TUBE (Transistor Utility for Blonde Emulation) · schematic of the Fender Champ amplifier is shown...

TUBE

(Transistor Utility for Blonde Emulation) First Semester Report

Fall Semester 2011

Full Report

By

Dave Anderson

Sean Byers

Prepared to partially fulfill the requirements for ECE401

Department of Electrical and Computer Engineering

Colorado State University

Fort Collins, Colorado 80523

Project Advisors: Dr. Mahmood Azimi-Sadjadi, Dr. Ali Pezeshki

Dave Anderson, Sean Byers Page ii

Abstract

In the audio industry, like any industry setting, is sensitive to cost and quality of components

implemented. The audio industry thrives on specific sounds as trademarks for their genre of

music or for a specific artist. A vacuum tube amplifier is one component that was used in the

rock era of the 60s producing a sound that is still used today. With the cost and lifespan of a

vacuum tube, transistors are becoming a preferred building block for any amplifier circuit

outside of audio. In this paper, the focus will be creating the specific sound that a vacuum tube

amplifier produces with the implementation of methods and algorithms to use strictly transistors.

Current technology has a couple of bottlenecks that appear in the cost or quality of the product.

Transistor amplifiers are generally not produced attempting to replicate the tube amplifier sound,

which resulted in a tin sound when amplified. Transistor amplifiers that did try to replicate are

either too expensive, poor quality, or replicating a specific tube amplifier that was produced.

When approaching this problem, three different types of amplifiers were used to compare in

order to produce a higher quality and cheaper price device. The Marshall MG15 amplifier

represents a transistor amplifier, Behringer TM300 represents a tube modeler, and the Fender

Champ amplifier represents the best tube amplifier base sound. These three amplifiers were then

tested in Wilson Recording Studio with 24 bit/sample for high resolution and 96 samples/kHz to

avoid antialiasing that occurs with vacuum tube amplifiers. Musical notes were inputted ranging

with varying amplitudes for each designated frequency. The amplifiers were also tested with

live playing of five different guitars with the output signals being captured by two different

microphones.

After analyzing the data produced by the testing method mentioned above, a Fourier Series

polynomial was extracted for the signals at 174.61Hz. This polynomial is able to replicate the

harmonics that are shown in the spectra produced by the Fender Champ amplifier with the same

amplitudes which is also able to follow the waveform that was produced within a small margin

of error. Future work would be to extract a polynomial at five other frequencies in the range

tested and determine the trend to implement an equation or a filter bank for varying frequencies.

Being able to change the amount the amplifier changes the amplitude of the inputted signals with

a dial without losing the tube amplifier characteristics is also in progress.

Dave Anderson, Sean Byers Page iii

Table of Contents Abstract ........................................................................................................................................... ii

List of Figures ................................................................................................................................ iv

List of Tables ................................................................................................................................. iv

Chapter I.......................................................................................................................................... 1

Introduction ................................................................................................................................. 1

Motivation ................................................................................................................................... 2

Chapter II ........................................................................................................................................ 3

Background ................................................................................................................................. 3

Current Technology .................................................................................................................... 3

Chapter III ....................................................................................................................................... 5

Research ...................................................................................................................................... 5

Chapter IV ....................................................................................................................................... 8

Signal Processing methods ......................................................................................................... 8

Chapter V ...................................................................................................................................... 18

Conclusions and Future Work .................................................................................................. 18

References ..................................................................................................................................... 19

Bibliography ................................................................................................................................. 20

Appendix A: Abbreviations .......................................................................................................... 21

Appendix B: Budget ..................................................................................................................... 22

Appendix C: Letters ...................................................................................................................... 23

Letter 1: Sponsorship proposal to Agilent Technologies .......................................................... 23

Letter 2: Response from Agilent Technologies ........................................................................ 24

Letter 3: Thank you to Agilent Technologies ........................................................................... 25

Acknowledgements ....................................................................................................................... 26

Dave Anderson, Sean Byers Page iv

List of Figures Figure 1 - Guitars and Tube Amplifier Tested ................................................................................ 2

Figure 2 - Fender Champ Amplifier Schematic .............................................................................. 4

Figure 3 - Tube vs. Transistor Output Characteristics .................................................................... 5

Figure 4 - Passive One-Port WDF Elements [1] ............................................................................. 5

