# Design

This webpage examines the components incorporated into the system's design. Each section outlines a major component, states and explains the design requirements, analyzes researched alternatives, and also documents and justifies the final decision reached by the team.

Note: All pictures link to a full-size version.

## Pickups

Post-Project Update: The team continued with the polyphonic (specifically quadraphonic) pickups from the PowerGig guitar. The pickups were satisfactory in performance, and delivered the signals to the microcontroller.

One aspect of the system that the team considered was how to analyze the signals generated by the strings. Through the use of pickups, string vibrations induce a current across a magnet. Pickups are necessary in order to translate guitar string vibrations into an AC signal which will be manipulated in the microcontroller. Given the nature of the project, the team needed pickups that allow each string’s frequency to be individually analyzed. Because each string is tuned individually, each string required a distinct AC signal across the pickups.

Aside from the distinction between the strings, the pickups needed to exhibit a high enough impedance so that a signal can be realized when the strings of the instrument are plucked. Typically, standard guitar pickups exhibit an impedance of anywhere between 6k to 17k ohms. The figure to the right shows typical DC resistance for different wire gauges, assuming wire length is 1000 ft.1 From this data, DC resistance can be interpolated for any coil size. For example, a standard stratocaster pickup is wound with 7500 turns of 42 gauge wire, which yields a DC resistance of about 5.5k ohms. DC resistance can be used as a substitute for the measurement of pickup impedance as the two concepts are closely related. DC resistance is used for DC measurements whereas impedance is a two-dimensional quantity used in AC circuits. Impedance is more difficult to measure as inductance and capacitance effects must also be taken into consideration.2 As a result, DC resistance measurements are often used to suggest the impedance of a pickup coil. A higher impedance yields a more “crisp” sound as the resonant peak of the pickup is more prominent.3 Due to the fact that the pickups used to receive the AC signal were not used for actually outputting the signal to an amplifier, the team only required that the pickup coil impedance was high enough to realize an AC current from string vibrations. Due to the breadth of technologies used for guitar pickups, the team narrowed down their decision through two criterion. First, the pickups chosen were able to allow each string to be analyzed separately. Second, in order to align with the team’s value on stewardship, cost will be the driving factor behind the purchase of pickups that meet the first criterion. The team holds a sovereign belief that all resources should be used in an efficient manner. Therefore, purchasing functional pickups at a low cost exhibits economic stewardship by reducing the budget for the project.

### Standard Pickups

Standard pickups are by far the most ubiquitous and widely used pickup on the market. They consist of magnets that rest under each guitar string. Wrapped around these magnets is roughly 7000 to 8000 feet of copper winding. As seen on the right, the coil windings are wrapped around the entire set of magnets which are housed in an insulated housing called a “bobbin."4 When a string is plucked, the magnetic components of the string (nickel and iron) cause the magnetic field in the pickups to fluctuate due to the oscillation of electrons. This fluctuation creates the AC signal to be realized by the microcontroller. Because standard pickups do not contain coil windings for each magnet, the string vibrations can not be analyzed individually without very complex signal processing techniques that break down a chord into individual note components. Because of this, standard pickups did not meet design requirements and were therefore not considered for use in the project.

### Polyphonic Pickups

Polyphonic technology is also commonly used in guitar pickups. Similar to standard pickups, polyphonic pickups also contain a magnet for each string. However, the distinction from standard pickups lies in that polyphonic pickups consist of a separate coil winding for each magnet (shown right).5 This feature allows for each string to be analyzed separately. Each individual pickup generates an AC current based on the vibration of the string above it. However, because the magnets are close together, some signal bleeding occurs between the individual pickups. When a string is plucked, the induced voltage will be largest in the pickup directly beneath the string, but a small amount of voltage will be realized on the adjacent pickups. Because the string spacing on a bass guitar is larger than a standard 6-string, less voltage bleeding or “cross-talk” will occur. However, while cross-talk will not significantly affect signal measurements (as each string is analyzed separately in a cascading order), this shortcoming is noted by the team. Because polyphonic pickups support the analysis of string vibrations in a separate manner, the team selected this option.

