Engineering Dimensionally Alternative Business Analysis
Practical Pickup Measurements
In this area, this is getting into measuring and resolving what really happens. Earlier studies in this series have shown that there is a quasi-stable magnetic field in the vicinity of an electromagnetic guitar pickup caused by the internal permanent magnet(s), and that a voltage is produced in the pickup coil that is proportional to the relative change in flux density of the magnetic field due to the string moving relative to the permanent magnet – and that sounds very Einsteinian!
In more simple English any time related change in magnetic flux density would produce a voltage in the pickup coil. How the flux density is changed is now up for brief discussion, as until now it has been only considered that string movement will change the flux density. Louis Clerk Maxwell’s discovery of the transformer (circa 1853) brought this to a new level where one winding on a coil assembly can induce into the other winding – and this is entirely by moving the flux density.
We already know that the electromagnetic guitar pickup is a very loosely coupled transducer, because the strings continue to vibrate in the magnetic field, and intensifying the magnetic field has virtually no effect on damping the strings vibratory motion. The two biggest damping effects on the string are the air that gets pushed around the string while it vibrates, and other mechanical damping like fingers over frets, neck and body weaknesses - all that also suck energy from the strings vibratory motion.
If you put a relatively powerful magnet near the strings, they may be very marginally pulled towards the magnet. The pitch is effectively not changed and the string still sustains as before. In other words, the string moves virtually freely through the magnetic field, and there is virtually no magnetic interaction to prevent the string from oscillating. Even with a pickup very close to the strings and the leads of the pickup shorted to form a shunt, so there is appreciable current in the pickup that will in itself create am opposing magnetic field that will oppose the string movement (see Lenz’ Law), then this also has virtually no effect – so it should now be obvious that the electromagnetic guitar pickup is very loosely coupled to the strings!
An oscillating string has a very high “Q Factor”. Another way to measure Q is to set a body in vibrating motion and count the oscillations before it dies down. In the case of a steel guitar string, this time will be several seconds, and considering that the fundamental resonance is about say 500 Hz then the Q is in the order of 2500, (with or without the vicinity of the magnet and coil of the pickup)!
What is not so obvious here is that we have a pseudo linear system that produces a voltage when the magnetic field in the vicinity of the pickup is disturbed. The obvious disturbance factor is a vibrating string, and another far less obvious disturbance factor is another electromagnetic field. This is now touching on “Field Theory” which is getting into heavy maths involving three-dimensional calculus with time varying situations. In practice using a reference field in the vicinity of a pickup will produce results that are highly repeatable – far more repeatable than using a plucked string.
Single Coil Pickups
The first consideration is to use a single coil pickup as a receiving reference. The reasoning behind this is that they are simple in design and should have repeatable results. (Well that is the thought – anyway!)
Making a practical reference field is much harder to conceive than to construct, or is that the other way around! What was needed was a ‘one sided’ magnetic field so that when it is energised by an oscillator/amplifier, it produces an oscillating magnetic field that emulates a similar effect to that of having a steel string vibrating near an electromagnetic pickup.
In this case, the answer came in part of a power transformer, where the secondary winding was used and the “E” laminations formed a one-sided doublet magnetic field. (All magnetic fields are loops – so you can’t have an isolated magnetic pole – which would be ideal.) This is the next best thing - for these measurements.
Practical Bench Setup
For consistency sake it was necessary to avoid all metallic objects where possible and rely on wood mounts. By mounting the pickups on wood blocks based on 75 x 35 mm building studs, it was relatively easy to position both the pickup and the exciter reference field and perform highly repeatable measurements – and these measurements told a wide range of stories that you will find fascinating!
Practical Reference Field
The purpose here is to establish a reference field that can be used in several experiments and the results can be tied to each other – and practice. The E Core chosen is from a 240 V 50 Hz 7 VA transformer made entirely of two sets of identical E laminations, touch welded on the outer edge extremities to make a closed magnetic circuit. The dimensions are:
Height 35.2 mm Outer Centre 22.3 mm
Depth 24.5 mm Width 16.7 mm
Centre Leg 9.65 mm Over Centre 11.35 mm
Outer Leg 5.00 mm
Back 5.00 mm Outer Stack 30.40 mm
Stack 15.0 mm Over Stack 16.45 mm
Nominally 30 laminations, each 0.5 mm thick make up the permeable magnetic path.
