Abstract— Electromagnetics are used in many ways to amplify and alter sound for the purpose of making music. The main focus of this paper is on the electric guitar, as this has been the most notable benefactor of electromagnetic technology. It describes in detail the operation of a basic electromagnetic pickup. Equations are included that can be used to model the principles that are at work. Great attention was given to experiments which explore the effects that different variables have on the sound that the pickups create.

In addition, a device called the EBow that can be used with electric guitars is examined. This handheld device works by creating a magnetic field which can be used to vibrate the strings of the guitar, resulting in sounds that could not be created by physically plucking the strings. It also plays a very significant role in the experiments.

Index Terms—Guitar, electromagnetic pickups, humbucker, single-coil pickup

I. INTRODUCTION

n the twentieth century radical new styles of music were developed. Like in ages past, new inventions have

encouraged different kinds of music, but never has the effect been so dramatic as it was when the electronics world began to intersect with the music world. The invention of the electric guitar made rock and roll what it is, and popular music has never been the same. Whether that’s good is not for this paper to decide.

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The driving force behind the electric guitar is the electromagnetic pickup. Speakers can create sound from a changing voltage and amplifiers can process that voltage. The pickups are where the voltage originates, in response to the vibration of steel strings. The process by which this happens is known as electromagnetic induction. It is what makes the operation possible, opening the door for musical creativity. This paper will examine what makes electromagnetic pickups able to convert vibrations into electrical signals by explaining the principles, modeling them with equations, and demonstrating them through experimentation.

M. Edwards is graduate of Calvin College in Grand Rapids, MI with a Bachelor of Science of Engineering with a concentration in electrical/computer engineering.

e-mail: medwards@ieee.org

II. BASIC ELECTROMAGNETIC PICKUPS FOR ELECTRIC GUITAR

A. Beginnings

Electromagnetic pickups began to take shape in the 1920’s. Lloyd Loar, an employee at the Gibson Guitar company, was believed to be the first person to design an electric guitar pickup1. In response to guitarist’s complaints that they could not be heard over other instruments he invented a detected vibrations in the soundboard of stringed instruments and converted them into electrical impulses. His design was not initially appreciated and although he continued to build electric guitars, the idea did not take off. In the late 1930’s Adolph Rickenbacker and George Beauchamp patented an electromagnetic pickup that was more like today’s models. It was around this time that electric guitars began to be used more in popular music and interest in them rose from there.

B. Construction of a Basic Single-Coil Pickup

The simplest pickups utilize only one coil of wire wrapped around the magnet. These are called single-coil pickups. Their behavior will be examined in detail with the modifications of more complex pickups explained in a different section.A pickup is usually a fairly simple device, composed of a coil of wire, often made of copper coated in enamel, wrapped around an insulating bobbin, which is often made of plastic. A bar magnet is mounted on the bottom of the bobbin, or in some cases inside of the bobbin. Typically cylindrical pole pieces rise off of the magnet, up through the coil and are positioned underneath each of the guitar strings. The distance of these pole pieces from the strings is a determining factor in the strength of the signal produced by the pickup. Other factors include the strength of the bar magnet and the number of turns in the coil. The most common material for these pole pieces is alnico, an alloy of aluminum, nickel, and cobalt. There are several variations of this material in use in guitar production currently. A section view of a fairly typical single-coil pickup can be seen in Figure 1 on the following page.

An Introduction to the Use of Electromagnetics in Musical Instruments: Basic Analytical and

Practical Approaches

Matthew Edwards, Student Member, IEEE1

Fig 1. A section view of a single-coil pickup as seen from a view perpendicular to the strings with all of them lined up. This pickup is slightly more elaborate than a basic model in that there is an insulating material between the pole piece and the bar magnets. Also, there is usually only one bar magnet. This image is borrowed from U.S. patent number 5,399,8022.

