Digital Signal Processing Implementation of a 1961 Fender Champ Amplifier www.AssignmentPoint.com

Outline Background Progress/Project Changes Objectives Restatement Functional Description Block Diagram Previous EE452 Schedule Lab Work Current Objectives

Solid-State Amplifiers Background Solid-State Amplifiers As solid-state technology has become more advanced in recent years, devices, such as transistors and ICs, are increasingly available to be used to design inexpensive guitar amplifiers. However, these analog solid-state designs require much feedback to improve their linear transfer characteristic.

Solid-State Amplifiers Background Solid-State Amplifiers This heavy feedback results in a sharp clipping characteristic that produces successive harmonics with high amplitudes when the configuration is driven at a high volume. Reference: Barbour, Eric. "The Cool Sound of Tubes.” Ed., Michael J. Riezenman. IEEE Spectrum August 1998.

Background Tube Amplifiers There are several theories to explain the tube guitar amplifier’s superior sound as compared to the solid-state amplifier’s sound. Overall, the tube amplifier configurations result in a frequency response with a dominant 1st harmonic component, followed by a 2nd harmonic component that is around half the magnitude of the 1st harmonic, and higher harmonics with decreasing amplitudes.

Background Tube Amplifiers Lower harmonics have the most presence and thus produce a louder sound than solid- state amplifiers at high volumes. Reference: Barbour, Eric. "The Cool Sound of Tubes.” Ed., Michael J. Riezenman. IEEE Spectrum August 1998.

Background Tube disadvantages: short life time fragility Tube Amplifiers Tube disadvantages: short life time fragility storage inconvenience (bulky size) high power and heat dissipation high voltage operation high impedances requiring matching transformers high cost (Fender Champ cost = $1,000)

Progress/Project Changes Objectives The goal of the project is to reproduce the output characteristics of a 1961 Fender Champ from a guitar input with a DSP nonlinear modeling algorithm The Champ has been chosen due to its popularity among vintage vacuum tube amplifiers and its simple design

Progress/Project Changes Objectives

Progress/Project Changes Objectives The DSP available for this project is the Texas Instruments TMS320C6711 For MATLAB 6.5, there is an Embedded Target for the TMS320C6711 where a Simulink design can be translated to ANSI C standard code This addition will allow more time to be spent improving the DSP algorithm for the amplifier model rather than spending hours learning the subtlties of the DSP board

Progress/Project Changes Objectives Several sets of data from sinusoidal and guitar inputs to the amplifier will be used to model the 1961 Fender Champ’s distortion characteristics This approach was used in the patents for similar projects (PAT. NO. 5,789,689 - Tube modeling programmable digital guitar amplification system) (PAT. NO. 6,350,943 - Electric instrument amplifier) Reference: http://www.uspto.gov/

Progress/Project Changes Objectives Since there are several differing views on the source of tube amplifiers’ unique distortion, this data collection approach is the most optimal and unified approach to the problem

Progress/Project Changes Functional Description Analog Audio Signal from Guitar DSP with C/C++ or Assembly Digital Filters Audio Output with Tube Amplifier Sound Interfacing Circuitry to Guitar Cable Inputs/Outputs Inputs - analog audio signal from either a guitar A/D interface or a saved audio file and software or hardware based volume selection will regulate the filters’ behavior Output - audio signal with tube amplifier effect

Progress/Project Changes Functional Description Analog Audio Signal from Guitar DSP with C/C++ or Assembly Digital Filters Audio Output with Tube Amplifier Sound Interfacing Circuitry to Guitar Cable Modes of Operation 12 volume settings similar to those provided with the 12-volume switch on the 1961 Fender Champ - (Only three will be implemented where ‘3’ is the first audible volume, ‘6’ is the middle selection, and ‘12’ is overdriven level for amplifier) linear effects will be omitted due to lack of time

Block Diagram ... ... Parallel Bandpass FIR Filter Approach BP BP BP Analog Audio Signal Input from Guitar or File Mode of Operation (Software) BP BP BP BP BP BP ... Nonlinear Transfer Characteristics BP BP BP BP BP BP ... Summer Parallel Bandpass FIR Filter Approach Final BP Equivalent Tube Amplifier Signal Output

Progress/Project Changes Block Diagram ... Analog Audio Signal Input from Guitar or File External Volume Selection 2 LP 2 LP ... 2 Mode of Operation (Software) HP ... LP 2 HP 2 ... ... ... ... HP ... 2 Nonlinear Transfer Characteristics 2 LP 2 LP 2 HP Equivalent Tube Amplifier Signal Output 2 LP 2 HP 2 HP Multirate Signal Processing Approach Reference: Digital Signal Processing: Principles, Algorithms, and Applications. John G. Proakis, Dimitris G. Manolakis. Third Edition. 1996. pp. 832-834.