### Piezoelectric Pickups

The third pickup variety that the team looked into is piezoelectric pickups. A cross-section of the piezoelectric pickup is shown on the right.6 These pickups are generally used in hybrid acoustic/electric guitars. Piezoelectric technology revolves around the concept of the translation of a mechanical vibration into an electric charge.7 In piezoelectric pickups, a tone is generated by the vibration in the guitar body when a string is plucked.8 Because the tone generated relies on the vibration of wood, acoustic guitars are best suited for piezoelectric pickups as the body is hollow. In a hybrid acoustic/electric guitar, the piezoelectric tone is what is sent as an output to the amplifier, thus creating the “electrical” aspect of the hybridization. Due to the fact that the guitar used in the project is an electric bass made from pressed wood, piezoelectric pickups did not meet the design criteria and were therefore not considered further for the project.

### Decision

After analyzing pickup alternatives through the lens of the design requirements, the team deduced that polyphonic pickups were the only feasible option. With cost as the driving factor, the team began looking for a set of aftermarket polyphonic pickups. It was quickly realized that the market for a standalone set of polyphonic pickups was small. Pickups are generally sold as an integrated guitar component so locating a standalone set was difficult. Furthermore, many aftermarket pickup sets are sold at a price that exceeds the team’s budget. In looking at the purchase of polyphonic pickups, the team narrowed down to the following possibilities:

### Component Alternatives

 Pickup Polyphonic Supports Bass Guitar String Spacing Inexpensive Roland GK-3 Yes No No Ubertar Quad Yes Yes No PowerGig Controller Yes Yes Yes

The Roland GK-3 pickup set is priced at \$170 and contains six polyphonic pickups together in a plastic housing.9 Since the bass guitar only consists of four strings at a greater spacing than the standard 6-string, the Roland pickups are not considered to be a feasible option as the deconstruction of the pickup set into separate coils to match string spacing may negatively affect pickup operation.

The Ubertar Quad pickup set consists of four separate coils that match the spacing of the strings on a bass guitar. This option meets design requirements and allows for easy installation and utilization. However, the Ubertar Quad is priced at \$135 and is outside of the financial scope for pickup purchases.10

The PowerGig Guitar Controller is a peripheral device used for the video game “PowerGig." Similar to the Guitar Hero games, PowerGig revolves around the concept of playing a song by strumming the notes that appear on screen. What separates PowerGig from Guitar Hero is that instead of pressing a combination buttons and strumming a plastic bar, the user strums actual strings and utilizes finger-position on the fretboard in order to play the notes or chords that appear on screen. In PowerGig, the user is essentially playing a real guitar while playing the music on the game. In order to for the game to determine whether or not the correct notes are strummed, the controller contains a set of integrated polyphonic pickups for the purposes of making the distinction between which string played which note. At around \$40, the team opted for this option and decided to strip the pickups from the plastic guitar for use in the project. Unlike the Roland GK-3 pickups, the polyphonic pickups in the PowerGig are easily taken apart and can be modified to fit the four string spacing of the bass guitar. The decision matrix above shows the decision process. The decision to purchase the PowerGig controller and strip the pickups from it aligns with the teams mission to create a reliable product. The PowerGig pickups are shown on the right. The standard pickups are on the bottom wrapped in a sheet of copper, and the hexaphonic pickups are on the top.

## Microcontroller

Post-Project Update: The team selected the BeagleBone Black as the optimal microcontroller for the project. The table below illustrates the qualities the team examined when selecting a microcontroller.