Figure 5 - Filter Bank Schematic on the left, and on the right are Analog Nobs to Vary

Implemented Filter Banks ............................................................................................................... 6

Figure 6 - Hamming Window with Transform [4] ......................................................................... 7

Figure 7 - base signal waveform produced for recording ............................................................... 8

Figure 8 - Fender Champ response to base signal showing amplitude scaling of different

frequencies ...................................................................................................................................... 8

Figure 9 - Audacity plot of the spectra of F3 frequency from base signal ..................................... 9

Figure 10 - Audacity plots of the spectra of amplifiers' responses to F3 sine wave portion of base

signal ............................................................................................................................................. 10

Figure 11 - Audacity plots of waveforms from various amplifiers at 5 different frequencies

(amplitude vs. time) ...................................................................................................................... 11

Figure 12 - Clipped Sine waveform in Audacity .......................................................................... 12

Figure 13 - Fig. 6 signal spectra in audacity ................................................................................. 12

Figure 14 - Response of Behringer clean to high amplitude sine wave showing clipping and

ripple ............................................................................................................................................. 12

Figure 15- Behringer clean impulse response ............................................................................... 13

Figure 16- Behringer clean response to low amplitude square wave (bottom) and square wave

convoluted with Behringer clean impulse response (top) ............................................................. 13

Figure 17 - base signal spectrogram (DFT size 4096) .................................................................. 14

Figure 18 - Champ base signal response spectrogram (DFT size 4096) ...................................... 14

Figure 19 - Base signal and Champ DFTs at F3 frequency .......................................................... 15

Figure 20- F3 waveform and spectra for Champ and 3rd order "Champ modeling" polynomial 15

Figure 21- Champ (blue) vs. 5th order "Champ modeling" polynomial (red) using polyfit method

....................................................................................................................................................... 16

Figure 22- Champ waveform (blue) vs. 5th order Matlab Fourier series fit (red) ........................ 16

Figure 23- Comparison of waveforms and spectra at F3 frequency for base signal, Champ,

Behringer clean and final "Champ Modeling" simulation using a Fourier series/ polynomial. ... 17

List of Tables Table 1 - Budget Balance after fall 2011 Semester ...................................................................... 22

Table 2 - Anticipated Budget Required for the Full Year ............................................................ 24

Chapter I

Introduction Vacuum tubes contain three terminals which are a cathode, plate, and grid. The vacuum tube

was invented in early 1900s and was used for all of the amplification required in circuits. The

ability to amplify signals enabled electrical guitar players to play for very big crowds for

increased sound projection capabilities. Having analog amplification is an inherent advantage of

vacuum tubes over transistor amplifiers which are digital. One thing that is required for live

performances is relatively no lag time between the musicians playing a chord and everyone at the

venue being able to hear the amplified chord. Replicating the tube sound is difficult because of

its nonlinear and dynamic frequency properties discussed in later in Chapters 3 and 4.

Transistor amplifiers were invented in 1950s, and slowly became more prominent with improved

efficiency of producing silicon wafers and the MOS transistor in 1960. The advantages of

transistor amplifiers having an increased lifespan, reliability, size, and cost just to name a few,

enabled transistors to replace the vacuum tubes’ role by storm. While transistors became the

main amplifying component, they did not have the ability the vacuum tube amplifier had to

distort signals by creating the “classic” rich tone that everyone was familiar with for music.

Replicating the desired sound with transistor amplifiers is the focus of this paper.

There are three different types of amplifiers compared to produce a higher quality and cheaper

device. The Marshall MG15 amplifier represents a transistor amplifier, Behringer TM300

represents a tube modeler, and the Fender Champ amplifier represents the best tube amplifier

base sound. In order to test the amplifiers, the signals produced were recorded at a recording

studio to try to get the purest sound possible. This means ideally blocking out all noises besides

the output signal.

The three amplifiers were tested at Wilson Recording Studio with 24 bit/sample for high

resolution and 96 samples/kHz to avoid antialiasing that occurs with vacuum tube amplifiers.

