DSP Implementation of a 1961 Fender Champ Amplifier

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DSP Implementation of a1961 Fender Champ
Amplifier

• James Siegle
• Advisor Dr. Thomas L. Stewart
• May 6, 2003

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Outline

• Background
• Objectives
• Functional Description
• Block Diagram
• Lab Work
• Final Results
• Further Research
• Conclusions
• Acknowledgements

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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.

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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.
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Background
Tube Amplifiers

• Guitar amplifiers based on vacuum tube designs
  have been known to produce a superior sound to
  solid-state amplifiers.
• There are several theories to explain the tube
  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.

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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.
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Background
Tube Distortion
Solid-State Distortion
vs.
Reference Barbour, Eric. "The Cool Sound of
Tubes. Ed., Michael J. Riezenman. IEEE Spectrum
August 1998.
8
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)

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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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Objectives
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Objectives

• The DSP available for this project is the Texas
  Instruments TMS320C6711

Reference http//www.ti.com/
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Objectives

• For MATLAB 6.5, there is an Embedded Target for
  the TMS320C6711 where a Simulink design can be
  translated to ANSI C standard code

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Objectives

• This Embedded Target feature allows more time
  improving the DSP algorithm for the amplifier
  model rather than spending hours learning the
  subtleties associated with the DSP board

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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 method 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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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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Functional Description
Analog Audio Signal from Guitar
DSP with C/C or Assembly Digital Filters
Guitar Cable Headphone Plug Attachment
Audio Output with Tube Amplifier Sound
Inputs/Outputs

• Inputs - analog audio signal from a guitar A/D
  interface and software based volume selection
  will regulate the filters behavior
• Output - audio signal with tube amplifier effect

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Functional Description
Analog Audio Signal from Guitar
DSP with C/C or Assembly Digital Filters
Guitar Cable Headphone Plug Attachment
Audio Output with Tube Amplifier Sound
Modes of Operation

• 12 volume settings similar to those provided with
  the 12-volume switch on the 1961 Fender Champ -
  (Only volume6, the middle selection, has been
  implemented)
• linear effects have be omitted due to lack of
  time (ie. echo, tremolo, reverberation, vibrato,
  etc.)

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

• Complete and simulate model of 1961 Fender Champ
  obtained from nonlinear transfer characteristics
  of 16-bit audio output of 1961 Fender Champ

Input
Output
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Lab Work
Approach

• Based on similarities and differences of
  nonlinear transfer characteristics, collect 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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Lab Work
Guitar Note Frequency Chart
Reference http//home.pacbell.net/vaughn44/m3.mus
ic.notes.6.pdf
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Lab Work
Nonlinear Transfer Characteristic
Determination from 16-bit Audio Output of 1961
Fender Champ
Volume 12 523.25 (Hz)
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Lab Work
Nonlinear Transfer Characteristic
Determination from 16-bit Audio Output of 1961
Fender Champ
Volume 12 523.25 (Hz)
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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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Lab Work
Highest Frequency from Guitar
Time Domain
Frequency Domain
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Lab Work
Input to 1961 Fender Champ at Volume 6 (Output
of Guitar)
Time Domain
Frequency Domain
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Lab Work
Fender Champ Response at Volume 6 to 1952
Fender Telecaster
Time Domain
Frequency Domain
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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
• 250 - 450 (Hz)
• 450 - 700 (Hz)
• 700 - 900 (Hz)
• 900 - 1200 (Hz)
• 1200 - 1500 (Hz)
• 1500 - 2000 (Hz)
• 2000 - 3000 (Hz)
• 3000 - 4500 (Hz)
• No significant information was present around DC

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Lab Work

• FIR coefficients were generated for these filters
  with FDATool in MATLAB due to the time spent
  fitting the nonlinear transfer characteristic
  curves

Filter Design and Analysis Tool Window
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Lab Work
Previous Output of DSP Model of 1961 Fender
Champ at Volume 6
Time Domain
Frequency Domain
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Lab Work
Output of DSP Model of 1961 Fender Champ at
Volume 6
Clipping seen from extra gain of 8 FIR filters
being applied to nonlinear transfer
characteristics defined for a -1 to 1 input
range and incorrect transfer characteristic curve
fits.
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Final Results
Simulated Output of DSP Model of 1961 Fender
Champ at Volume 6
Time Domain
Frequency Domain
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Final Results
Comparison of Simulated DSP Model of 1961 Fender
Champ at Volume 6 to Actual Amplifier Output
Time Domain
Frequency Domain
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Final Results
Simulink DSP Model of 1961 Fender Champ at
Volume 6
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Final Results
Actual Output for DSP Model of 1961 Fender Champ
at Volume 6

• After setting the appropriate simulation
  parameters in Simulink to generate and build the
  C code to program the TMS320C6711 for the actual
  amplifier demonstration, the output exhibited a
  clean sound for lower frequency guitar notes,
  and higher frequency guitar notes overdrove the
  speakers depending on the guitars volume gain
  setting
• Currently, this output cannot be captured with
  any DSP Sinks in Simulink so that the actual
  frequency response from the board can be compared
  to the actual Champ output and the MATLAB
  simulation

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Further Research

• Investigate the source of the C code generation
  from a Simulink model with MATLAB 6.5s Real-Time
  Workshop
• Record the amplifier model output from the board
  with a DSP Sink in Simulink
• Analyze the 1961 Fender Champ circuit based on
  the tube and transformer data available and based
  on PSPICE Simulations
• Nonlinear transfer characteristics can be
  determined for separate stages of the circuit for
  wider frequency ranges
• Amplifier model can be simplified
• Transformer was shown to significantly affect the
  frequency response of the Champ around 1000 (Hz)

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Further Research
Transformer Effect on 1961 Fender Champ
Frequency Response Around 1 (kHz)
1961 Fender Champ Output Preceding Transformer
1961 Fender Champ Output Following Transformer
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Conclusions

• The amplifier model sound from the board can be
  improved with analysis results successfully
  captured with a Simulink DSP Sink block
• The 1961 Fender Champ DSP model was successfully
  implemented on a DSP evaluation board
• Only designs with little complexity have been
  produced for past DSP boards
• DSP boards are difficult to program as a result
  of poor accompanying documentation and external
  peripheral layouts
• This projects model was complex and implemented
  on a DSP evaluation board in less than a week
• MATLAB 6.5s Embedded Target for the TI C6000
  feature is a powerful tool for implementing
  DSP-based designs without the time-consuming
  programming task

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Acknowledgements

• Dr. James H. Irwin, Jr.
• Acoustics Laboratory equipment use for capturing
  the 1961 Fender Champ output
• Rob Schaller
• Computer and TMS320C6711 board use for initial
  demonstration of model
• MathWorks, Inc.
• Texas Instruments Embedded Target for the TI
  C6000 Platform

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Any Questions?