Here is the unit mounted on a 70 mm by 35 mm by 100 mm long block of wood. The centre of the E laminations is about 50 mm from the base, and with pickups mounted on similar wooden blocks, their centres are also nominally 50 mm up from the base – so the reference field virtually aligns with the centre of all pickups.
This structure was chosen very carefully, as the standard length if the mounting blocks is 100 mm so mounting a pickup in the edge plane of one of these neatly positions the centre of the pickup at 50 mm from the base (the same as the centre of the exciter coil), and horizontally, if a pickup is positioned on a second mounting block (nominally 35 mm) then the ‘x’ plane axis sits at 52.5 mm which aligns to about 2.5 mm of the centre of the exciter coil.
The ‘E’ core fixed with a couple of turns of electrical tape is a very firm arrangement and it makes measurements quite easy – and replicable. The picture on the right hand side is an approximation of the field seen around and through the ‘centre lamination’. From in front, this field looks like two little hemispheres with their flat sides stuck to the front faces of the laminations over the ‘E’ laminations face.
This winding on this coil is a secondary coil that is bifilar (pair) wound and series connected as a 9 V + 9 V winding. As this winding is highly inductive, and we know that it was used in a closed core to deliver 18 V ac at 50 Hz, then this core is not going to saturate. This coil has an inductance of about 4.8 mH at 1000 Hz.
This coil produces a doublet magnetic field that has two vertically associated ‘bumps’ in it. It is important to understand this field, as it is not equal on all axes – no magnetic field is! This little exciter coil is very useful for producing a fluctuating magnetic field and this field can be used for a very wide range of well controlled laboratory/garage related tests. The only problem with this unit is that when tested against fields that are 90 deg to it, this doublet can cancel out with each half and give misleading results, and a classical case is when testing a lateral (side-by-side) Hum Bucker coil.
To get around this problem a second unit was made like a tuning fork out of a strip of 20 mm * 5 mm iron bar, formed into a 100 mm * 120 mm angle bracket with the longer arm sunk into a wood mount, a ferrite magnet glued to the shorter arm and another exciter coil positioned to make the shorter arm vibrate. This has a natural resonance at about 210 Hz, and the amplitude can be finely adjusted by the using amplifier volume control. The 100 mm arm vibrates like an iron string, and the pickup reacts with it – just as though it was a string!
With both of these coils; the ‘x’ axis is parallel to the surface of the laminations and passes along the centre of the laminations, and cuts evenly through the coil. The ‘y’ axis is normal to the laminations and passes through the centre of the centre leg, and cuts through the coil. The ‘z’ is parallel to the surface of the laminations, passes through the centre of the centre leg and is the rotational centre of the coil. These axis were chosen on purpose as the ‘x’ and ‘y’ axis coordinates are 90 deg shifted from the guitar pickup structure.
Mini-Tutorial on dB and all that Stuff!
In days of old when all telephone lines were constructed with telephone poles and aerial wires, the nominal impedance was 600 ohms + 2 uF in series. To all intents and purposes, over the voice frequency band (300 Hz to 3400 Hz) this impedance is roughly resistive, and the reference power level was 1 mW (milliwatt), which is 1/1000 watt, and this is a real power as the load that it is measured into is virtually resistive!
Apart from our ears working logarithmically for both level (loudness) and pitch (frequency), it is very difficult and somewhat meaningless to work in absolute power levels in this technology, especially when in most cases the power levels are compared with each other as a ratio. To greatly simplify matters the decibel (1/10 of a bel) - after Alexander Graham Bell - was created as the standard unit of logarithmic ratio. This has the formula:
Ratio in dB = 10 log (Power 1 / Power 2)
In terms of a constant voltage and load resistance, power is directly related to the voltage squared as follows:
Power (watts) = (E^2) / R
By referring to two voltages E1 and E2 as voltages read across resistance values that are common in both conditions (for example they are both 600 ohms), and substituting this back into the dB equation, the equation becomes:
Ratio in dB = 10 log ((E1^2)/R / (E2^2)/R)
Now because the resistances are common (the same), this then simplifies back to:
Ratio in dB = 20 log (E1 / E2)
So now all we have to do is read two voltages with a high impedance voltmeter and drop these values directly into this rather simple equation and we have the ratio of the two powers in terms of dB. So we have a linear perception of the differences in relative power levels in logarithmic terms! Remember - our ears work logarithmically.