Progress/Project Changes Block Diagram Current Selection Parallel Bandpass FIR Filter Approach (1st approach) is the best approach due to the nonlinear transfer characteristic addition that is applied in the time domain and the large delay inherent to the Multirate Signal Processing Approach

Progress/Project Changes Previous EE452 Schedule Approach Weeks 1-4: Complete and simulate model of Fender Champ in MATLAB from obtained 12AX7 and 6V6GT tube data sheets Weeks 5-8: Complete software to program the actual DSP board and interface the appropriate hardware to the ADC and DAC Weeks 13-14: Senior 2003 Expo Preparation Weeks 15-16: Senior Project Presentation There is a 4-week window that is intended to allow for setbacks

Progress/Project Changes Lab Work Approach Changes Complete and simulate model of 1961 Fender Champ obtained from nonlinear transfer characteristics of 16-bit audio output of 1961 Fender Champ Based on similarities and differences of nonlinear transfer characteristics, take more 16-bit audio output of 1961 Fender Champ from sinusoidal inputs Determine frequency ranges of approximate nonlinear transfer characteristics from data and guitar frequency chart Record output from 1952 Fender Telecaster directly for 1961 Fender Champ response simulation verification Verify highest frequency input from the guitar

Progress/Project Changes Lab Work Reference: http://home.pacbell.net/vaughn44/m3.music.notes.6.pdf

Progress/Project Changes Lab Work Nonlinear Transfer Characteristic Determination from 16-bit Audio Output of 1961 Fender Champ Volume ‘12’ 523.25 (Hz)

Progress/Project Changes Lab Work Nonlinear Transfer Characteristic Determination from 16-bit Audio Output of 1961 Fender Champ

Progress/Project Changes Lab Work Nonlinear Transfer Characteristic Determination from 16-bit Audio Output of 1961 Fender Champ Eight more sinusoidal inputs were used to record 16-bit audio output of 1961 Fender Champ Frequency, time domain, and transfer characteristics of this data were plotted and analyzed ‘polyfit’ in MATLAB used to provide curve fits for eight selected transfer characteristics

Progress/Project Changes Lab Work Highest Frequency from Guitar

Progress/Project Changes Lab Work Input to 1961 Fender Champ at Volume ‘6’ (Output of Guitar)

Progress/Project Changes Lab Work Fender Champ Response at Volume ‘6’ to 1952 Fender Telecaster

Progress/Project Changes Lab Work Nonlinear transfer characteristic curve fits were performed for eight frequency ranges where the curve was selected for one frequency to be approximate to characteristic curves of surrounding frequencies The frequency ranges were the following: 0 - 250 (Hz) 250 - 450 (Hz) 450 - 700 (Hz) 700 - 900 (Hz) 900 - 1500 (Hz) 1500 - 2000 (Hz) 2000 - 3000 (Hz) 3000 - 4500 (Hz)

Progress/Project Changes Lab Work FIR coefficients were generated for these filters with FDATool in MATLAB due to the time spent fitting the nonlinear transfer characteristic curves The nonlinear transfer characteristics for Volume ‘6’ were performed on guitar output

Progress/Project Changes Lab Work Previous Output of DSP Model of 1961 Fender Champ at Volume ‘6’

Progress/Project Changes Lab Work Output of DSP Model of 1961 Fender Champ at Volume ‘6’ Clipping seen from gain of 7 FIR filters being applied to nonlinear transfer characteristics defined for a -1 to 1 input range.

Progress/Project Changes Lab Work Current Output of DSP Model of 1961 Fender Champ at Volume ‘6’ Filter Bank 5 divided into 900-1200 (Hz) and 1200-1500 (Hz)

Progress/Project Changes Lab Work Comparison of DSP Model of 1961 Fender Champ at Volume ‘6’ to Actual Amplifier Output

Current Objectives Discover source of high frequency with DSP model of 1961 Fender Champ in MATLAB code Implement the MATLAB code simulation in Simulink If there is no time to get the code ready for the Texas Instruments TMS320C6711 DSP board or the Embedded Target cannot be obtained, the processed output from MATLAB will be sent through the board’s D/A converter for demonstration Otherwise, the code will be generated for the DSP from the tools available from Simulink