Measuring the Electrical Properties of Guitar Pickups
Sept 24, 2016 12:22:48 GMT -5
redefinerefine, pablogilberto, and 5 more like this
Post by antigua on Sept 24, 2016 12:22:48 GMT -5
This write up owes a lot to a couple very helpful online resources:
www.buildyourguitar.com/resources/lemme/
www.syscompdesign.com/assets/images/appnotes/guitar-pickups.pdf
I have also received a lot of help from..
Ken Willmott kenwillmott.com/blog/archives/152
John H guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator
Helmuth Lemme also wrote a pickup measurement guide similar in intent and content to this write up, www.planetz.com/wp-content/uploads/2014/10/Pickup_Measuring_Technique.pdf Read both. Read'em all!
Introduction...
For about two years I have been conducting tests on guitar pickups in order to uncover technical aspects in greater detail than what is shared by the pickup makers themselves.
This write up is meant to serve two purposes:
1) If you are interested in learning more about the technical side of pickups you have on hand, or about pickups in general, hopefully there is enough detail here that you can follow along and conduct these same tests yourself.
2) If you see the results of my own tests in other threads or on other forums, and you'd simply like to learn more about how they were conducted, or to scrutinize the methods used, then all of that detail is here.
How do guitar pickups really work?
Guitar pickups mostly come down to a coil of wire wrapped around a magnet. Though it seems simple, there are actually four components all in one: 1) a resistor, represented by the resistance of the long copper wire, 2) a high inductance inductor, represented by the substantial coil of wire, 3) a capacitor, represented by the close proximity of all that fine copper wire, and 4), an AC voltage source, represented by a magnetized guitar string which moves around in close proximity to the many loops of wire, creating a voltage via induction. It is also possible to create a guitar pickup that generates a voltage and creates an impedance with two separate components, and the Lace Alumitone is an example of such a pickup, but most guitar pickups on the market make use of high inductance coils with many "turns" of wire in order to perform both tasks at once.
The guitar pickup generates a voltage by way of Faraday's Law of Induction. First, the pole pieces under the guitar strings endow the strings with a magnetic polarity. Now the six guitar strings then contain their own magnetic fields that each extend down into the coils of the pickup. From this point forward, you can just suppose that the strings themselves are the magnets. When you pluck the strings, the amount of magnetic field with the coils increased and decreases rapidly, as the string moves up and down, nearer and further from the pickups and it's coil(s), and per Faraday's Law of Induction, a current is generated in the coil. The current is alternating. When the guitar strings approach the pickup, the current flows one way, and when the string move away, the current flows the other way.
As an aside, because current is induced when the magnetized strings move near and from from the pickup, the side-to-side movement of the string cannot be heard audibly, because side-to-side movement does not cause the string to become significantly nearer or further from the pickup. Therefore, even though a guitar string moves along an x and y axis above the pickup, you only ever hear the movement in relation to the y axis. This is part of what gives an electric guitar it's distinct tone.
If current is analogous to the flow of water, then voltage is analogous to water pressure. You can have a flow of water, or a flow of current through a large conduit or conductive wire, without a large change of water pressure, or voltage, respectively. In order to get a significant change of water pressure or electrical voltage, you need some source of resistance. The way a guitar pickup produces resistance (technically referred to as "reactance" in this context), and hence a voltage, is by containing an inductor. The same coil which generates the current by way of Faraday's Law of Induction, happens to have so many winds (anywhere from 5,000 to 10,000), that as current flows though the wire, it generates a second, relatively strong, magnetic field in and around the coil, as any common inductor will. This inductive magnetic field pushes back against the alternating current produced by the moving magnetized guitar string, due to Lenz's Law, and thus you have resistance (technically referred to as "reactance" in this context), and because you have that secondary "magnetic resistance", you have voltage. That secondary magnetic field in the coil technically also pushes back against the guitar string, again per Lenz's Law, though it does so with very little force, and so it is said, in electrical terms, that the pickup and the guitar strings are "very loosely coupled".
The primary reason there are "hot pickups" and "vintage" or "cool pickups" is on account of that inductor, or the "inductance" of the pickup. A coil is not merely an inductor, though. To an extent, it is also a capacitor, because electric charge attempts to attract along all of the windings in the coil. As you know from measuring guitar pickups with a multimeter, pickups also have some resistance; usually between 5k and 10k, on account of the resistance in the copper wire. So all together you have resistance "R", inductance "L" and some capacitance "C". Therefore, every inductor, or guitar pickup, can be said to be a "parallel RLC circuit". A parallel RLC circuit will form a "resonant peak", and at the frequency of the "resonant peak" the resistance (referred to as impedance in this context) reaches a maximum, and therefore causes the pickup to produce the most voltage at that particular frequency. The lower the inductance L and capacitance C, the higher the resonant peak will be, while higher values of L and C will result in a lower resonant frequency. This is the underlying reason why there are "hot pickup" and "cool pickups". When a pickup is "hot", it has more winds on the coil, therefore it has higher inductance as well as a higher capacitance, and so it has a lower resonant peak, ultimately producing more voltage at low frequencies rather than high frequencies.
The job of the resistance "R" in the parallel RLC circuit is to determine what the Q factor of the resonance will be, but I'll go over that further down the post.
What do we want to know about guitar pickups?