As the reference power level used in telephony is 1 mW, and the standard (characteristic) impedance of most aerial wire on telephone poles is nominally 600 ohms, then the reference voltage is 774.6 mV rms (0.7746 volts rms). If this voltage value was deliberately put into the dB equation as E2, then only one voltage measurement would be enough to give a dB value, but this value is then referred (or referenced) to 1 mW, and the reading would be a relative power level with the notation dBm, where the ‘m’ signifies being referenced to a milliwatt!
This is a major leap and it needs to be thoroughly understood. If the above paragraph is not clearly understood then it is worth reading and considering again till it becomes crystal clear. Communications Level meters are calibrated in dBm, making dB measurements all too easy!
With the technology change to twisted pairs in cables, the voice-band impedance is usually a highly capacitive value that is highly dependent on frequency and this is called ‘complex impedance’. Real power relates to power measured in a resistive load, but in this case the power is a mix of real and imaginary (out of phase returned) power due to the non-resistive nature of the cable impedance.
As the voltage is still be measured by a high impedance meter, the reference voltage is still the equivalent voltage that produced 1 mW in 600 ohms, and that is 774.6 mV rms. This apparent power level is referred to in terms of dBu and other signal levels can be readily measured in dBu with reference to the 774.6 mV rms and this is 0 dBu.
In another branch of electronics, scientists used 1 volt as the reference level and then used the dBV where the reference is 1 V rms = 0 dBV. Again in some communications (Cable TV) the reference level is 1 mV, so the reference level is 1 mV = 0 dBmV. There should be a pattern forming here!
Acoustic levels are measured in dB with reference to sound pressure level (SPL) and in this case the reference is 2 * 10-5 newton/metre2, which is the threshold of audibility (very faint). The standard nomenclature for acoustic sound is dBA, where the ‘A’ means acoustic, referred to the reference SPL. Acoustic levels are bandwidth related and (unfortunately) the human perception of acoustic level is also somewhat bandwidth related for faint and/or background noise. This maths gets very complex very quickly, and very few people get it right!
To compound the acoustic issue much further, there are three very different acoustic 'Equalisation Curves' that correspond to human hearing and these were worked out by Fletcher and Munson in the 1930s. The easy curve to comprehend is the Threshold of Pain curve (which is virtually flat) and this is called the 'C' curve. The other main curve is the Threshold of Hearing (which has the low audio frequency response attenuated by about 60 dB compared to the centre frequencies, and the upper frequencies attenuated by about 20 compared to the centre of the audio spectrum) and is called the 'A' curve, and the 'B' curve sits halfway between. Most people who are doing loud acoustic measurements, get an acoustic meter and set it to the A curve, thinking they have the dBA for Acoustic, not the 'A' weighting; then they incorrectly use this weighted scale to measure sound levels at the Threshold of Pain, and get readings lower what they really should be, as the meter should be on the dBC weighting curve for these Threshold of Pain measurements.
Once you have used measurements using dB for a few days, you will never go back! By the way, the University of New South Wales put out a very easy to read WebPage on dB and Sound Pressure Level and it is worth reading.
Reference Send Level
To energise the magnetic field, the energiser coil is fed from a very low impedance amplifier set to produce 0 dBV (that is with reference to 1 V rms, where the difference in volts is 0 dB). In terms of a telecomms level this would be +2.22 dBu. The reference frequency is about 400 Hz, but we already know that at this frequency the system will have a virtually level frequency response with a high impedance load from the pickup.
To prove the response of the transmitting exciter coil, another identical 18 V core was used as the receiver. Butted up to the exciter the output level was 0.0 dBV, and the response was virtually flat (+/‑ 0.2 dB) up to 20 kHz. With the coil assemblies separated by about 10 mm the level was about –20 dBV and the frequency response remained virtually flat to 20 kHz – so we know that the exciter coil is virtually flat up to 20 kHz too!