C. Electromagnetic Induction

To understand how the vibration of the strings can be used to generate a current, it is first necessary to understand some of the properties of these strings. Stringed instruments in general use strings of different thickness and strung at different levels of tension to produce different pitches. The strings that produce lower pitches are thicker. Melodies are played by sounding different strings or just by changing the length of the string by pressing it down to the neck at certain points. Most strings for solid-body electric guitars are made of either steel, nickel or an alloy of the two metals. These materials are classified as ferromagnetic3. A dipole moment is created in every atom of such a material by unbalanced electron spin moments. In sections of the material with many atoms close together the moments line up in the same direction, leading to a dipole of more significant strength. These sections are called domains, and the reason that ferromagnetic materials have no magnetic moment as a whole is because the dipoles of the various domains oppose each other. The strings have no magnetic field then, until the field due to the magnets of the pickup is brought near to them. At that point the size of the domains with a magnetic field in the same direction as the applied field increase and their internal magnetic fields become greater than those of the domains that were previously canceling them out. The magnetic field of the ferromagnetic strings can now take affect. A rough illustration of this can be seen in Figure 2 below.

Figure 2A. Regions of ferromagnetic strings before an external magnetic field is applied.

Figure 2B. Regions of ferromagnetic strings with application of external magnetic field.

The oscillation of the strings causes a disturbance in the magnetic field of the permanent magnet of the pickup. As the field changes so does the flux in the coil surrounding the magnet. This induces an alternating current with a voltage described by Faraday’s Law:

This equation states that the electromotive force generated in the coil is equal to the negative of the rate of change of the magnetic flux through the coil. It is this voltage that is sent to the amplifier, processed, and used to drive the speakers. A detailed mathematical explanation of the principles will be presented later on under the heading: Simulations and Calculations to Model Pickup Behavior.

D. Variations in electric guitar pickups

A serious problem with single coil pickups is that they also tend to pick up the background hum that is present in the surrounding environment. The most common way to deal with this problem is with a second coil and additional pole pieces added to the pickup, wired in a different direction such that the outside noise will be canceled out. The extra six pole pieces are usually placed with an opposite direction of their polarity compared to the other six. The result is what is known as a humbucker pickup. It is essentially two single-coil pickups set close together that always work in cooperation. One exception to this cooperation is in guitars which are equipped with a coil tap, allowing just one of the coils to be selected. When a switch is flipped the other coil is shorted out, and the pickup would then function as a basic single-coil. This is another way for luthiers (guitar makers) to increase the versatility of the instrument. A top view of a humbucker pickup is shown in Figure 3 on the following page.Another key benefit of a humbucking pickup is that since there are two coils responding to flux changes, a much greater length of the strings is read, and the resulting sound seems “thicker” and more robust. To observe this phenomenon, the output of an electric guitar was probed with an oscilloscope. No vibrations were induced in the strings. The results can be seen in Figure 4 on the following page.

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Fig 3. A diagram of a humbucker pickup including a standard mounting bracket. All six strings can also be seen. The pole pieces have hexagonal depressions in them to allow them to be turned with an Allen wrench. This picture is also borrowed from U.S. Patent No. 5,399,8024

Noise Picked Up by Single-Coil Dut to Background Conditions

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Fig 4A. Waveform from oscilloscope with strings motionless using the middle position single-coil pickup. Oscilloscope settings were at 1.00 mV per division with a 10x probe and 4.00 ms per division. The wave seems small but can result in audible noise.

Noise Picked Up by Humbucker Due to Background Conditions

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Fig 4B. Waveform from oscilloscope with same settings but the humbucker pickup is used. There is a noticeable reduction in the noise.

The humbucking effect can also be achieved to a lesser extent simply by selecting two single-coil pickups at the same time, assuming that they have been wired with an opposite polarity of each other. This proved to be true on the Parker Nitefly, the guitar being used in all experiments featured in this paper, and it could be seen that there was less noise in the signal when both single-coil pickups were used.The pickups used on Parker Guitars have an insulating gap between the pole pieces and the bar magnet. This lessens the strength of the magnetic fields on the strings, while still having a base magnet with full strength. A magnetic field

that is too strong can alter the vibration of the string, making the output sound unnatural. Failure to fully magnetize the permanent magnet can result in it losing strength fairly quickly and needing to be replaced5.Other common variations of basic pickups have a cover over the pole pieces to reduce the effects of outside noise. Some pickups don’t even have pole pieces and just use one solid magnet.