There are several metrics to be known about a guitar pickup, but there are a few in particular that go the furthest in terms of defining how they will sound, in order of significance:
- The resonant peak (f) of the pickup, under typical volume / tone control load conditions
- The pickup's inductance (L)
- The pickup's DC resistance (R)
- The pickup's capacitance (C)
If you know the resonant peak of a pickup, it is easy to make an educated guess as to how that pickup will compare to others like it.
The same can be said of inductance to a large degree, because the resonant peak is a product of the capacitance and the inductance, and since most pickups of a given type have fairly similar capacitance values, you can guesstimate that the resonant peak will track closely with the inductance.
Finally, the DC resistance is not a bad metric to base judgements from, because it does strongly indicate the amount of wire that is on the pickup, and the amount of wire ultimately determines the inductance value of the pickup. For a given type of guitar pickup, the DC resistance and the inductance track rather closely, though the inductance climbs slightly faster than does the DC resistance. Also note that when a pickup is wound with thinner 43 or 44AWG wire, the DC resistance will be higher than if that pickup were wound with 42 AWG, because the finer wire puts up more resistance per length of wire.
Since the resonant peak of the pickup is determined by both the inductance and the capacitance, the capacitance is definitely a good value to know, if you can figure it out. The reason is it not as important as inductance is simply that, for a given pickup type, the deviation of capacitances is a lot smaller than the deviation of inductance. The bigger reason capacitance is less important is that the guitar cable introduces a parallel capacitance that is typically about three to four times larger than the capacitance of the pickup itself. Suppose the pickup has 100pF (picofarads) capacitance, and the cable adds another 400pF, then the pickup's capacitance is ultimately only one fifth of the overall capacitance at play. On the other hand, there are some pickups that, due to how they're constructed, can see a capacitance of as much as 250pF, and in that case, the pickup's capacitance will account for closer to two thirds of the overall capacitance, and so it is good to know the capacitance, if you are able to solve for it.
Finding the "resonant peak"
Everyone knows you can find the DC resistance with a cheap multimeter. Finding the resonant peak requires the use of a frequency generator and an oscilloscope. Fortunately, we live in the future, and both of these things can be had in a single USB device that only costs about $160
The basic idea is to impose a changing magnetic field directly upon the pickup at every frequency between 100Hz and 30kHz, and then measure the output voltage at multiple frequencies in order to plot the pickup's frequency response. This is not unlike how a magnetized guitar string works; as the string moves back and forth, it too imposes a changing magnetic field upon the pickup, at multiple frequencies.
Ken Willmott supports an even cheaper testing method, making use of a computer audio interface and the RightMark audio software - potentially costing nothing to set up. You can find more information about that setup here kenwillmott.com/blog/archives/152
.. but for the setup I've used here, the following is a parts list:
- A USB oscilliscope with built in fucntion generator and bode plotter. I recommend the Velleman PCSGU250 www.amazon.com/Velleman-PCSGU250-Usb-Pc-Scope-Generator/dp/B006DXCO3E/ref=sr_1_1?ie=UTF8&qid=1473995997&sr=8-1&keywords=velleman+pcsgu250 Velleman also has a cheaper unit called the PCSU200 which works as well, but it doesn't come with any probes, and the function generator output is RCA, so the BNC probes and a male RCA jack have to be acquired separately.
- An extra BNC probe, as you need two and the Velleman only comes with one www.amazon.com/Hantek-100MHz-Oscilloscope-Probes-Accessory/dp/B0030KWM30/ref=pd_sim_328_1?ie=UTF8&psc=1&refRID=2SN2NHZ1020HVFDDQM36
- Magnet wire. The gauge of the wire doesn't really matter. The ultimate goal is to get about 200 winds of the stuff on a bobbin, but the exact number doesn't matter, so long as it's less than the number of turns on a guitar pickup, which tend to have 3,000 turns at a minimum. Example: www.amazon.com/Remington-Industries-36SNSP-25-Enameled-Diameter/dp/B00L5IUWZY/ref=sr_1_1?ie=UTF8&qid=1473989627&sr=8-1&keywords=magnet+wire If you have a spare pickup that you can destroy, you can simply use wire from a guitar pickup.
- A suitable bobbin. I recommend taking a cheap Strat ceramic pickup, removing the magnet(s), pole pieces and wire so that you are left with just the plastic bobbin. It is critically important that even the pole pieces be removed, or else the pole pieces will factor into the electrical measurement and distort the results. www.amazon.com/Musiclily-Single-Pickup-Fender-Electric/dp/B00CS0J8E4/ref=sr_1_11?ie=UTF8&qid=1473996875&sr=8-11&keywords=strat+pickup+ceramic
Setting up the hardware
Step 1) Create a driver coil using the Strat pickup bobbin and the magnet wire.
Wrap the magnet wire around the bobbin about two hundred times, or enough to fill the bobbin. This will give the coil an inductance of a several millihenries, and a resonant peak that is beyond the audible range, which makes it suitable for this purpose, since its own resonance will be very far away from the pickup's resonance. Either solder lead wires to the coil as seen in the picture, or use the ends of the magnet wire as the leads. You will have to sand off the insulation coat from the wire in order to get to bare copper for soldering, or for making electrical contact. On this and other forums, this coil is sometimes also called an "exciter coil", "excitation coil", "external coil" or "field coil", all mean the same thing.
A large driver coil using a Strat bobbin (forgive the nasty appearance)
A tiny driver coil on the end of a Popsicle stick:
Step 2) Install the USB oscilloscope and install the software. Besides the Velleman PCSGU250, I know that the Syscomp CGR-101 can be used, but I don't recommend it, as it uses more crudely written software.
