DSP Implementation of a 1961 Fender Champ Amplifier

1
DSP Implementation of a1961 Fender Champ
Amplifier

• James Siegle
• Advisor Dr. Thomas L. Stewart
• April 8, 2003

2
Outline

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

3
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.

4
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.
5
Background
Tube Amplifiers

• There are several theories to explain the tube
  guitar amplifiers superior sound as compared to
  the solid-state amplifiers 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.

6
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.
7
Background
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)

8
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

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Progress/Project Changes
Objectives
10
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

11
Progress/Project Changes
Objectives

• Several sets of data from sinusoidal and guitar
  inputs to the amplifier will be used to model the
  1961 Fender Champs 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/
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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

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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

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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

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Progress/Project Changes
Block Diagram
Analog Audio Signal Input from Guitar or File
External Volume Selection
Mode of Operation (Software)
BP
BP
BP
BP
BP
BP
...
Nonlinear Transfer Characteristics
Summer
Equivalent Tube Amplifier Signal Output
Parallel Bandpass FIR Filter Approach
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Progress/Project Changes
Block Diagram
Analog Audio Signal Input from Guitar or File
External Volume Selection
Mode of Operation (Software)
FFT
FFT Parallel Filter Network Approach
BP
BP
BP
BP
BP
BP
...
Nonlinear Transfer Characteristics
Summer
IFFT
Equivalent Tube Amplifier Signal Output
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Progress/Project Changes
Block Diagram
...
2
Analog Audio Signal Input from Guitar or File
External Volume Selection
LP
2
LP
...
2
HP
Mode of Operation (Software)
...
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.
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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

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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

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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

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Progress/Project Changes
Lab Work
Reference http//home.pacbell.net/vaughn44/m3.mus
ic.notes.6.pdf
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Progress/Project Changes
Lab Work
Nonlinear Transfer Characteristic
Determination from 16-bit Audio Output of 1961
Fender Champ
Volume 12 523.25 (Hz)
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Progress/Project Changes
Lab Work
Nonlinear Transfer Characteristic
Determination from 16-bit Audio Output of 1961
Fender Champ
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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

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Progress/Project Changes
Lab Work
Highest Frequency from Guitar
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Progress/Project Changes
Lab Work
Input to 1961 Fender Champ at Volume 6 (Output
of Guitar)
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Progress/Project Changes
Lab Work
Fender Champ Response at Volume 6 to 1952
Fender Telecaster
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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)

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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

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Progress/Project Changes
Lab Work
Previous Output of DSP Model of 1961 Fender
Champ at Volume 6
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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.
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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)
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Progress/Project Changes
Lab Work
Comparison of DSP Model of 1961 Fender Champ at
Volume 6 to Actual Amplifier Output
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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
  boards D/A converter for demonstration
• Otherwise, the code will be generated for the DSP
  from the tools available from Simulink