E. Supporting On-Board Circuitry

It is very important for a guitar player to be able change some aspects of the sound before the signal reaches the amplifier. For the Nitefly, there are two switches used to determine which pickups are driving the output. A three-way selector determines whether the output of the piezoelectric pickup, selected electromagnetic pickup, or output of both is sent out from the guitar. A five-way selector switch allows the guitarist to select the output of one individual electromagnetic pickup or a combination of the middle pickup and one other. It is not possible on most guitars to select more than two pickups at once, or to select both the neck position pickup and the bridge position pickup if there are more than two pickups. There are three potentiometers used to modify the signal. One acts as a volume knob for the piezoelectric pickup, one receives the signal from the electromagnetic pickup or pickups being used (all three are wired to it) and acts as the volume knob for the those, and a third potentiometer is used to create a filter to shape the tone of the signal before it is even sent out from the guitar. After passing through all of this the signal is sent out by way of a ¼” output jack. A stereo cable is required to use both the piezoelectric and electromagnetic pickups. Stereo cables include an extra sleeve to conduct the two signals and one ground connection. If a standard cable is used, only the output of the electromagnetic pickups is transmitted. A photo of the guitar with the pickguard removed and flipped over is shown in Figure 5 below.

Fig 5. On-board electronics of the Parker Nitefly guitar. Two single-coil pickups can be seen, along with a humbucker. All three of these run to the five-way selector (top structure) and then into the potentiometer on the right, which is the volume control for the electromagnetic pickups. A black wire can be seen running from the bridge to the potentiometer on the lower left, which acts as the volume for the piezoelectric pickups. The top potentiometer is the tone knob for the electromagnetic pickups. The three way selector is between the tone knob and piezoelectric pickup volume. The pole pieces can be seen extending through the mounting brackets of the pickups.

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III. USE OF ELECTROMAGNETIC PICKUPS IN OTHER INSTRUMENTS

A. Acoustic 6-String Guitars: An Example Featuring the Lace Sensor

With acoustic guitars certain difficulties arise that do not present a problem in solid body electrics. Feedback and outside interference can often be overwhelming in acoustic guitars due to their resonance. For these reasons and because of tone preferences, many acoustic-electrics are fitted with piezoelectric pickups or even a microphone.But there are electromagnetic pickups that are made for acoustic instruments. The Lace Sensor, made by Actodyne General, can be used with electric guitars, acoustic guitars and other stringed instruments6. The pickup is designed to combat two major problems, the damping effect exerted on the strings by traditional pickups and the electromagnetic interference of the background noise.The damping effect refers to the way that traditional electromagnetic pickups have a tendency to make the vibrations of the strings die out early because of the magnetic field. This effect tends to be most profound when the greatest amplitude of the string motion occurs right over the pole piece of the magnet corresponding to that string. The Lace Sensor solves this problem by forcing the polarities of the magnets in a different direction. Usually the magnetic flux fields are generated by opposing magnetic poles. The Lace Sensor uses an arrangement of two identical poles situated side by side. The principles of magnetic repulsion are used to shape the magnetic flux fields. This causes the flux fields of the pickup to be compressed in the region where the strings align. The difference in these flux fields make the Lace Sensor less prone to altering the natural string vibrations and it is more sensitive to certain harmonics than a conventional electromagnetic pickup.The Lace Sensor’s construction begins with the cover, which consists of a long ferromagnetic channel lined on the inside with barium ferrite anisotropic rubber-bonded magnetic materials. These magnetic pieces are all lined up so that the polarity inside of the ferromagnetic channel will be the same from each piece. The flux fields are generated by a magnet on each side of the channel and three bonded to the bottom. This alignment causes the flux fields to be in compression with one another. The repulsion that these fields exert on each other forces them into flux fields going out from the edge of the ferromagnetic channel. Inside this channel is a ferromagnetic bobbin with a copper coil wound around it. The bobbin is shaped with a row of teeth facing outwards. The bobbin causes the flux fields from the bottom magnets to be concentrated onto the upper edges of the channels, and the flux density is increased. The teeth of the bobbin exist to create variations in the flux density from one region to the next and this contributes to the shape of the exterior, overall flux field shape. The repetition of this layout of areas of varying flux density which compress and repel each other induces canceling current flows in a string that oscillates in the flux field. The attractions that typically cause string damping are cancelled

by the effects of these current flows. This results in the Lace Sensor’s ability to sense all modes of the string’s harmonic motion, giving it a greater sensitivity to the vibrations of the string in the vertical and horizontal direction.Another advantage of the Lace Sensor is that the symmetry of the magnetic flux field patterns create a barrier, protecting the coil from electromagnetic interference. This allows it to accomplish the second desired characteristic of a quality acoustic pickup.