Connect the included probe to "Channel 2" output, and connect the included alligator clips to the function generator output.
Step 3) Connect the grounds of the function generator alligator clips and the "Channel 2" probe to one of the leads of the driver coil, then connect the positive leads of the probe and the function generator alligator clips to the other lead of the driver coil, as seen in the picture.
Step 4) Connect the extra probe to "Channel 1", and then connect it's lead and ground to the pickup being tested.
This is how the full setup will look:
Setting up the software
I'll presume you're using the Velleman PCSGU250. Any USB oscilloscope will work as long as it provides built in bode plotting against a function generator, and it's settings will be similar.
Looking at the main screen:
- Make sure both probes have "x10" highlighted, and make sure that the little switch on the actual probes are set to "x10" as well.
- Make note of the voltage slider on the far right. This is where you can adjust the amount of voltage that is sent to the driver coil.
- Click "Circuit Analyzer"
Looking at the Circuit Analyzer screen:
- Click "Options", select "Show Multiple Traces"
- Click "Options" again, select "Automatic Voltage Scale", this will automatically increase resolution as the voltage input decreases.
- Click "View", select "Markers f & V", and "Audio Range 30kHz"
- Under "Vertical Scale", select "5db/div". This can be set to 1dB/div if it's determined that the pickup has a low Q factor, and it will yield a higher resolution.
- Under "Frequency Range", select 30khz
- Under "Frequency Start", select 100Hz
- Uncheck "Log. Freq. Steps"
Finally, place the driver coil over the pickup and attempt to create a bode plot. Click the "Start" button to fire off the process.
When you measure a humbucking pickup (even single-coil sized rails humbuckers), you must position the driver coil on it's side, as shown below. This is because the current runs in opposite directions within the two coils, and by laying the driver coil on its side, the coils will receive magnetic flux that is of the correct polarity for each coil.
Using the setup above, I created a plot for Fender NoCaster, and a Donlis Chinese humbucker:
From the plot above, a few things can be learned a) the specific resonant peak of NoCaster Bridge and the Donlis humbucker, and the relative Q factor of the pickups can be compared. It's clear that the NoCaster bridge has a much higher Q (steeper peak) than the Donlis, as evidenced by the more pointy plot line it created.
This effectively becomes a metallurgical analysis, because when you see the steepness of a peak drop, it means that you are seeing eddy current losses caused by the metal used in the construction of the pickup. The reason the Donlis has a lower peak than the Tele bridge pickup is because the steel used in the humbucker has a higher conductivity and permeability than the AlNiCo in the Tele bridge, and higher permeability and/or conductivity means more eddy current losses. This method therefore allows you compare the qualities of various metals used in the construction of pickups. A high DC resistance in a pickup will also reduce the Q factor somewhat, but if the DC resistances of two pickups are within, say 25% of each other, and you see an obvious difference in Q factor, the cause in this case will be the eddy currents in the metal parts. A counter example, would be two pickups that are alike but have very different DC resistances, for exmaple an Seymour Duncan SSL-1 has a DC resistance of 6.5k, while the SSL-5 has a DC resistance of about 14k, but both pickups have all the same parts otherwise, the SSL-5 has a lower Q factor because it's DC resistance is more than twice that of the SSL-1. Eddy current losses and DC resistances have a similar, but not exactly the same, effect upon the Q factor.
Note that AlNiCo magnets are metal, and therefore subject to the same qualities of permeability and conductivity as the rest of the metal used in the pickup (mostly steel). Ceramic and neodymium magnets are special in that they are neither permeable, nor conductive, and so they are like air, in terms of their electrical effects. AlNiCo has a much lower permeability and slightly conductivity than steel, so if you take a Strat pickup, remove the AlNiCo pole pieces and replace them with steel pole pieces, the pickup's inductance increases by about 50%, and the Q factor also drops by about 50%, and this largely what sets AlNiCo Strat pickups apart from AlNiCo Strat pickups, not the ceramic magnet underneath, as is generally assumed.
When a pickup has a lower resonant peak frequency, as the Fender Tele bridge appears to have based on the plot, it must mean that it has a higher amount of inductance and/or capacitance. If you purchase a good LCR meter, such as the DE-5000 (set it to measure "L" with series losses "SER" mode, and the lowest test frequency possible, 100Hz or 120Hz), you can determine the inductance of the pickup separately, then it's easy to work out the capacitance specifically with an online calculator, by entering the resonant peak and the inductance value. Similarly, an LCR meter like the DE-5000 with a very high test frequency (a minimum of 100kHz is recommended), the capacitance can be measured (set to measure "C", assuming parallel losses "PAR" mode, and the highest test frequency available), and then from that L and C you can determine the resonant peak with the same online calculator.
There are many other uses for this pickup testing technique:
*** You can compare two or more pickups to find which pickup is hotter than another, determine if pickups that should be alike are in fact alike, or if you buy a new set of pickups, and you want to see how they differ from the old pickups on a technical level, this plot will elucidate that difference.
*** You can determine how much of an effect a particular part of a pickup has on it's Q factor and resonant peak. For example, you can plot a humbucker, the remove all the screws, or anything you want, then plot it again, and you will be able to determine the contribution of thsoe component by comparing the difference with and without those parts included. Of if you bought a bunch of pickup arts on eBay and you are unsure of their quality or consistency, this method will reveal any unwanted deviations immediately. Or do as I have recently, measure the difference a steel "base plate" makes on the underside of a Fender pickup, and conclude what I concluded; not much.
