STRINGS and MAGNETS and COILS

These notes were in the last 3 pages of the old "brown catalog" first printed about 1982. It will be fun to add some good computer graphics to this as soon as time permits.

String Motion

When the pick releases the string it causes two ripples to move along the string, one toward the bridge and the other toward the nut or fret. Figure 1 shows typical string ripples at several intermediate stages during the first half cycle of vibration.

The ripples are reflected from the nearest fixed end of the string then travel along the
string to the opposite fixed end where they are reflected again.

Viewed along the string the motion is an elliptical path that changes in orientation as its amplitude decays. Figure 2 shows the string orbits during the first few cycles of oscillation.

The complex motion shown in Figure 1 and 2 is equivalent to a sum of harmonics that varies during the attack and decay of a note.

Figure 3 shows the fundamental and the first 4 harmonics and also the relationship between a note and the fifth and the octave above it.

The fundamental of the note is at 100Hz; its harmonics occur at multiples of that frequency. The fundamental of the octave is at 200Hz, twice the frequency of the lower note.

.Every harmonic of the octave agrees with every other harmonic of the lower note.

..The fundamental of the fifth above the note is at 150Hz, 3/2 the frequency of the lower note.

...Every other harmonic of the fifth agrees with every third harmonic of the lower note. ....The small circles show the harmonics in agreement.

In acoustic instruments the string motion is coupled to the soundboard by the bridge.

. Only those components of the string motion that can move the bridge up and down will be amplified (because the bridge cannot move sideways - Figure 3)

.. This lack of symmetry in the coupling of string to the soundboard contributes strongly to the complex tone quality of plucked acoustic instruments.

...Our Hi-A label was derived from " high asymmetry" and the ability of our polyphonic designs to sense string motion in the same way as the bridge of an acoustic guitar.

The resonances of the acoustic body also contribute to the tone quality of the instrument by
enhancing some of the harmonics of each note.

Pickups

In most electric instruments the string ripple is sensed by magnetic pickups. These pickups usually consist of magnets, coils, core materials and/or polepieces.

.The magnetic field of the magnet links the elements of the pickup (magnets, coil, cores, polepieces,etc.) and the string.

..Changes in the string position cause small changes in the total magnetic flux linking the pickup elements and the string.

...As the string gets closer to the magnets or polepieces, the total magnetic flux linking the elements of the pickup increases.

....The pickup coils produce electrical pulses that correspond to changes in the magnetic flux that passes through the coils. When the string moves suddenly from position (a) to position (b) and stays there, the voltage signal at the coil ends rises and then settles back to zero.

.....Together, the pickup coil and its core materials are a real inductor, meaning that it has some capacitance, it is not a pure inductance.

......Because of the capacitance, which comes from the proximity of each wire turn to the others, the real inductor will have a resonance

.......Its impedance will show a peak (maximum) at that resonant frequency.

.......The resonance of the pickup coil can enhance some harmonics of the note being played and change its tonality.

Aperture

The length of string sensed by the pickup contributes strongly to its tonal quality of the pickup.

This "window" (Figure 4) through which the pickup "looks" at the string ripples is called the "aperture" of the pickup.

Narrow aperture pickups(single coil) sense the shuttling string ripples most accurately and yield more clearly defined sound.

Wide aperture pickups ("humbuckers") sense the ripples at a different time at each poletip.

The combination of both signals can diminish or even cancel some of the upper harmonics while enhancing the lower harmonics of the note.This effect produces the mellower tonality of humbuckers.

When the separation between sensing coils is wide enough (like in a Strat in the intermediate switch positions) the cancellations between pulses from the same ripple can be clearly heard as " out-of-phase" sounds.

Pickups coils are real inductors with resonant peaks usually in the audio range.

Their impedance rises from the DC resistance value to a maximum (at the resonance)of several hundred thousand ohms at several kilohertz and drops again at higher frequencies.

The inductance of the coil must be measured at frequencies well below the resonance to avoid the effects of coil capacitance.

The value of the winding capacitance labeled C in Figure 5 and the high frequency losses to magnets, core materials, shielding and other things near the coil (AC resistance) cannot be measured directly but can be implied from the impedance curve.

The frequency and Q of the resonant peak are the major features of the pickup response curve. The Q value of the pickup is the width of its response curve 3dB below the maximum divided into its resonant frequency.

The higher the Q value the narrower and taller the resonant peak.

Figure 6 compares a high Q design (Strat) with a low Q design (1C).The Strat features a treble peak at the coil resonance. In the 1C that peak has been damped out the response covers a wider frequency range.

The square wave magnetic pulse test shown of Figure 7 is a slalom course for pickups. The test pulse at left switchesquickly from one magnetic polarity to the other 2000 times per second. The actual switching was too fast for the film and did not leave a trace. The dotted lines are hand
drawn. The outputs of the pickup coils in the magnetic field are displayed on the oscilloscope. The pickups are loaded with a 500K-ohm resistor.

The 3A follows the test pulse most accurately, showing a small, well-damped oscillation after each "gate". Its frequency response is smooth and free of resonances in the audio range.

The 5J and 8S pickups also show well-damped recovery as they follow the test pulse. Both have a smooth frequency response very similar to the 1C.

The Strat or LC40 curves show oscillation that damps out slowly. This is equivalent to a peak in the frequency response curve at the resonant frequency.

GH is a patented Gibson humbucker with an intermediate frequency response curve.

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