B. Bass Guitars

Bass guitars differ from 6-string guitars mainly in the fact that their strings are tuned to produces lower frequencies, their strings are thicker, and typically there are only four strings, although models with 5 or more can be found. All of these factors must be taken into account in designing a pickup for an instrument.

C. Other Stringed Instruments

Electric violins, cellos, and mandolins are also made with pickups to allow the sound to be amplified. While many of these may use a microphone or a piezoelectric pickup, there are some that employ electromagnetic pickups. One type of pickup used is the Lace Sensor mentioned earlier. It is difficult to find many manufacturers of electromagnetic pickups for bowed instruments, but one such company is Bowtronics. They produce a single coil pickup that mounts temporarily on the end of the fingerboard of a violin or viola7.

IV. THE EBOW

A. What It Is and Why It Is Included

The EBow is an accessory for electric guitars that first came about in the late 1960’s and developed into roughly what it is today in the 1970’s8. The name is a result of its ability to function somewhat like a violin bow on the strings. It is a hand-held device that generates a magnetic field which is able to vibrate a guitar string and create a positive forced feedback loop with the pickups. The circuit behind the functioning of the EBow is shown in Figure 6 on the next page.The circuit shown comes from the original patent for the device. Although this circuit shows a variable gain operational amplifier, the EBow that is sold does not include this feature. The purpose of it was to allow the user to control the feedback level with a knob on the outside of the device. The circuit contains two coils that include permanent magnetic cores, one is for input, and the other for output. The input coil (seen on the left by the word IN) uses electromagnetic induction to produce a current from the vibrations of the string. This current is amplified by the amplifier circuit and sent to the output coil. The output coil then produces a time-variant magnetic field with the same frequency as the electrical signal from the input coil which sustains the vibrations of the string. The device is able to

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cause the string to vibrate even from what seems to be a resting state because of background noise and a strong positive feedback loop. The flux from the output coil also creates a strong effect on the signal produced by the pickups of the guitar. The two coils are placed in line with each other along the length of a string. They are kept in a fairly constant position by two grooves that the adjacent guitar strings (on both sides of the string being stimulated) settle into. This allows the player to easily find a position that will create a good tone, just by resting the device on the strings. Changes in the magnitude of the signals produced by the pickups can be produced by changing the distance between the coils of the EBow and the strings.

Fig 6. The EBow circuit, borrowed from U.S. Patent No. 4, 075,921 9. A 9V battery serves as the DC source.

A later model of the EBow includes a switch which reverses the direction of current flow through the output coil. This causes a magnetic field which dampens the fundamental frequency of the string vibrations while accentuating the harmonic frequencies.

V. CALCULATIONS TO MODEL PICKUP BEHAVIOR

A. Mathematical Equations

The electromagnetic principle that needs to be modeled in order to understand the workings of an electric guitar pickup essentially revolve around Faraday’s Law, which has already been introduced. When considering the emf generated in a coil, the basic equation must be multiplied by a factor N, representing the number of turns in the coil.

Working backwards, the flux through the coil can be found using the following equation:

This equation states that the magnetic flux through the coil is equal to the integral of the magnetic flux density over the area. If it is easier to find the magnetic field intensity than the flux density, this definition would be useful:

The most difficult step may actually be modeling the changing magnetic field with an equation for either B or H. Due to the vibrations of the string, the B field will be changing in a periodic state of decay. The string vibration occurs in all three dimensions, making the equation of its motion very complicated. If the string only vibrated up and down, the equation for B may look something like this:

This equation models a periodic wave with a linear rate of decay. It is doubtful that the rate of decay of the string’s vibrations is actually linear. The constant A refers to the amplitude of the magnetic flux density, B. The frequency in Hz is defined by f and the phase shift is defined by phi. In the damping component, td is the time it takes for the string’s amplitude to drop from its maximum down to zero at a constant rate. Defining the rate of decay with an inverse time relationship might be more accurate, but the aforementioned damping effect of the pickups complicates things further. Modeling the string vibration accurately could be a lengthy study in a different branch of physics.