Generally speaking, when the the resonant frequency decreases, it means the metallic component you have added has increased the inductance of the pickup, due to its having a higher permeability. If the resonant frequency increases, they the opposite is true, so you will find that as you remove slugs, screws, spacers, etc. that the resonant peak frequency increases.
Generally speaking, when the resonant peak amplitude decreases in amplitude, which is to say, "the Q factor has dropped" or "the mountain has become a hill", it means the metallic component is imposing eddy current losses, or resistance upon the pickup, meaning the metal is conductive. Higher permeability will also increase the eddy current resistance, but it is only necessary that the metal be conductive. The more conductive and permeable the metal, the greater the eddy current resistance, and the shorter the mountain" will be. This is especially useful for testing the quality of cheap brass versus better nickel silver covers, and figuring out if an eBay seller has screwed you or not. Also note that any kind of series resistance in the circuit, and not just eddy current resistance, will also lower the Q factor. Resistance that is parallel to the pickup also lowers the Q factor, but in that case, a lower resistance lowers the Q factor, and higher resistance increases it.
*** You can even perform this test with the pickup still in your guitar, and see the resonant peak and Q factor with the pickup(s) loaded down by the tone and volume posts. You can see how the resonant peak changes when you tweak the knobs on your guitar, or combine pickups. You can compare one guitar to another, one pickup to another, and on and on.
Taking things further, you could plug your guitar cable into the guitar, then plot the result from the end of the guitar cable, and witness how much the resonant peak drops on account of the guitar cable, and find out which guitar cables are higher quality than others. I've done some guitar cable testing here using an LCR meter guitarnuts2.proboards.com/thread/7725/capacitive-coupling-various-guitar-parts
In order to better understand the physics involved, it's worth reading up on how core materials effect inductors, by aiding their performance with permeability, and detracting from it through hysteresis and eddy current losses, though only the latter will audibly effect guitar pickups powerelectronics.com/content/inductor-core-material-heart-inductor due to the relatively low frequencies involved. One notable difference is that inductors and often utilize ferrite cores, and transformers utilize steel laminations to achieve a very high Q factor, but as a high Q factor is not generally desirable in a guitar pickup, these techniques are dispensed with. In fact, the parallel circuit resistance of the tone and volume pot lower the Q factor of a pickup, and this is generally considered a good thing. To deliberately retain a higher Q factor, you can use 1 meg or no-load control pots.
Producing plots that are more "realistic"
One small problem with the absolute resonant peak frequency is that a small amount of capacitance can cause it to change by a lot. Pickups only feature about 100pF to 200pF capacitance inherently, and this can cause the resonant peak to shift by several kilohertz. In practice, your guitar cable adds 500 to 1,000pF capacitance, driving the resonant peak way down, and this is how we hear pickups; through guitar cables.
Therefore, it helps to test pickups with a "dummy load", which is arbitrary values of capacitance and resistance that are meant to stand in for a guitar cable and the volume and tone pots. In this tiny community of guitar pickup testing, some of us had decided upon 470pF capacitance, and 200k ohms resistance across the pickup. This value simulates a 10' to 15' guitar cable, and potentiometer values that fall somewhere between a Strat and a Les Paul.
The resonant plots you create with a dummy load will be more indicative of how the pickup actually performs in real life. You should also find that pickups that might seem very different at first glance are actually very similar in the context of the dummy load. Strat pickups tend to end up with resonant peaks near 4kHz, while humbuckers have peaks that are between 2.5kHz and 3kHz. I hope that should you measure pickups and wish to share the data, that you will also measure the pickups with 470pF and 200k ohm dummy loads so that we will also have this additional data point to use for comparing and contrasting.
This is the "dummy load" I use. I tried a lot of resistors and capacitors to ensure that I arrived at exactly 470pF and 200k ohms, and then I attached alligator clips for convenience:
An even better way to plot frequency responses...
The plots above are sufficient to make a variety of determinations about guitar pickups, but there is a way they can be presented that makes them even more useful.
The reason why these plots look like "mountains" is because, as frequency rises with a constant current in the driver coil, so the rate of change of flux increases. According to Faraday's law, as the rate of flux change increases, induced voltage also increases, and it does so at a rate of 6dB per octave.
Since an actual, working guitar pickup exhibits this same +6dB/octave slope, these mountain shapes graphs are an honest representation of how a guitar pickup performs, but for the sake of comparison, it is helpful to isolate just the RLC properties of the pickup, with the +6dB/octave component deliberately neglected. It makes the aspects that separate one guitar pickup from another more obvious to the naked eye, and it aids in taking measurements, such as the Q factor, the rise in decibels at resonance, and to generally observe how a pickup deviates from a "flat" response curve.
Below is a graph showing the "mountain" shaped plot in red, the sort that were created above, and an integrated plot in green, which has a -6dB/octave attenuation:
The green plot line, -6dB/octave slope, exposes the RLC characteristics of the pickup, where you have a 0dB slope ahead of the resonant peak, and a -12dB/octave slope beyond the resonant peak, on account of the inductor in series (the coil itself), and the capacitance in parallel (the parasitic capacitance of the coil).
