1. The result shows that as the frequency increases, the output voltage decreases, effectively allowing only low frequencies to pass. Guitar Electronics: From Humbucking to Tonal Control Rob Schweitzer Mentor: Dr. Ed Deveney Department of Physics, Bridgewater State College, Bridgewater MA, 02325 Abstract: The essence of sound, vibrations, begins in the case of a guitar with a plucked string. Our study centers on how that vibration is then be picked up, transformed, amplified and filter electronically by the inner working of an electric guitar. We have worked theoretical and quantitative models of all aspects of this process and have built our own guitar electronics. We use an existing humbucker – first explaining how this ‘pickup’ works – then built amplification and filtering electronics using both passive and active (op-amps) circuits. We also wrote data acquisition software code to analyze using Fourier analysis how our entire system worked and in particular the amplification and tonal (frequency filtering) control. This is a fun project with physics from sound to state of the art electronics that is affordable and ideal for students at many levels including high school. How does the tone knob on my guitar change the sound? The tone knob on an electric guitar is in fact nothing more than a simple low-pass filter, a basic and extremely useful device in analog electronics. The basic function of a low pass filter is to allow low frequency signal to be transmitted, and effectively negate all high frequency signals. What does the signal coming from the pickups look like? In an ideal world, each note from a guitar would be a perfect sine wave at the frequency of the note. However it is in fact a very complicated wave that is a linear combination of an infinite number of harmonics of the fundamental frequency, as Fourier Analysis can show for all periodic functions. If a string were to vibrate at a set frequency, one could expect a sine wave at that frequency. However the wave is quite a bit more complicated. The wave below was output by a guitar string into a humbucking guitar pickup using LabView: Pickups: How do they work? A pickup has a permanent magnet that polarizes and makes a magnet on the metal string. When this string vibrates, an alternating current is induced in the coil or wire around the permanent magnet, creating a signal to be amplified. Magnetic field lines from the string in blue. Humbucking: The downside of a pickup is that it can pick up external noise. To counter this, or to “buck the hum”, two pickups are wired together with magnets in opposite directions. This way, external noise is cut out, and vibrations from the strings are doubled. Magnetic field lines from the string are in blue; noise is in purple. Current from strings in green, from noise in pink. Tone adjustments with the filter: The following diagrams show how the filter changes the output signal as resistance is increased. The upper left is the input signal, upper right the output (amplified), and lower portion is the Fast Fourier Transform of the output. Passive Low-Pass Filter: The capacitor lets high frequencies to go to ground, and allows low frequencies to pass. We show that the voltage divider has a result of where and Active Low-Pass Filter: The active low-pass filter works similarly, however it is built into an operation amplifier. It amplifies the low frequencies while not amplifying (or even reducing) high frequencies. We show that where and finally Active vs. Passive Low Pass – Which to use? Use for example an active low pass filter that would amplify by a factor of 10, and then after a passive add an amplifier that amplifies by a factor of 10 as well. If R2 of the active filter is equal to the R of the passive filter, the amount of amplification for each frequency is the same. However to adjust how much high frequency each filter adjusts you need to adjust the resistance. When doing this with the passive, the amount of amplification for even the lowest frequencies is still a factor of 10. However by adjusting the resistance in the active filter, you adjust the level of amplification, which would be very undesirable in a musical amplification. You would not want to adjust your tone on stage and have your volume suddenly shoot through the roof!