VI. EXPERIMENTS WITH ELECTRIC GUITAR PICKUPS

A. Background of the Experiments

Most of the experiments were conducted using a Parker Nitefly solid-body electric guitar. The Nitefly has three electromagnetic pickups and one piezoelectric pickup. Of the electromagnetic pickups, there is a humbucker near the bridge, a single-coil near the neck, and another single-coil in between. These can be made to operate one at a time or in some combinations of two at a time, as mentioned earlier. The strings on this guitar are extra light gauge nickel-plated steel. For this experiment only the electromagnetic pickups will be used, and usually just one of them at a time. This helps to keep the experiment simple. At the input jack of the guitar, leads are attached to the ground and electromagnetic output wires. The easiest set-up was to plug a cable into the guitar, plug that into an input jack with nothing attached to it, then probe that jack. The

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ground and output wires are hooked up to an oscilloscope using a 10x probe. This can be seen in Figure 7 below.

Fig 7. The setup for the experiments. An input jack was connected to the magnetic pickup output lead with two wires soldered to it to allow easy probing for the oscilloscope. The orange lead (top) is for the output of the piezoelectric pickup. The PlusEBow can be seen resting on the strings.

B. Relationship Between Pitch Frequency and Voltage Signal Frequency

It is important in this experiment to realize what the sort of function to expect when measuring the output of the pickups. It may be easy for someone with little experience with sound to make the mistake of thinking that if a guitar is playing the note A440, that means that the note can be represented by a 440 Hz sine wave. If it were that simple there would be no distinguishing between the same note played on a piano. The reason that a guitar has a different timbre (sonic color) from a piano or even another guitar is because each note that is played is composed of not just the fundamental frequency, but also a number of harmonics. Harmonics are higher frequency waves that are generated simultaneously with the fundamental by the vibration of the string. While these waves are of a much lesser amplitude, they are what give the sound its character. One hypothesis to be tested is the idea that the voltage produced by the fundamental frequency vibrations will have the same frequency as that of the pitch that was played. After carefully dialing in oscilloscope settings that would allow easy reading (more difficult than one might imagine), the high E string was plucked with string depressed just behind the fifth fret to produce A440. The resulting waveform can be seen in Figure 8 below.

Waveform Resulting in A440 Plucked

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Fig 8. Waveform of approximate 440 Hz frequency. In this case the idea that the voltage signal coming from the pickups is the same as the sound wave was reinforced.

The period was measured from the oscilloscope to be approximately 2.3 ms. This results in a frequency of about 435 Hz, close enough to be considered a match. It is unfortunate that saving the oscilloscope data points to disk and creating an Excel plot does not generate the exact same image as is seen on the screen. On the oscilloscope one of the peaks was positioned almost perfectly on the dependant axis and the details of the shape of the wave are somewhat different. The signal would have been easier to measure if it were possible to zoom in on just one period without causing the waveform to move all around, but it did not stay in place when smaller time divisions were selected. As another check, the frequency of a signal was measured one octave up. It was more difficult to get good measurements, but the frequency was somewhere between 870-910Hz, close enough to the expected 880 Hz. At an octave below the signal did in fact have a period close to 220Hz (220-230 Hz measured), but the signal at that frequency was unusual in that it had three crests and three troughs within each period. It could be seen that they were still within the same period though because the three crests and troughs were all at different heights. This effect may suggest that the harmonics play a stronger role in the character of the signal at lower frequencies, or perhaps just on the thicker strings.For many guitars there is no difference in construction between the different pickups on one guitar. What makes the differences in the timbre of each pickup is the position of the pickup along the length of the string. The strengths of the harmonics and even whether they exist or not in the voltage signal depends on what part of the string is being monitored by a pickup. On a Fender Stratocaster there are three identical single coil pickups (although newer models may have some differences)10. The one positioned closest to the bridge has a timbre that is “tinnier” or brighter sounding, because the upper harmonics are sounded strongly near the ends of the string. The output of the pickup closer to the neck sounds more mellow because the fundamental frequency is a more significant contributor to the sound relative to the harmonics. Knowing this, one might hypothesize that the magnitude of the voltage representing the harmonics, especially the higher

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order ones, would be less coming from the neck position single coil than from the bridge position humbucker.Without any filtering or amplification, the signal from even just one pitch can be very hard to read. What is observed appears to be many sinusoidal waves occurring at the same time, as if many notes were being played. A picture of the waveform can be seen in Figure 9. They are similarly shaped but that is a rough estimate, because they are constantly changing and die out in a matter of a few seconds. Initially it was believed that the number of waves was due to the upper harmonics generated by the strings.