Here is an example of how the -6dB/octave bode plot makes eddy current losses more apparent. This diagram, borrowed from Helmuth Lemme's site linked above, shows the expected loss in voltage transfer as a result of eddy currents:
Offsetting the reactances with a -6dB bias makes that eddy loss easy to visually spot, and measure, in an actual bode plot:
The device needed to accomplish is called an integrator, and it would be placed in between the guitar pickup and the input interface. Ken Willmott, who's blog is linked to above, designed an created several integrator circuits. You can either make one with a breadboard by following one of his schematics, or inquire with him about receiving an complete PCB version. His blog contains a contact form:kenwillmott.com/blog/archives/152
Once you've created a plot using the integrator, it becomes very easy to measure the dB increase at the resonance by selecting "View" -> "Marker f & dV", which will place two horizontal guides onto the grid, which you can position at the base and the crest of the peak. The distance between the two horizontal markers will indicate the gain in decibels, which is shown below the grid:
Here is the integrator I use in the setup:
Inside if a hand made version of the integrator circuit, generously provided to me by Ken Willmott.
Determining a pickup's inductance
The inductance of the pickup essentially tells you the overall output of the pickup. The resonant peak is great and all, but when it comes to how loud a pickup is, or how hard it will push an amplifier, we're talking almost exclusively about inductance. If you know the flux density at the pole tops, which is described in the next section, you can make an educated guess as to the amount of generated current that will be produced between the strings and the pickup, and the generated current in conjunction with the inductance will determine the actual output voltage of the pickup.
If two pickups are physically alike, and are known to use the exact same magnets, say AlNiCo 5, then you can presume that the generated current will be the same, and therefore the inductance will tell you the entirely of the difference in output. This makes comparing the output of, say, several Strat pickups, or PAF style humbuckers, using only the inductance as your data point, very effective.
You need a good quality LCR meter in order to measure the inductance of a pickup on account of the fact that they produce an uncommonly high inductance and low Q factor, compared to more inductors that are used in electrical applications. The Extech 380193 LCR Meter appears to be the favored LCR meter among pickup people. It costs $220 from most retailers www.amazon.com/Extech-380193-Passive-Component-Meter/dp/B00023RTYU Make sure the Extech is set to "SER", or series mode, when measuring guitar pickups in order to get an accurate inductance measurement. Helmuth Lemme suggests that 120Hz is the optimal testing frequency, and that this same meter goes by the name "PeakTech PKT-2165" and "Voltcraft 4080", so be sure to search for all these various re-seller designations in order to find the best price.
The DER-EE-DE-5000 is also a well reviewed LCR meter, it costs less and features more test frequencies than the Extech: www.deree.com.tw/de-5000.html
Here is the Extech reporting that the NoCaster bridge produces 3.7 henries inductance.
You can also use the Extech 380193 to measure the capacitance of various guitar parts and accessories in order to determine the extent to which each component degrades high end response, as seen in this thread: www.tdpri.com/threads/a-double-cream-humbucker-set-that-isnt-dimarzio-and-costs-only-25.666998/page-4#post-7165576
Determining a pickup's inductance without a meter
I find that using the Extech saves me a ton of time and hassle, but if you want to find the inductance of a pickup without a meter, you can also determine the inductance if you A) have a capacitor on hand that is of a much higher value than that of the pickup (pickups contain roughly 100pF capacitance on average), and B) a way to measure the resonant peak of the pickup.
A variety of capacitor values can be used in theory. The trick is to choose a value that will combine with the pickup in parallel which will result in a low resonant peak, and one that is easy to identify. I'd recommend using a capacitor that results in a resonant peak near 1kHz, and a 10 nanofarad capacitor should accomplish that, though I would keep slightly lower and higher value capacitors on hand, just in case.
When you're ready to test, you put the 10 nanofarad capacitor in parallel with the pickup, and you measure the resonant peak, using the USB oscilloscope and the driver coil as described above. Let's suppose you find that the resonant peak is only 1kHz, and that's a very low resonant peak for a pickup, but the 10nF of capacitance drives the frequency down that far.
Now you take your values, 10nF capacitance and 1kHz resonant peak, and you plug them into a calculator that solves for inductance, such as this one: www.sengpielaudio.com/calculator-XLC.htm You enter the capacitance in terms of "microfarads", so 10nF becomes "0.01uF", and you enter the frequency in terms of hertz, so 1kHz becomes "1000Hz". You enter those values into the calculator, and you press "calculate", and you get a calculated inductance of 2533.03 millihenries, or 2.533 henries. Due to the lack of precision involved with this method, it is probably best to round off to the first decimal place, and call it 2.5 henries, or 2.5H. Be sure to make it known that you have determined a "calculated inductance".
Ken Willmott told me about this method, though his method included a few extra steps for added accuracy. I just call it "capacitance swamping", as I don't know the more technical term, if there is one.
Determining a pickup's capacitance
You get capacitance any time two conductors in the same circuit are nearby each other. The close and larger the conductors are, the higher the capacitance. Guitar cables have capacitance, because the lead wire and the shielding represent to such conductors that are large (by way of length) and very close together. A guitar cable also has a lot of capacitance, owing to the windings of the coils being very close together.
In order to measure the capacitance of a pickup, an LCR meter must be used that features a very high test frequency, because pickups are only purely capacitive at frequencies beyond their resonance. The Extech 380193 has a max test frequency of 10kHz, which is too close the resonant frequency of a guitar pickup to determine its capacitive value, but an LCR meter such as the DE-5000 has a test frequency of 100kHz, which is about ten times greater than the resonant frequency of a typical guitar pickup, and therefore is suitable. To do this, you set the meter to the highest test frequency, 100kHz or higher, and set the meter to measure "C" capacitance in "PAR" parallel mode.
