF Single Triode Stage Amplifier WDF G Chord results 27

Conclusion ● In this project, a digital emulation of an analog valve amplifier has

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. 28

Future Work ● Model distortion characteristics of real amplifier using cascaded amplification stages and

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 29

Questions? Thank you! 30

Questions? Thank you! 30

[1] M. Karjalainen and J. Pakarinen, "Wave Digital Simulation of a Vacuum-Tube Amplifier, "

[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: 10. 1109/ICASSP. 2006. 1661235 [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. 313 321, 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. 2012. [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 31