Fig 9. A picture of a waveform produced in the early stages of the experiment. Two waves can be seen on the screen at once.

Two facts suggest otherwise. After enough adjustments on the oscilloscope, a view was established that showed just one function that moved sideways on the screen. It started out large and gradually faded. A snapshot illustrating this can be seen in Figure 10. Also, when the strings were vibrated with the EBow, a device capable of sustaining the strings indefinitely at the same level, one solid wave was observed. The conclusion drawn from this is that the oscilloscope sometimes responds to a signal that is rapidly changing by showing different instances of it at various times all at once. The harmonics are still present certainly but their effect does not seem to be as pronounced as what was expected.

Fig 10. A waveform of the output seen when the same string is plucked, but a longer time scale is used.

C. Relationship Between Height of Pole Pieces and Magnitude of Output

The humbucker pickup on the Nitefly is equipped with adjustable pole pieces. With nothing but an Allen wrench the distance between each individual pole piece and its corresponding string can be tweaked. A closer proximity to the strings will result in a greater change in the magnetic flux, and in turn, a greater induced current. Also, for more dramatic changes across the whole pickup, there are positioning screws for each electromagnetic pickup to raise or lower the entire pickup. Using this capability, this next experiment attempted to study the relationship between the output of the pickups and the distance between the magnets and vibrating strings.While originally it was intended for this experiment to be run without the EBow, it was later determined that using the EBow was by far the most convenient way to apply a constant stimulus to the strings. Without that, an accurate comparison could not be made. By resting the EBow on the strings at the same place over the pickup each time, it was possible to keep the string vibrations constant. Any changes in the damping of the strings due to the proximity of the magnet was neglected.

D. Effects of the EBow on Output Voltage, Qualitative

A final experiment was included which examines the output of the pickup when the EBow is applied to it. The device can drastically increase the volume that can be obtained simply by plucking the strings. The first part of this experiment was qualitative in nature; it only sought to describe the unusual characteristics of the signal produced using the EBow. As noted previously, the EBow creates a signal of constant magnitude that is much easier to measure than the signal created by a plucked string. With the tone knob turned all of the way down, the volume all of the way up, and the middle single-coil pickup selected, the EBow was rested above the A string of the guitar, and operating in normal mode. The output appeared to be like a sinusoid with a couple lumps in it. These lumps repeated themselves nearly identically within each period. The magnitude was constant, remaining at just over 100mV (a 10x probe was used). It was therefore much larger than any signal obtained by merely plucking the string. The frequency was about 330 Hz. This first observation can be seen in Figure 11 in the form of an Excel graph created from the oscilloscope data.It was demonstrated that use of the EBow does result in a marked increase in voltage of the output, and therefore volume. No level of plucking seemed to be able to produce an output with magnitude greater than 20mV, even for a brief, passing moment.A very interesting result was found when the tone knob was turned up. The shape of the signal gradually lost its smoothness and very high peaks resulted. To the guitar player this results in a signal that is often unpleasant to listen to, but provides an impressive range of sounds. This transformation is illustrated in Figure 12.

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E-bow on the Open A-String

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Fig 11. First oscilloscope waveform of pickup output stimulated by the EBow. EBow is in normal mode, the open A string is vibrated with the tone control turned all the way down and the middle single-coil pickup in operation.

E-bow Output with Tone Knob at an Intermediate Setting

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Fig 12A. As the tone knob is turned up the lumps in the wave shift and peaks began to sharpen.Fig 12B. With the tone knob all of the way up the wave becomes quite jagged with very high peaks reaching a magnitude almost twice as great as the wave output with the tone knob turned all of the way down.

A feature found on the PlusEbow that was not built into the original model is the “harmonic mode”. The next experiment was conducted to observe the differences in outputs produced by the EBow in harmonic mode compared to normal mode. As can be seen in Figure 13, the EBow produces a smoother wave when operated in the harmonic mode with the tone knob turned all of the way down.