Another, possibly more reliable way to determine the capacitance of the coil, is to calculate "C" based on the inductance and the resonant peak. Both of these values can be acquired using the methods above, using the bode plot and the LCR meter. Online calculators such as this one allow you to easily calculate the capacitance www.sengpielaudio.com/calculator-XLC.htm . For example, suppose you have a NoCaster bridge pickup with an inductance of 3.821 henries and a resonant peak of 6.81kHz, you would type in 3821 millihenries and 6810 hertz into the calculator, hit "calculate", and it return 0.000143 uF (microfarads), which we convert to picofarads, since that's a more practical unit at this scale, 0.000143uF = 143 pF (picofarads).
That's not quite the end of the story, though. Some of that 143 picofarad capacitance didn't come from the guitar pickup, it came from the BNC oscilloscope probe. All you have to do is figure out what the capacitance is of that proble, and subtract it from your measurement. Therefore, if your probe has a capacitance of 20pF, you can subtract 20pF from your measurement, and conclude that the pickup contains 123pF (143 - 20) picofarads of capacitance caused by the windings of the coil. Additionally most humbuckers feature shielded hookup wire, and this hookup wire will generally add about 70pF capacitance for every twelve inches in length. I usually don't measure the capacitance without the lead wire, since removing it for the sake of testing is quite a chore.
The reason why capacitance is higher or lower in a pickup depends on a number of factors, such as the shape of the coil, the magnet wire insulation thickness, and grounded metal parts (mostly shielding) that cause capacitive coupling between the hot and ground sides of the circuit. If you have two pickups that are otherwise alike, it can be interesting to see how near or far their capacitive values are, and try to determine why they differ, if they do.
Determining flux density at the poles and strings
One major aspect of a guitar's function that is not addressed by the driver coil is the amount of flux change / voltage the pickup is able to acquire from the moving guitar strings. The more powerfully the pickup can charge the strings, the more flux change will occur within the coils, and the more voltage will be generated. Certain grades of AlNiCo, as well as certain magnetic assemblies made out of steel (PAF humbucker) will produce more or less flux density at the strings. Aside from voltage output, another reason to observe the flux density of a pickup is to determine how much magnetic pull can be expected between the pickup and the guitar strings. For example, AlNiCo 5 pole pieces in Strat pickup usually measure a very high strength of ~1050 Gauss, and these pickups are known to cause unpoleasent sounds when they are set too close to the guitar strings, especially the thicker wound strings.
In order to determine how much flux density the pickup has to offer the guitar strings at the pole tops, you need a magnetometer. The Spin Doctor magnetometer is commonly used by pickup testers gravitastech.weebly.com/spin-doctor.html , and costs just under $100. This type of magnetometer exploits a Hall effect sensor in order to measure flux density. The Spin Doctor is no longer being produced, but there are similarly priced alternatives, such as the WT10A , which shows values in milliteslas. To convert milliteslas to Gauss, just multiple the value by 10. 100mT = 1000G.
Also make note that twice the flux density, as might be seen between AlNiCo 2 and AlNiCo 5, does not mean twice the generated voltage, since there is not a linear relationship between voltage and remnant flux density, but rather the voltage owes to the rate of flux change through the coil, as the string moves, and these two things don't have a linear relationship. Doubling the magnetic flux might only increase the voltage by about 15%, based on observational data. The voltage output will also increase if the pickup's pole pieces have a higher permeability, because this higher permeability increases the overall flux change as well. Therefore, a pickup with a strong AlNiCo pole piece may generate less voltage than a pickup with steel pole pieces and a weaker overall magnetic field, because the permeability of the steel pole pieces nevertheless increases the overall flux change as the guitar string moves nearer and further.
As mentioned in the first paragraph, a more useful take away might be how the pickup's magnetic pull effects the guitar string. At it's most extreme, it can cause "Stratitus", or "wolf tones" which is an easily audible inter-modulation and beating of two frequencies that are close together, but even at the non extremes, experiment shows that even minor changes in magnetic pull changes the output waveform as the guitar string's energy decays, and in my opinion, when the differences between magnets are discussed, it's the difference in how the magnet pulls upon the guitar string that is being spoken of.
In conclusion...
In order measure resonant peaks, f, and Q factor losses as described here, you need a USB oscilloscope with function generator and bode plotting capabilities, costing in the area of $160. Ken Willmott is a proponent of creating voltage-by-frequency response plots using the RightMark audio software in conjunction with an audio interface. This setup can potentially cost you nothing, and he describes this setup at his blog kenwillmott.com/blog/archives/152
In order to measure the inductance L, you'd want a quality LCR meter, costing about $120, or use the capacitor swamping method described above. When you know the resonant peak and the inductance, you can then calculate the capacitance C, or you can also attempt to determine C with an LCR meter with a test frequency that is at least ten times the resonant frequency of the pickup (~100kHz). A simple $10 multi-meter can tell you the resistance R.
Finally, you can measure the flux density B with a Spin Doctor magnetometer or the WT10A, costing about $110 om Amazon.
This accumulation of these data points will leave little, if any, mystery remaining as to how a pickup will perform, and how it will compare to other pickups. This data can be directly applied to the electrical modelling of guitar pickups, such as is seen with the GuitarFreak interactive spreadsheet guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator , from which you can virtually design and analyze a pickup, or the wiring of an entire guitar, without every breaking out the soldering iron or a multi-meter.