Musical notes ranging from 174.71Hz to 1318.51Hz were used which correspond to F3, C4, G4,

D5, A5, and E6 on the guitar. Each frequency that was put through the amplifiers had their

amplitude varied from -125dB to 0dB. The amplifiers were also tested with live playing of five

different guitars with the output signals of the amplifiers being captured by a large diaphragm

condenser and Old Shure 545 microphones. The five guitars used consisted of the Epiphone

Dot, 57 Telecaster, 71 Single-Coil SG100, 84 Kubicki, and Zia Guitar.

Dave Anderson, Sean Byers Page 2

Figure 1 - Guitars and Tube Amplifier Tested

In Chapter 2, the background of the project will be discussed giving more details into the

amplifiers available and their effects. Chapter 3 will discuss our research and Chapter 4 will

discuss the team’s decisions.

Motivation Many studio professionals still enjoy the sound of vacuum tube amplifiers over transistor

amplifiers when they need to create the best sounding music. Even though transistors are

cheaper to manufacture, the vacuum tubes’ distortion produces a higher quality sound that is

worth the higher price resulting in continued use by some studio professionals. In order to

produce the same sound quality as a tube amplifier, transistor amplifiers require techniques to

deliberately change the output signal discussed in Chapter 3.

Current silicon transistor technology produces relatively inexpensive amplifiers compared to

tubes; creating a transistor circuit to replicate a tube sound is worth investigating as this paper

shows because of its ability to reduce the cost to produce identical functioning product. The

main question this paper investigates is how to implement this idea practically to produce a high

quality product.


Chapter II

Background Evaluating an output signal that passes through a system knowing the input will give insight of

how the system distorts a signal. The same idea was used on a vacuum tube when it produced a

signal. The signals produced from the tube amplifier are periodic and nonlinear. Since it is not a

linear signal the black box approach to take the input signal and output signal to define a filter

for all frequencies will not work. Nonlinear signals are signals that do not have outputs directly

proportional to their inputs. The main method for analyzing nonlinear signals is by using

waveshaping. Waveshaping can be done by using a lookup-table, filter bank, polynomials, and

Fourier Series. Using a lookup-table is the only method not utilized due to its infinite

possibilities for outputs.

Filter banks are used to implement different conditions to the input signal depending on the

frequency of the signal. The idea behind a filter bank is to account for the changing equations

depending on the input frequency that a vacuum tube inherently implements. With frequencies

between two filters there will be what is called a weighting of the filters depending on the

frequency to have one of the filters have a greater impact on the output signal’s characteristics.

Polynomials are similar to Fourier Series when the a sine input is plugged into the x(t)’s of

( )

∑

Fourier series differs because it says that for every periodic signal the Fourier Series is able to

represent the signal by a combination of sine and cosine inputs at different frequencies.

Current Technology Vacuum tube amplifiers like the Fender Champ amplifier are becoming very expensive as the

vacuum tubes required to replace the existing ones become increasingly difficult to obtain. The

schematic of the Fender Champ amplifier is shown in Figure 2. A transistor amplifier that

emulates a vacuum tube amplifier that is commercially available and is readily available is the

Peavey Vypyr which costs $100 and has terrible quality for its emulation. Transistor amplifiers

that emulate general tube amplifiers would be similar to the Behringer TM300 Tube Amp

Modeler. The problem with this product is that many if not all of its settings give poor quality

and even produces awful quality distortion when the amplification is increased. Specific tube

emulating amplifiers like the Boss FBM-1 costs around $300 which is relatively cheap for

recording studios, but still relatively expensive for your average person. This device emulates

the 59 Fender Bassman in specific.


Software tube emulators are good at producing the tube sound that is desired, but is designed to

work in studios where the device can have time to process the information. Whereas a live

performance would require the device to immediately process the signal to be synchronized with

the rest of the band. This is the main reason why this project is avoiding software emulation.

Figure 2 - Fender Champ Amplifier Schematic


Chapter III

Research

Triode vacuum tubes are similar to transistor amplifiers with their gate characteristics. The

difference that is apparent between them is the tube amplifier doesn’t have clean linear

characteristics with changes in the curves because of secondary emission from the tube itself.

This plays a key role when trying to emulate the tube amplifier because of this characteristic.

Wave Digital Filters (WDF) could be used to emulate tube amplifier sounds. The problem with

WDF is the modeling is meant for linear time invariant (LTI) circuits. There is a way of having

port resistances in the circuit to acquire the nonlinearities. This however takes a lot of

computation and is complicated meaning the processing would be slow and not plausible for our

goal to be able to use the device in live shows.