In this case the primary winding of the power transformer with its ‘E’ core around it makes an ideal reference pickup. We know that the voltage ratio is 240V: 9V + 9V = 13.3333, and this relates as 22.5 dB if the coupling is virtually perfect – as in a transformer. With the core faces spaced by say 100 mm, the coupling will be much less, and the frequency response of the 240 V winding was tested as a measure with the following interesting results:
Although the windings with low turns had a very high self resonance and resulted in a virtually flat response from the exciter coil, the 240 V coil with high turns has a self resonance of about 11.5 kHz (much like many guitar pickups), but because the winding resistance was much lower than for standard guitar pickups, there was a very noticeable 14.5 dB peak in the response. (This is not going to be used as a pickup – but it shows what can happen with self-resonances!)
Using 400 Hz as a test frequency and changing the spacing between the two ‘E’ core sections, the above right-hand table showed that the transferred power drops away with distance. In a table this does not look all that obvious, but when put into a graph an interesting picture forms as follows:
By applying ‘x’ axis symmetry on the left hand side graph, it turns out as the right hand side graph and looks similar to a ‘normal’ or Gaussian curve. This structure will be extensively used from this point.
Frequency Response Tests
In this case, each pickup is placed nominally 20 mm from the exciter coil (and in the case of a Hum Bucker offset to give a maximum response), then the frequency responses measured with differing load resistors (50 M ohms, 1 M ohm, 100 k ohms and 10 k ohms). These different loads give differing results, and these have been graphed because it is rather difficult for most people to visualise numbers. The Test figures were put into an Excel Spreadsheet, then graphed, and changed to log axis, and then made into a picture.
The above graph is the practical results obtained using the Strat 02 pickup with different resistive loads. Referring back to the earlier analysis where predicted values gave almost identical results, it is now clear that all these pickups will follow the same general family of frequency responses, and that response can be predictably tuned by changing the load resistor (and the load capacitor).
There are three different scenarios going on here:
This graph is extremely powerful as it links the measured electronic values (resistance and inductance) of any electromagnetic pickup to a predictable frequency response – knowing the load resistance and load capacitance; which can be set as desired.
Now there is a lot more! Not only can we predict with reasonable confidence the size and shape of the pickup response (to get that special sound), but the transient response can also be estimated with reasonable accuracy too. Underdamped frequency responses will have an overshoot in the transient like a knife blade being held over the edge of a table and flicked. The notes in that range ring on and can give a presence or ‘crisp/crunchy’ sound.
Just to get a picture if transients a ‘square wave’ was fed into the exciter coil and by looking with an oscilloscope to see the output, it is clear that when the frequency response has a ‘resonant peak’ then the transient response will also have a ‘ringing’ response.
So one pickup can give a wide range of predictable frequency responses – just be changing the load resistor and capacitor! All we need is the formulae!
Tests Along the String
In this case, the tests performed were as though only one part of the string was vibrating at nominally 400 Hz, and the load was ultra-high impedance, so the frequency response between different pickups would not have been an issue. Two sets of tests were done, one at 10 mm and the other at 5 mm. The Exciter was positioned and the pickup then positioned opposite and spaced by 10 mm, then on the ‘y’ axis, the pickup was stepped in 10 mm increments as though the moving part of the string was further along the string. Instead of producing a whole set of figures, these results are graphed as below:
This is a very interesting picture as it shows that with single coil style pickups, the magnetic path is focussed and by about 10 mm away from the poles (along the string) the signal is already down by about 3 dB and falling! Somewhere between 38 and 50 mm away from the ‘y’ axis on the pickup, the phase reverses and there is a null, then it rises to be about 33 dB down then continue to fall away at about 16 dB per 100 mm. (July 2007 This null is caused by a doublet magnetic field in the source, and the response should be a 'simple' bell shaped curve.)
The Kinman pickups are different, as these are both vertical Hum Buckers, and by about 25 mm away they have their null, sit on a short shelf at about 25 dB down then fall away at about 45 dB/100 mm and at about 80 mm offset (with about an 8 dB advantage over the single coil pickups) then fall away at about 16 dB/100 mm.