Here is a reference chart I made generalizing the tonal consequences of differences that arise in the bode plots:
www.buildyourguitar.com/resources/lemme/
www.syscompdesign.com/assets/images/appnotes/guitar-pickups.pdf
I have also received a lot of help from..
Ken Willmott kenwillmott.com/blog/archives/152
John H guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator
Helmuth Lemme also wrote a pickup measurement guide similar in intent and content to this write up, www.planetz.com/wp-content/uploads/2014/10/Pickup_Measuring_Technique.pdf Read both. Read'em all!
Introduction...
For about two years I have been conducting tests on guitar pickups in order to uncover technical aspects in greater detail than what is shared by the pickup makers themselves.
This write up is meant to serve two purposes:
1) If you are interested in learning more about the technical side of pickups you have on hand, or about pickups in general, hopefully there is enough detail here that you can follow along and conduct these same tests yourself.
2) If you see the results of my own tests in other threads or on other forums, and you'd simply like to learn more about how they were conducted, or to scrutinize the methods used, then all of that detail is here.
How do guitar pickups really work?
Guitar pickups mostly come down to a coil of wire wrapped around a magnet. Though it seems simple, there are actually four components all in one: 1) a resistor, represented by the resistance of the long copper wire, 2) a high inductance inductor, represented by the substantial coil of wire, 3) a capacitor, represented by the close proximity of all that fine copper wire, and 4), an AC voltage source, represented by a magnetized guitar string which moves around in close proximity to the many loops of wire, creating a voltage via induction. It is also possible to create a guitar pickup that generates a voltage and creates an impedance with two separate components, and the Lace Alumitone is an example of such a pickup, but most guitar pickups on the market make use of high inductance coils with many "turns" of wire in order to perform both tasks at once.
The guitar pickup generates a voltage by way of Faraday's Law of Induction. First, the pole pieces under the guitar strings endow the strings with a magnetic polarity. Now the six guitar strings then contain their own magnetic fields that each extend down into the coils of the pickup. From this point forward, you can just suppose that the strings themselves are the magnets. When you pluck the strings, the amount of magnetic field with the coils increased and decreases rapidly, as the string moves up and down, nearer and further from the pickups and it's coil(s), and per Faraday's Law of Induction, a current is generated in the coil. The current is alternating. When the guitar strings approach the pickup, the current flows one way, and when the string move away, the current flows the other way.
As an aside, because current is induced when the magnetized strings move near and from from the pickup, the side-to-side movement of the string cannot be heard audibly, because side-to-side movement does not cause the string to become significantly nearer or further from the pickup. Therefore, even though a guitar string moves along an x and y axis above the pickup, you only ever hear the movement in relation to the y axis. This is part of what gives an electric guitar it's distinct tone.
If current is analogous to the flow of water, then voltage is analogous to water pressure. You can have a flow of water, or a flow of current through a large conduit or conductive wire, without a large change of water pressure, or voltage, respectively. In order to get a significant change of water pressure or electrical voltage, you need some source of resistance. The way a guitar pickup produces resistance (technically referred to as "reactance" in this context), and hence a voltage, is by containing an inductor. The same coil which generates the current by way of Faraday's Law of Induction, happens to have so many winds (anywhere from 5,000 to 10,000), that as current flows though the wire, it generates a second, relatively strong, magnetic field in and around the coil, as any common inductor will. This inductive magnetic field pushes back against the alternating current produced by the moving magnetized guitar string, due to Lenz's Law, and thus you have resistance (technically referred to as "reactance" in this context), and because you have that secondary "magnetic resistance", you have voltage. That secondary magnetic field in the coil technically also pushes back against the guitar string, again per Lenz's Law, though it does so with very little force, and so it is said, in electrical terms, that the pickup and the guitar strings are "very loosely coupled".
The primary reason there are "hot pickups" and "vintage" or "cool pickups" is on account of that inductor, or the "inductance" of the pickup. A coil is not merely an inductor, though. To an extent, it is also a capacitor, because electric charge attempts to attract along all of the windings in the coil. As you know from measuring guitar pickups with a multimeter, pickups also have some resistance; usually between 5k and 10k, on account of the resistance in the copper wire. So all together you have resistance "R", inductance "L" and some capacitance "C". Therefore, every inductor, or guitar pickup, can be said to be a "parallel RLC circuit". A parallel RLC circuit will form a "resonant peak", and at the frequency of the "resonant peak" the resistance (referred to as impedance in this context) reaches a maximum, and therefore causes the pickup to produce the most voltage at that particular frequency. The lower the inductance L and capacitance C, the higher the resonant peak will be, while higher values of L and C will result in a lower resonant frequency. This is the underlying reason why there are "hot pickup" and "cool pickups". When a pickup is "hot", it has more winds on the coil, therefore it has higher inductance as well as a higher capacitance, and so it has a lower resonant peak, ultimately producing more voltage at low frequencies rather than high frequencies.
The job of the resistance "R" in the parallel RLC circuit is to determine what the Q factor of the resonance will be, but I'll go over that further down the post.
What do we want to know about guitar pickups?
There are several metrics to be known about a guitar pickup, but there are a few in particular that go the furthest in terms of defining how they will sound, in order of significance:
- The resonant peak (f) of the pickup, under typical volume / tone control load conditions
- The pickup's inductance (L)
- The pickup's DC resistance (R)
- The pickup's capacitance (C)
If you know the resonant peak of a pickup, it is easy to make an educated guess as to how that pickup will compare to others like it.