Figure 4 - Passive One-Port WDF Elements [1]

Figure 3 - Tube vs. Transistor Output Characteristics


Waveshaping is a method of developing and computing nonlinear waveforms. The most

straightforward theoretical method of waveshaping is by using a lookup-table to produce an

output given an input. The problem this method has is that creating a high-resolution lookup-

table would take a lot of memory and if that were not used a low resolution table would have an

audible difference to an actual tube amplifier that it would sound bad. Oversampling of a signal

is many times required due to the nonlinear characteristics of the signal there could be aliasing

that exceeds the Nyquist frequency.

Another way of computing a nonlinear waveform would be to break the desired output into

multiple sections for frequency to break it up into more of a linear system. This would enable

the bands to dominate for certain frequencies and overlap with frequencies in the middle to give

a better blended output signal rather than having an abrupt change at the boundaries of

frequencies. This idea is known as customized waveshaping or using filter banks to create the

different outputs for various frequencies. This means that each frequency band would have some

sort of polynomial approximation to emulate the tube amplifier sound at that frequency and as

the frequency changes the polynomial would have less effect on the circuit when getting closer

to another frequency band until the previous polynomial ideally plays no part in the output

signal.

To analyze the signals that were produced required knowing information regarding waveform

properties that was already discussed, types of windowing methods and spectra analysis. The

type of window can have an effect on what is shown over an interval. The Hamming window

was predominately used in the project because it is a raised cosine shown in Figure 6 helps

represent audio signals giving the system a less than 1% error in the system.

Figure 5 - Filter Bank Schematic on the left, and on the right are Analog Nobs to Vary Implemented Filter Banks


Figure 6 - Hamming Window with Transform [4]

Spectra analysis which is also shown in Figure 6 is important because the representation can give

the frequency domain’s characteristics. The characteristics involve the dominate frequency,

power, distortion, harmonics, bandwidth, and other spectral components that are not easily

detectable in the time domain waveforms. When using a hamming window along with the

frequency domain, the noise and dominate frequencies will be distinguishable with a high

enough amplitude.


Chapter IV

Signal Processing methods The actual signal processing and analysis work started as soon as we went to the recording

studio. We went to Wilson studios in Longmont, CO and did nearly 7 hours of recording,

accumulating 18:35 of recordings at 96 kHz and 24-bit resolution, making for 187 MB of data.

The recording studio served several purposes for us. First, it allowed us to get very high quality

digital recordings using high quality equipment, like cables and microphones. Secondly, it

allowed us to spend quite some time talking with Chuck Wilson, our producer, who has spent

many years in professional audio and could lend us some very good advice as to where to take

the project.

We came up with a very thorough recording scheme prior to the session, with Chuck's help. We

knew that we were going to evaluate several amplification methods: the Fender Champ, the

Marshall MG15, the Behringer TM300 on four different settings (bypass, clean, hi-gain, hot),

and every signal recorded directly without any amplification. In order to do the recordings

effectively, there needed to be some kind of a standard signal driven the same way through every

amplifier. Therefore, just having a guitar played through every one of them would not work, as it

would be different every time and there would be no sort of control. We decided to go with a

standard signal made in Matlab that would contain sine waves with a range of amplitudes and

frequencies as well as guitar notes corresponding to the same frequencies as the sine waves. The

periodic sequence of a guitar string vibrating is very different than a sine wave but it also very

predictable, meaning that both portions of the base signal turned out to be very important. The

base signal is shown below in its amplitude vs. time graphical interpretation in Audacity.

Figure 7 - base signal waveform produced for recording

The first half of the signal shows 6 signals increasing in amplitude. The first is a sine wave

corresponding to the musical note F3 at 174.61 Hz. It increases from an amplitude of 0 to an

amplitude of 1 (or 0 dB). The following five sine waves follow the same amplitude increase

pattern but are notes corresponding to C4 (261.63 Hz), G4 (392.00 Hz), D5 (587.33 Hz), A5

(880.00 Hz), and E6 (1318.51 Hz). The second half of the signal has the same 6 frequencies

played on guitar. The picture below shows the signal produced by the Champ in response to the

base signal, which obviously resembles the base.