(July 2007) There is something very special about vertical Hum Buckers sensitivity responses that needs to be understood, and it is much easier if you also have a knowledge of antennae theory - in particular Log-Periodic antennas (like those used for some household television antennae). The Log-Periodic antenna has a 'multiple anti- phased dipoles' and these are spaced to act like a mirror, so it has a 'directional response' that is very similar to that of a vertical Humbucker. The Vertical Humbucker has an 'anti-phased' coil mounted further away from the strings than the main pickup coil, and this is what causes the notch at about 15 mm off centre, and the steeper skirt - and that is why it is comparatively noiseless - compared to the single coil pickup coil.
(2005) With lateral (side-by-side) Hum Bucking pickups, the story is again slightly different, because the magnetic field extends along the strings between the magnet pole pieces and not ‘through and back as in a single coil pickup. When we use the exciter coil (and it aligns with the centre of the Hum Bucker pickup ‘x’ axis field) then there is a null position and gives a very false set of readings. By avoiding the null reading, and normalising to the maximum levels for each set of readings, the following set of curves follows:
Unsurprisingly, the string is sensitive over a longer length (about 45 mm) before the response drops off and this is because there are two sets magnets for each string - where they have an additive effect over the pickup and a subtractive effect beyond the pickup. The 'skirt' appears to drop off very quickly and forms a false null because of the exciter coil's (doublet) field. The real response follows the more gentle curve that is about 40 dB down by 100 mm off centre of the pickup.
(July 2007) What is surprising is that the 'skirt' shape is virtually identical to that of the single coil pickup (when it is offset by the magnet head spacing), and this indicates that the magnetic coupling is rather poor. This lateral pickup will however not sound like the Strat pickup because the interaction of the magnetic field with the string is 'skewed' across the face of the pickup, from one row of magnets to the other row of magnets or iron pole piece, but in the case of the Strat; the magnetic field sits up like pineapple leaves from a single row of magnets - more later.
In the above graph, the legend with the suffix ‘S’ means the one coil is acting as a single coil, which is (naturally) offset from the zero axis, as the centre of the two coils was used as the measure reference. Note the second bump near the centre – caused by induction into the other pole pieces. These responses are however very similar to the Strat curves.
The two curves with the legend suffix ‘SS’ indicate a Series aiding Series connected pair of windings, and these have a characteristic flat top (after removing the null reading from them). (July 2007) Note that the shape of the skirts are virtually identical to that of the Single Coil Strat, and even the HMB02 has a somewhat similar shape
The reading with the legend suffix ‘PP’ indicates a parallel (aiding) connected pair of windings, and this curve also is flat over the top with clean skirts down to about -35 dB, and this is a voltage ratio of about 56:1.
The ‘notches’ in the ‘greater than 25 mm offset area’ are where the voltages developed on the two coils cancel each other out and as the distance is increased the signal becomes out of phase. The fact that the symmetry is poor beyond the immediate active area indicates that the symmetry in manufacture is not there either – but with this being quieter than 35 dB down – who is to be concerned about this? Well, a Hum Bucker is supposed to remove as much background noise as possible, and without a symmetric construction then it is compromised from the start!
Across The Strings
By placing the exciter coil close to the pickup face, then stepping the pickup pole by pole and past by one, a fair estimation of the relative (vertical) string movement with relation to each pole in the pickup. Again the same ‘centre of axis rule’ applies for lateral Hum Bucker coils so they were not done with the exciter coil. As before, the results were put on an Excel spreadsheet and then graphed as the picture tells the stories much better in these cases. Here are the single coil pickups:
Again this is an interesting graph as it shows that most results are within +0.1 dB, -0.8 dB for magnet pieces 2,3,4 & 5, and that poles 1 & 6 are typically about 4 dB down, and the exceptions are the staggered pole pieces with varying height – and that would be expected as there are a few millimetres difference here. But the difference in level measured with adjacent poles is incredibly small – except at the extremities (poles 1 and 6).