### Alternatives

 Microcontroller # of ADC Input Channels Sample Rate (kHz) Includes FFT Optimization Resolution (bits) Power Consumption Processor Speed (MHz) Arduino Uno 12 10 No 10 130-800 mA @ 5V 16 Arduino Due 6 10 No 10 130-800 mA @ 3.3V 84 ADS8556EVM 6 630 Yes 16 2.6W 100 BeagleBone Black 8 200 No 12 210-460 mA @ 5V 1000

At \$39, the Arduino microcontroller is a general use microcontroller that was developed as a resource to educate beginners on how to utilize microcontrollers. As a result the specifications of this microcontroller are modest as is reflected by the microcontroller decision matrix. The Arduino Uno has a 10 bit ADC and a 5V input voltage threshold. The Uno is capable of sampling at a rate of 10 kHz.12 This configuration yields a sample resolution of 4.9 mV.

The Beaglebone Black (BBB) is another alternative considered by the team. Like the Arduino, Beaglebone boards are designed as multi-purpose microcontrollers that can be utilized in a wide variety of applications. Sold at \$45, the BBB contains an ARM AM3358 processor that encompasses an 8-channel ADC and exhibits a 12-bit resolution. Additionally, the processor’s ADC supports up to 200k samples per second.

The team also examined the ADS8556EVM, an ADC evaluation module (EVM) from Texas Instruments. This board offers a 16-bit ADC with six channels, which is more than what is needed for a four-stringed bass guitar. Tim Theriault, the industrial consultant for the team, recommended the use of a Texas Instruments evaluation module for the microcontroller. Tim’s advice played a significant role in the decision for which microcontroller to use. Although the signal processing capabilities of the Arduino boards and the Beaglebone Black may be adequate, Tim stated that qualities such as the high processing power of the ADC and the tailoring of EVM applications for audio processing make Texas Instruments microcontrollers the ideal solution. Furthermore, Texas Instruments sponsors a University program where students may receive evaluation modules, development environments, and other product samples free of charge.

The table above illustrates the specifications considered when selecting a microcontroller. It is important to note that the attractiveness of receiving a high quality microcontroller for no cost, coupled with Tim’s recommendations resulted in the team’s decision to work with Texas Instruments in order to receive an evaluation module that meets project specifications. However, the team was unsuccessful in contacting Texas Instruments, and so changed gears to use the BeagleBone Black, which suited the team's needs.

## Tuning Motors

Post-Project Update: The final motors used to turn the tuning mechanism were Black & Decker screwdrivers from Lowe's. These were required because the amount of torque required to turn the tuning mechanism was approximately 36 in-lbs, more than any inexpensive motor on the market. The large torque meant the team had to sacrifice a small footprint and low current draw in order to be able to tune the bass.

Below are the alternatives the team considered prior to the Spring Semester:

### Alternatives

 Servo Motor Sufficient Torque Meets Footprint Requirements Current Draw Under 800 mAh Supports Continuous Rotation Inexpensive FS90 No Yes Yes Yes Yes HS-322HD3 Yes Yes Yes Yes Yes GWS S35 Yes No Yes Yes Yes HS-422 Yes Yes Yes No Yes HS-645MG Yes Yes Yes Yes Yes

Stepper motors are essentially brushless DC motors that divide rotation into several small steps The size of the “steps” can range in degree. Some stepper motors operate on upwards of 10 degree increments, while others can split rotation into steps as small as 1.8 degrees. The figure on the right highlights the construction of a stepper motor. Notice that the grooves in the rotor are what dictate the number of steps in a rotation. Because the project design requirements specify that the guitar must be tuned to within the just-noticeable difference, stepper motors are not considered a feasible option as they are generally heavy, loud, and their rotation capabilities are limited by the degree of each step. It is possible that even a 1.8 degree step may not be small enough to accurately tune the guitar to a desired note with a +/- 2 cent error. Because stepper motors divide rotation into steps, the team quickly shifted its focus on other motor options.

Servo motors use a sensor to provide position feedback. Servos are generally used for very precise rotation applications and as a result, many servo motors will only turn 180 degrees in either direction. Still, some servo motors are also used to drive components and support continuous rotation. The team requires that the motors be able to rotate continuously as knobs may need several full turns in order to correctly tune the guitar. Many servos are made from plastic material. This is attractive to the team as a lightweight motor is a design requirement. Servos also do not make much noise when rotating and although quietness is not a design requirement, the team maintains the goal of purchasing quiet motors if possible.