Figure 8 - Fender Champ response to base signal showing amplitude scaling of different frequencies


We ended up doing several recordings for each amplifier, rather than just the standardized signal.

Since this is an audio application, the signal sounds are more important than whether it is

identical to what is recorded, we recorded with many different types of guitars in order to get a

very well rounded idea of what effect the amplifier was having. In addition to the standard

signal, we recorded with an Epiphone Dot guitar, a 1984 Kubicki guitar that had active pre-

amplified pickups, a 1971 Gibson SG with Single coil pickups, a Zia guitar with humbucking

pickups, and a 1957 Fender Telecaster. The Telecaster was particularly interesting for two

reasons. For one, it was the guitar that the Fender Champ amp was originally designed to

amplify, meaning that the signal distortion we get from the Telecaster would be the one worth

the most attention. Secondly, this particular guitar was used by the Saturday Night Live band for

a few years. When the guitars were played, a standard playing scheme was used that included

chords, single notes, and chopping, which is essentially playing notes and not letting them ring

out. Overall, we really feel that we got quite a wide range of recordings done which accurately

represent the way that all of the amplifiers are distorting the signals.

The first analysis done in finding what made the tube amplifier sound so much better than the

transistor amp and the modeling pedal was to look at the spectra of the signals collected at the

studio. We knew that the spectra of each signal should contain the base frequency, but that it

would certainly contain something different and that this is what probably gave the amplifier its

characteristic sound.

The spectra was first analyzed in Audacity, a free audio analysis program. This was initially used

rather than Matlab due to the ease of use of the program and the fact that it is able to graph the

spectra in a way tailored to audio, so that only the range of human hearing is on the graph and

that peaks actually have their corresponding musical notes written out. The program allows the

user to graphically select a section of data and compute the FFT of it. For the first set of graphs,

we did not necessarily choose any part of the signals, just made sure to get only the parts that had

a constant amplitude change. An example of the spectra plotted from a chosen part of a signal is

shown below as well as the spectra produced by Audacity.

Figure 9 - Audacity plot of the spectra of F3 frequency from base signal


The gray area selected of the signal is the part which Audacity computes the spectra. We can see

that the spectra is what we expect: A single peak at 174 Hz with some side frequencies caused by

the windowing of the function. In this case, it can be seen on the spectra window that a Hann

window was used. This process was repeated for all of the frequencies and all amplifiers. It

would take far too much space to show all of the spectra here, so to save space only the spectra

for the F3 note similar to that above will be shown.

Figure 10 - Audacity plots of the spectra of amplifiers' responses to F3 sine wave portion of base signal

There are obvious differences in the spectra. The lower frequency spike in the two amplifiers is

due to AC power at 60 Hz, and is not present in the Behringer since it was powered by a battery.

However, it is very clear that all the amplifiers produce a large number of harmonics with


varying amplitudes. This was not easy to mathematically analyze in Audacity so in the future we

used Matlab for spectra.

The additional focus was on the waveforms of the various signals. What was very interesting was

that all of the waveforms turned out to be very different. The waveforms are shown below for the

F3 frequency.

Base signal

Fender Champ

Marshall MG15

Behringer – bypass

Behringer – clean

Behringer – hi-gain

Behringer - hot

Figure 11 - Audacity plots of waveforms from various amplifiers at 5 different frequencies (amplitude vs. time)


The signal distortion analysis always had to do with transforming the base waveforms into

whatever was created by the amplifier, and there are many different ways to have this occur. The

first investigations had to do with the Behringer pedal, from which it was obvious that there was

clipping happening. A program was written in Matlab that would clip the base signal. This signal

and its spectra are shown in the graphs below.

It is very reasonable that clipping will create harmonics, which matches the harmonics from the

Behringer pedal, at least for the first four above the base frequency. The waveforms from the

clipping program do not really match the Behringer waveforms, though. From here, it was

assumed that the Behringer had clipping mixed with an impulse response, which is why it shows

a slight ripple before flattening out, as shown in the figure below.

To test this assumption, we tested the response of the Behringer pedal to

impulses and to single amplitude sine waves and single amplitude square

waves. The amplitudes of these waves had to be scaled down until there was

no clipping happening. The impulse response of the Behringer is shown

below.