In the second case the response with the Hum Buckers acting as single coils also had virtually similar sensitivities, and there were no surprises there. This tells the story that the pole strength appears to fall off with the outer extremity strings. The fact that the fret-board is slightly curved, and that in most cases the magnet as form a flat plane, the centre four poles will be fractionally away from the strings in comparison to the outer strings. To exercise that point slightly, a second set of readings was done at nominally 10 mm from the pole faces of the pickups and the graph shows below:
The non-normalised figures show that there is about a 2.5 dB difference in levels between 10 mm and 5 mm, and this difference drops to about 2 dB at pole pieces 1 and 6. So with a slightly curved fret-board, the centre strings are typically about 0.5 mm closer to the edge pole pieces, and this would give an almost unnoticeable difference in comparative string levels.
The shape of these curves bears a close resemblance to band pass filters like those used in dial-up modems, ADSL filters, Television picture and sound channels, FM receivers etc. Minimising the error across the fret-board/pickup conjures up the maths developed by Tchebyshev with ‘ripple’ in the pass-band to minimise the overall error.
The Hum Buckers – wired as single coils, act just like other single coils and they all tell the same story that the pickup is too narrow for the strings, and it should extend by another 2 poles to provide a field with minimised magnetic fringe effects. It is also obvious that the errors in placing the pickup at the extremities is far larger than placing the pickup with poles as the references – and this is shown by the spread in values on the sides of the graphs!
Putting a magnet near a vibrating string makes an almost imperceptible change in the pitch and sustain qualities of the vibration, and from that we have to understand that the magnetic field is very loosely coupled to the vibrating string. Putting an electromagnetic guitar pickup close to the (magnetic) strings also makes an almost imperceptible change in the pitch and sustain qualities of the vibrations.
Because the sustain factor shows that an electric guitar string will sustain form several seconds, and the fundamental frequency is typically 120 to 800 Hz, the ‘Q’ factor typically about 2500. If this magnetic field interfered with the sustain of the vibration then the sustain would quickly drop to much less than a second. As this does not happen, the electromagnetic guitar pickup is by its very nature a very loosely coupled transducer.
Emulating the physical string movement in practice as a constant amplitude waveform is extremely difficult – mainly because of physical resonances in the audio band. An alternate approach by utilising a transformer winding with an open magnetic path has a similar effect as a moving magnetic string, and the test equipment designed here is virtually flat over the audio frequency range, making it an ideal exciting tool for practical measurements.
A second exciting device using a resonant iron bar has been created and this is frequency range limited – but because it is used in a known virtually flat frequency response area, this can emulate constant string vibration with good precision.
Mini Tutorial on dB
The mini tutorial on dB was included here as from this point most of the results will be in decibels. To stabilise results, a reference send level was created at 0 dBV and a reference frequency was chosen at nominally 400 Hz.
Tests with the high number of turns other transformer half showed that this (240 V) winding had a self-resonance at about 11.5 kHz, and that the low voltage windings had self-resonances well above the audio band – making the low voltage windings very suitable for unequalised measurements, greatly simplifying the measurement process.
The output level verses separation distance followed a curve that closely aligned with the shape of a Gaussian normal distribution.
Frequency Response Tests
The emulation coil (or exciting coil) together with real pickups in a controlled bench situation produced frequency response results that were highly repeatable, and that followed the predicted results in the earlier experiments.
These pickups all generally follow a family of second order responses that can be pre-determined by measuring the pickup internal resistance and inductance together with known loads of resistance and capacitance.
Transient responses match with the frequency responses and some examples have been shown.
This technique removes the ‘black art’ of pickup sounds and places the frequency and transient responses directly into highly predictable engineering terms.
Pole - String Sensitivity
When measuring along the line of the strings, single coil pickups are sensitive for about 10 mm either side of the centre of the pole pieces. For lateral hum bucker pickups, this sensitivity follows a similar pattern also extending about 10 mm past the nearest pole pieces with a flat sensitivity between the two pole-piece arrays.
The sensitivity across the strings is virtually flat with the exception of the outer two pole-pieces, which are relatively about 4 dB down. So the pole pieces do not need to be directly under the strings, but extend out beyond the strings to get a more even relative response.
|Copyright © Malcolm Moore, 2003. Comments and Corrections are welcome|