After considering several different servo motors for use in the system, the team created a simple decision matrix to identify the best option. Several servo motors that initially seemed to meet design requirements were analyzed in depth. From the options considered, both the HS- 322HD3 and HS-645MG fell within the bounds of system design requirements. The HS-645MG did not, however, fall within the financial scope of the project as it costs over \$30. Therefore, the HS-322HD3 was chosen as the cost was significantly lower than the HS-645MG. The HS-322HD3 is sold for only \$10.

## Power Supply

Post-Project Update: The team utilized four screwdriver batteries, which had been supplied with the screwdriver motors used to turn the tuning mechanism. In order to be able to supply all four motors with current, the batteries were arranged as shown on the right: two parallel sets of two batteries. This provided a large enough voltage to power the H-Bridge and a large enough current to turn all four motors simultaneously.

## DSP Algorithm

Post-Project Update: The team continued to use the Fast Fourier Transform (FFT) as the algorithm of choice. A C++ library for the FFT, called the Fastest Fourier Transform in the West (FFTW), was freely available, and so was utilized.

The tuning system has to be able to quickly and efficiently analyze the frequency of each individual string. The speed and the quality of this information is based heavily on the type of frequency analysis technique chosen. The algorithm will be implemented on a sample of data collected by the pickups from the analog input of the microcontroller. The algorithm will have to analyze these samples fast enough so that it can instruct the motors on what to do and then continue to update that information based on feedback from the algorithm. The system will function by repeating the aforementioned process for each the four strings on the instrument. In order to tune the guitar in less than 15 seconds the system will have to implement the algorithm in excess of 20 times. The quality of the frequency analysis is dependent on the amount of samples that are provided. The microcontroller specifications will determine how fast the system is able to sample and therefore will affect how many samples the algorithm has to analyze the frequency. The chosen algorithm shall be able to provide results that are accurate based on a limited number of samples.

### Alternatives

The Goertzel algorithm is among the most efficient signal processing algorithms. It is an adaption of the Discrete Fourier Transform (DFT) that analyzes individual terms. This algorithm recognizes the presence of a specified frequency. As a result it is not very useful for application in this system. The system must be able to analyze a signal and determine what frequency it is at. This algorithm would provide information on what frequency the string is not. Several forms of the Goertzel Algorithm are shown on the right.

The Fast Fourier Transform is similar to the Goertzel in that it is also an adaption of the DFT. However, the FFT yields all of the frequencies present in the signal as a result. This algorithm is fast compared to its DFT counterpart because it was created to simplify the operation. The FFT is a common DSP algorithm implemented in many devices that utilize DSP technology. As a result the FFT algorithm is commonly optimized in DSP microcontrollers for general use. These factors contribute to making the FFT the most efficient choice for the DSP algorithm.

The wavelet transform excels at analyzing signals that vary slowly with time. However, this algorithm is also good at analyzing signals with higher frequencies.

The FFT was determined to be the best alternative because it is the fastest of the algorithms considered. Speed is the primary requirement for the algorithm. This decision is not surprising because as mentioned before, the FFT is very common in DSP applications. The FFT is easier to handle by nature and is optimized to be even faster on many microcontrollers.

## User Interface

Post-Project Update: The team desired to utilize a simple interface that was easy to navigate and understand. Because of this, the team selected a small 16 x 2 character LCD screen with mechanical buttons to navigate the user interface.

### Alternatives

A touchscreen interface would be a modern feature on the tuning system. The touchscreen would be mounted on the body of the guitar and provide the user with on-screen buttons for starting and stopping the tuning process, selecting a tuning, and creating presets.

Another alternative would implement a small LCD screen with mechanical buttons to navigate the interface. The LCD screen would display information regarding the tuning process, selecting a tuning, and creating presets. This was the alternative the team selected, as noted above.

A simpler display involves a hex display that would show the tuning for each individual string. Buttons would allow switching between and creating presets. A physical switch would activate or deactivate the tuning sequence.