Figure 12 - Clipped Sine waveform in

Audacity

Figure 13 - Fig. 6 signal spectra in audacity

Figure 14 - Response

of Behringer clean to

high amplitude sine

wave showing

clipping and ripple


The graph above shows the convolution of the Behringer's impulse response with the same

square wave that was driven through the Behringer, as well as the Behringer's response to it.

The two waveforms are so close to each other that we feel as though the Behringer's method has

been successfully determined as a mixture of clipping and an impulse response, to give a mix of

harmonics and waveshaping. However, after quite a bit of waveform and spectral analysis, we

began to think that the Behringer pedal was not really coming close to the actual Champ.

Therefore rather than using the Behringer's distortion methods as a building block for the

Champ, we attempted to show that our methods could come closer to the actual Champ than the

Behringer. The spectrograms of the Champ versus the base signal turned out to be very

informative. The spectrograms of the base signal and the Champ's base signal response are

shown below.

Figure 15- Behringer clean impulse response

Figure 16- Behringer clean response to low amplitude square wave (bottom) and square wave convoluted with Behringer clean

impulse response (top)


Figure 17 - base signal spectrogram (DFT size 4096)

Figure 18 - Champ base signal response spectrogram (DFT size 4096)

Though it was difficult to obtain any real quantitative data from a spectrogram graph, it was very

apparent that the Champ was adding harmonics to the sine wave portion of the signal. These

harmonics were also determined to be integer multiples of the original frequency, which is what

a polynomial would do to a sine wave. When a sine wave is plugged in to a third order

polynomial, we derived that the output signal would be equal to either

A(sin(x))+B(sin2(x))+C(sin

3(x)) or (A + 3C/4)sin(x) + (B/2)sin(2x) + (C/4)sin(3x). By using the

magnitudes of these harmonics in the spectra as the coefficients of the equation with the

multiples of x, we could solve for the coefficients in the polynomial equation. The DFT that was

used to calculate the first polynomial is shown below.


Figure 19 - Base signal and Champ DFTs at F3 frequency

By using the peaks' intensities relative to each other of base = 1, first harmonic = 0.171, second

harmonic = 0.116, we came up with the coefficients for the polynomial of A = 0.826, B = 0.342

and C = 0.232. The F3 sine wave can be plugged into this polynomial to obtain the waveforms

and spectra shown in the graphs below.

Figure 20- F3 waveform and spectra for Champ and 3rd order "Champ modeling"

polynomial


It is very promising that the polynomial was able to so well approximate the first two harmonics

above the base frequency. This meant that a polynomial was certainly a step in the right

direction, since it could be quantitatively adjusted and fit to both the spectra and/or the

waveform. The next experiment was to use the Matlab polyfit function to match the input sine

waves used in the studio to the Champ waveforms using a least squares fit. The waveform match

up of the 5th order polynomial against the actual Champ signal is shown below.

It is clear that the polynomial can match the main waveform of the Champ, but there is a slight

hump before the main peak of the polynomial which cannot be matched, even with a high order

polynomial. Fortunately, Matlab also provides a curve fitting tool that can fit data with a Fourier

series. The 5th order Fourier series fit to the same section of data is shown below.

This 5th order Fourier series fit to the data is better at first glance because it is able to simulate

the hump that occurs before the main peak, and if it is at the same order as the original

Figure 21- Champ (blue) vs. 5th order "Champ modeling" polynomial (red) using polyfit

method

Figure 22- Champ waveform (blue) vs. 5th order Matlab Fourier series fit (red)


polynomial it can have the same spectra. As a preliminary derivation, the difference between the

polynomial fit and the Champ waveform is found. The original sine wave is then filtered using a

digital derivative filter to create a cosine wave. Another Polynomial fit is done to find the best fit

between the remaining signal (the difference between the Champ waveform and the first

polynomial) and the cosine wave. In this way, a Fourier series fit for the original amplitude

varying signal was determined. We were able to obtain results that fit both the waveform and

spectra of the F3 frequency very closely, as shown below.

The actual polynomial derived by our program is an ( ( )) ( ( )), where

( )

( ) ( ) ( ) ( )

The simulation shows both an improvement over the Behringer waveform and spectra when

compared with the actual Champ amplifier. Our original goal for the semester was to create an

algorithm that would model the champ with better results than the Behringer pedal and we can

say with confidence that we were successful in reaching this objective.