E-Bow in Harmonic Mode With Tone Knob Turned All the Way Down

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E-bow in Harmonic Mode With Tone Knob All the Way Up

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Fig 13A. Output of pickup with the open A-string stimulated by the EBow at the pole piece of the middle position pickup. The tone knob is turned all the way down.Fig 13B. On the bottom the same output is shown with the tone knob turned all the way up. Note the extra changes in inflection for each period of the wave.

The lumps that were found when using normal mode are almost completely smoothed out. The magnitude is slightly less in harmonic mode than it was in normal mode. What is really interesting however, was the difference in frequency between the output in harmonic mode and the output in normal mode. In harmonic mode, the frequency of the signal becomes 540 Hz, up from 330 Hz. These readings were both taken by using the EBow to sound the A-string open, which should create a pitch two octaves below A440. Even in normal mode the EBow increases the frequency of the output signal above the expected 110 Hz.The extra curves in the waveform produced by using the EBow in harmonic mode with the tone knob turned all of the way up shows that it really does emphasize the harmonics more in comparison to the fundamental frequency, since they are such a strong contributing factor to the wave.

E. Effects of Distance Between Pole Pieces and Strings on Output

The other part of this experiment was to measure the magnitude of the voltage that is produced with different distances between the strings and the magnetic pole pieces. First the middle position single-coil pickup was tested. By tightening or loosening screws on each side this pickup can be raised or lowered. It was decided that measuring the small changes in distance from the strings to the pickup would be too inaccurate. Since there is a direct relationship

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between the number of times the screws are turned and the change in distance to the strings, a comparison of voltage of the pickup output against the number of times the screw is turned would have the same relationship as a graph of the voltage against the actual distance. It was decided that the height that the pickup was at before this experiment would be deemed zero, and negative turns would be turns resulting in the pickup moving away from the strings. The data shown in Table 1 was collected.

TABLE I

Single-Coil, Whole Pickup Turns Max. Magnitude (mV)

-5 63-4 70-3 75-2 81-1 920 1001 1092 1223 1444 154

Data of experiment examining effect of changing pickup height relative to the strings on the magnitude of the signal produced by the pickup. Turns refers to the number of times the screw was turned to raise or lower the pickup from its initial position. On the fourth turn in the positive direction the screw was becoming very difficult to turn and that was chosen as a stopping point for fear of breaking something

There is a clear reinforcement of the concept that the less distance there is separating the strings from the pickups, the greater the signal magnitude. A graph of this data is shown in Figure 14.

Signal Magnitude vs. Pickup Magnet Heighty = 101.83e0.1x

R2 = 0.9928

020406080

100120140160180

-6 -4 -2 0 2 4 6

Turns From Beginning Position

Vo

lta

ge

(m

V)

Fig 14. Graph illustrating the relationship between distance from pickup to string and signal magnitude.

Although the trend was fairly weak and inconsistent, there was a slight pattern of the changes in magnitude becoming greater for each change in distance the closer the pickup got to the strings. An attempt was made to fit an exponential function to the data. An R^2 value of 0.99 suggests a good fit, but the equation was not that far from being simply linear. A linear regression was able to produce a function with an R^2 value of 0.96. Finally, a similar study was done of the humbucker pickup. This time only the pole pieces corresponding to the string being played were moved. Since it is a humbucker pickup (double-coil), this required moving two pole pieces each time. Each pole piece is threaded with hexagonal indentation

on top so that they can be easily raised or lowered simply by using an Allen wrench. This experiment was run in a similar manner to the last. The pole pieces were never dropped below their starting height since they were nearly flush with the bobbin to begin with, so each turned exposed more of the pole piece and brought it closer to the pickup. The data collected is contained in Table 2.

TABLE II

  Pole Pieces on Humbucker

Turns Max. Magnitude (mV)

0 851 902 943 1004 1095 120

Data collected in experiment examining the effect of raising only the pole pieces of the pickups on the magnitude of the signal coming from the pickup.