Figure 23- Comparison of waveforms and spectra at F3 frequency for base signal, Champ, Behringer clean and final "Champ

Modeling" simulation using a Fourier series/ polynomial.


Chapter V

Conclusions and Future Work Overall, we are very satisfied with the results of first semester. We have successfully formulated

a signal processing algorithm capable of matching both the spectra and the waveform of the

signals produced by the Fender Champ vacuum tube amplifier. After experimenting with

clipping, static waveshaping, FIR filters for waveshaping, and a polynomial, we determined that

the most effective solution was using two polynomials: one with the regular input and one with

the derivative of the input, or essentially a Fourier series.

We plan to put the algorithm into action, test its robustness, and develop different polynomials

for different frequencies that can be implemented into a filter bank. We are also looking to create

actual hardware for these algorithms, and we are not yet sure how to do that. A lot of it depends

on how the work goes early on. If there is a lot of work to do on the algorithms, we may spend

more time on those rather than on the hardware design. This would mean that we would probably

be using a DSP development board, and the two we are looking at currently are the Freescale

Symphony Soundbite and the Pandaboard. If the algorithms are robust enough early on in next

semester, we will probably attempt to design a much less expensive DSP system; this should

allow the PSOC development board to be used that was given by Cypress and Arrow electronics.

Some of this choice also depends on budget. Studio time is expensive and if we need to pay for

more recordings then we will most likely not be able to afford a development board. At this

point, we do not foresee needing any more studio recordings but we are cautious not to let our

budget run out as well.


References [1] J. Pakarinen and M. Karjalainen, "Enhanced Wave Digital Triode Model for Real-Time Tube

Amplifier Emulation," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Digital Object Identifier 10.1109/TASL.2009.2033306, Apr.

2010.

[2] J. Pakarinen and D. T. Yeh, "A Review of Digital Techniques for Modeling Vacuum-Tube

Guitar Amplifiers," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Center for Computer Research in Music and Acoustics, Stanford

University, Palo Alto, CA, Computer Music Journal, 33:2, pp. 85–100, Summer 2009.

[3] J. Pakarinen and M. Karjalainen, "WAVE DIGITAL SIMULATION OF A VACUUM-

TUBE AMPLIFIER," Dept. of Signal Processing and Acoustics, Helsinki University of

Technology, Helsinki, Finland, Rep. 142440469X, 2006.

[4] J. Smith, “Spectral Audio Signal Processing,” Center for Computer Research in Music and

Acoustics, Stanford University, Dec. 2011


Bibliography [1] U. Zolzer, Digital Audio Signal Processing, Hamburg, Germany: Wiley, 2008.


Appendix A: Abbreviations FFT: Fast Fourier Transform

DFT: Discrete Fourier Transform

WDF: Wave Digital Filter


Appendix B: Budget

Table 1 - Budget Balance after fall 2011 Semester

In total, $230.00 has been spent on the project out of a total budget of $400.00. We do not

anticipate needing more than the remaining $170.00 for the second semester of our project.


Appendix C: Letters

Letter 1: Sponsorship proposal to Agilent Technologies DSP for Audio Signals:

A digital modeling system for a wide variety of tube amp sounds.

October 15, 2011

Dan Ferguson

Agilent Corporation

Dear Mr. Ferguson,

I want to thank you in advance for considering sponsorship of student-originated Senior Design

projects at Colorado State University. It takes a lot of work and motivation to design a project

and learn to be your own boss, all the way from concept to implementation. We would like to

introduce our project idea and team members to you before beginning to discuss our proposed

budget.

Our project concept is the creation of a digital modeling system for old tube guitar amps. Ask

any guitar aficionado: tube amps have cleaner sound and warmer tone than solid-state amps.

Unfortunately, many of the original tone machines are either too expensive or too rare to make

them of much use to anyone who wants to play them live. Software and Hardware

implementations of modeling systems like this are common but most of them are very limited in

their use. Every tube amp sounds different, and so every modeling algorithm will produce a

different sound. Our idea is to work with recording studios to record an old tube amp, the Fender

Champ, that has never had a specific model made for it. We will also look at some algorithms

already in place in commercial hardware, in order to find general differences between those and

a real tube amp. Using these comparisons, we will create hardware that will simulate a wide

variety of tube sounds and have use in both an analog (eg. Live blues concert) and digital (eg.

Sampling software) worlds.

Our team includes Dave Anderson, Sean Byers, and professor Mahmood Azimi. Dave is an

electrical engineering student with a strong interest in computer programming, signal processing

and, above all, music. Sean Byers is also an electrical engineering student with an interest in

analog electronics. Professor Azimi works with signal processing at CSU.


Type of expense Hourly Cost # of hours Total Cost

Studio Time $50 12-15 $600-750

Behringer TM300 pedal N/A N/A $26

Hardware Design and

Components

N/A N/A $400

Total Cost $1026-$1176

Money Raised so far $400

Money required $626-776

Table 2 - Anticipated Budget Required for the Full Year

We would like to request a $500 sponsorship from Agilent for the full academic year. We would

love to see our project fully realized, and with primarily student funding this just is not possible.

If you choose to sponsor our team and project, we thank you very much in advance for such an

exciting opportunity.

Letter 2: Response from Agilent Technologies Hi Dave, Thank you for submitting your proposal. After reviewing all the project submissions,

I’ve decided to award $100 to your team from Agilent Technologies. I will work with Olivera to

get those funds transferred to your project team, and we’ll keep you informed of that process. I

would also like to give some feedback to you and your project mates regarding the proposal:·

First of all, I enjoy any project that combines your engineering studies with personal

interests/passions. Your project seems to be a great example of that – modern implementation of

old school guitar amplifiers! Very interesting…· I know the time frame to create your

proposal was short, and I understand that creating a 1-2 page proposal is also tough. Having said

this, though, I have these comments: I’d like to see more about timelines and milestones for

your project. I have a high-level understanding, but would like to have seen a project schedule

that shows how you’ll converge towards your desired final outcome. With all the tools available

these days for creating documents, I’d like to have seen a more “visually attractive” proposal –

one that made use of color, or diagrams, or pictures, etc., to help convey the information. You

did include a table for your budget – that was important. But I’d like to have had more

information about the actual project, conveyed in an engaging format. You introduce your team,

which is important. I’d like to have known more about the specific roles of each member – what

subsystems each was involved with, what each person was accountable for, etc. This could have

been easily incorporated in a project milestone table, for example. In particular, I’d like to have

understood more about the actual “comparative study” you mention – a study to compare the

recorded sounds of the actual Fender Champ to the fabricated sounds of the algorithmic

implementation. That would seem to be very intensive – so many sounds to compare, so many


combinations of sounds, etc. This seems to be a key element in your project, so would like to

have seen a little bit more information about that stage. Again, thanks for submitting your project

for funding. It seems a very interesting project, and I’ll look forward to hearing more about it as

you approach E-Days. Also, note that Agilent will have another funding round offered in the

Spring – it will be a bit more formal, but there will be another chance for you and your team to

apply for additional funding. Stay tuned… Dan Ferguson

Electronics Manufacturing Test

Americas Service & Support Manager

Agilent Technologies

(970) 679-3641

[email protected]

Letter 3: Thank you to Agilent Technologies Hi Dan,

Thank you very much for the award! We really appreciate not only the money but the

recognition of our project and of our hard work.

We would also like to thank you for the feedback on our proposal. We will undoubtedly be

writing more of these as the year goes on and it really helps us.

Thank you again. If you have any questions about the project or us please do not hesitate to let us

know. We will be sure to acknowledge this contribution on our website and in our

documentation.

Dave Anderson and Sean Byers


Acknowledgements We would like to thank:

Dr. Mahmood R. Azimi-Sadjadi for formulating the original idea for this project.

Dr. Ali Pezeshki for advising this project and helping us with mathematical signal processing.

Olivera Notaros for leading the senior design program in the college of Electrical and Computer

Engineering at CSU.

Chuck Wilson for recording us in his studio, lending us his many years of audio expertise and

suggestions, finding a 1960 Fender Champ for us to record and giving us a huge discount on

recording costs.

Agilent Technologies for supporting our project with a $100 donation.

The ECE department for giving us $300 of funding for our project.

TUBE (Transistor Utility for Blonde Emulation) · schematic of the Fender Champ amplifier is shown...

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