Some basic observations were made during the experiment. First of all, turning the pole pieces produced a lot of shavings of a waxy substance. Many pickups today are wax potted, that is, wax is poured into the holes that the pole pieces are to be fit into to keep the pole pieces from vibrating11. It is easy to see why this could be important since the vibration of ferromagnetic elements is what induces the current in the first place. Unwanted vibration could result in unwanted distortion. Secondly, when the pole pieces were raised up a lot it could be seen that they are not the same diameter all of the way through. The top is a wider sort of head connected to a narrower neck. It is unlikely that the pole pieces were meant to ever be raised more than a quarter of an inch or so above the bobbin. It is possible to raise the entire humbucker pickup so that the magnets can be brought closer to the strings without such a protusion from the bobbin. Last of all, when the pole pieces were turned a sixth time, the output that they created in conjunction with the strings and the EBow was very unstable. The wave was always shifting and even the audible sound generated from the vibration of the strings with the guitar unplugged seemed different. It is possible that when it was that close to the strings the magnet was having a stronger effect on their vibration, as in the damping effect mentioned earlier. A graph was made of this data as well and it is shown in Figure 15.

Signal Magnitude vs. Pole Piece Height on the Humbucker

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Turns Up From Beginning Position

Vo

ltag

e (m

V)

Fig 15. Graph of relationship between height of pole piece and the signal magnitude.

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The results of this experiment were similar to the results of the previous experiment. The magnitude increased as the distance to the magnets decreased, and that effect increased slightly as the separation distance became less.

VII. CONCLUSION

The purpose of this paper was to explore the principles of electromagnetics as they apply to musical instruments and see how they are used to achieve different sounds. It is important to know the theory, to understand how something called electromagnetic flux changes inside a coil and creates a current in it. And it is also important to be able to use equations to describe such relationships. But until one sees these principles in action there are always gaps in the knowledge, and that persons idea seems like it is merely an abstract vision. To fully comprehend these principles, the value of witnessing their effects should not be overlooked, and that was the main goal of this project.

VIII. REFERENCES

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11 Stewart MacDonald Onlinehttp://www.stewmac.com/tradesecrets/electronics/ts26fralin/ts26fralin.html

Works Consulted

Halliday; Resnick; Walker “Fundamentals of Physics” 5th edition, John Wiley & Sons Inc.

Duncan. “Electromagnetic pickup for a stringed musical instrument having

ferromagnetic strings and method”, U.S. Patent No. 4,524,667

Tumura. “Electric stringed instrument having a device for sustaining the vibration of a string and an electromagnetic driver for the device”, U.S. Patent No. 5,585,588

Tumura. “Electromagnetic pickup for an electric stringed instrument”, U.S. Patent No. 5,508,474

Brain, Marshall “How Electric Guitars Work”,www.howstuffworks.com David, John; Widzer, Josh; Rosner, Brad. “Basic Workings of a Single-Coil Electric Guitar Pickup”, http://wildcat.phys.nwu.edu/classes/2002Fall/Phyx135-2/Projects/Guitar_pickup/electric_guitar_pickups/basicworkings.html

fact-index.com, http://www.fact-index.com/p/pi/pickup.html

Arnold Magnetics, http://www.arnoldmagnetics.com/products/alnico/

GHS Strings Web Site, http://www.ghsstrings.com/index3.htm

IX. BIOGRAPHY

Matthew R. Edwards is graduating from Calvin College in Grand Rapids, MI with a B.S.E. with a concentration in electrical/computer engineering. He is currently seeking employment. His interests include digital logic and audio systems. This last year he was the president of the Calvin chapter of the IEEE and is an Engineer-In-Training.

1 Anonymous “For those about to rock, we salute you” Technology Review. Cambridge: June 2002. Vol. 105, Iss. 5;  pg. 104

2 DiMarzio. “Electromagnetic Pickup for Stringed Musical Instruments” U.S. Patent No. 5,399,802

3 Hayt, William H. “Engineering Electromagnetics” 6th edition, Tata McGraw-Hill 2001 p. 288-291

4 DiMarzio. “Electromagnetic Pickup for Stringed Musical Instruments” U.S. Patent No. 5,399,802

5 DiMarzio. “Electromagnetic Pickup for Stringed Musical Instruments” U.S. Patent No. 5,399,802

6 Lace, Jeff. “Magnetic Field Shaping in Acoustic Pickup Assemblies”Sensors 1995. Vol. 12 Iss. 3. pgs. 55-56 7 Bowtronics Web Site,http://members.aol.com/bowtronics/index.htm

8 Official EBow websitewww.ebow.com

9 Heet, Gregory. “String Instrument Vibration Initiator and Sustainer”, U.S. Patent No. 4,075,921

10 GM Arts Home Page,http://users.chariot.net.au/~gmarts/index.html

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