The same can be said of inductance to a large degree, because the resonant peak is a product of the capacitance and the inductance, and since most pickups of a given type have fairly similar capacitance values, you can guesstimate that the resonant peak will track closely with the inductance.
Finally, the DC resistance is not a bad metric to base judgements from, because it does strongly indicate the amount of wire that is on the pickup, and the amount of wire ultimately determines the inductance value of the pickup. For a given type of guitar pickup, the DC resistance and the inductance track rather closely, though the inductance climbs slightly faster than does the DC resistance. Also note that when a pickup is wound with thinner 43 or 44AWG wire, the DC resistance will be higher than if that pickup were wound with 42 AWG, because the finer wire puts up more resistance per length of wire.
Since the resonant peak of the pickup is determined by both the inductance and the capacitance, the capacitance is definitely a good value to know, if you can figure it out. The reason is it not as important as inductance is simply that, for a given pickup type, the deviation of capacitances is a lot smaller than the deviation of inductance. The bigger reason capacitance is less important is that the guitar cable introduces a parallel capacitance that is typically about three to four times larger than the capacitance of the pickup itself. Suppose the pickup has 100pF (picofarads) capacitance, and the cable adds another 400pF, then the pickup's capacitance is ultimately only one fifth of the overall capacitance at play. On the other hand, there are some pickups that, due to how they're constructed, can see a capacitance of as much as 250pF, and in that case, the pickup's capacitance will account for closer to two thirds of the overall capacitance, and so it is good to know the capacitance, if you are able to solve for it.
Finding the "resonant peak"
Everyone knows you can find the DC resistance with a cheap multimeter. Finding the resonant peak requires the use of a frequency generator and an oscilloscope. Fortunately, we live in the future, and both of these things can be had in a single USB device that only costs about $160
The basic idea is to impose a changing magnetic field directly upon the pickup at every frequency between 100Hz and 30kHz, and then measure the output voltage at multiple frequencies in order to plot the pickup's frequency response. This is not unlike how a magnetized guitar string works; as the string moves back and forth, it too imposes a changing magnetic field upon the pickup, at multiple frequencies.
Ken Willmott supports an even cheaper testing method, making use of a computer audio interface and the RightMark audio software - potentially costing nothing to set up. You can find more information about that setup here kenwillmott.com/blog/archives/152
.. but for the setup I've used here, the following is a parts list:
- A USB oscilliscope with built in fucntion generator and bode plotter. I recommend the Velleman PCSGU250 www.amazon.com/Velleman-PCSGU250-Usb-Pc-Scope-Generator/dp/B006DXCO3E/ref=sr_1_1?ie=UTF8&qid=1473995997&sr=8-1&keywords=velleman+pcsgu250 Velleman also has a cheaper unit called the PCSU200 which works as well, but it doesn't come with any probes, and the function generator output is RCA, so the BNC probes and a male RCA jack have to be acquired separately.
- An extra BNC probe, as you need two and the Velleman only comes with one www.amazon.com/Hantek-100MHz-Oscilloscope-Probes-Accessory/dp/B0030KWM30/ref=pd_sim_328_1?ie=UTF8&psc=1&refRID=2SN2NHZ1020HVFDDQM36
- Magnet wire. The gauge of the wire doesn't really matter. The ultimate goal is to get about 200 winds of the stuff on a bobbin, but the exact number doesn't matter, so long as it's less than the number of turns on a guitar pickup, which tend to have 3,000 turns at a minimum. Example: www.amazon.com/Remington-Industries-36SNSP-25-Enameled-Diameter/dp/B00L5IUWZY/ref=sr_1_1?ie=UTF8&qid=1473989627&sr=8-1&keywords=magnet+wire If you have a spare pickup that you can destroy, you can simply use wire from a guitar pickup.
- A suitable bobbin. I recommend taking a cheap Strat ceramic pickup, removing the magnet(s), pole pieces and wire so that you are left with just the plastic bobbin. It is critically important that even the pole pieces be removed, or else the pole pieces will factor into the electrical measurement and distort the results. www.amazon.com/Musiclily-Single-Pickup-Fender-Electric/dp/B00CS0J8E4/ref=sr_1_11?ie=UTF8&qid=1473996875&sr=8-11&keywords=strat+pickup+ceramic
Setting up the hardware
Step 1) Create a driver coil using the Strat pickup bobbin and the magnet wire.
Wrap the magnet wire around the bobbin about two hundred times, or enough to fill the bobbin. This will give the coil an inductance of a several millihenries, and a resonant peak that is beyond the audible range, which makes it suitable for this purpose, since its own resonance will be very far away from the pickup's resonance. Either solder lead wires to the coil as seen in the picture, or use the ends of the magnet wire as the leads. You will have to sand off the insulation coat from the wire in order to get to bare copper for soldering, or for making electrical contact. On this and other forums, this coil is sometimes also called an "exciter coil", "excitation coil", "external coil" or "field coil", all mean the same thing.
A large driver coil using a Strat bobbin (forgive the nasty appearance)
A tiny driver coil on the end of a Popsicle stick:
Step 2) Install the USB oscilloscope and install the software. Besides the Velleman PCSGU250, I know that the Syscomp CGR-101 can be used, but I don't recommend it, as it uses more crudely written software.
Connect the included probe to "Channel 2" output, and connect the included alligator clips to the function generator output.
Step 3) Connect the grounds of the function generator alligator clips and the "Channel 2" probe to one of the leads of the driver coil, then connect the positive leads of the probe and the function generator alligator clips to the other lead of the driver coil, as seen in the picture.
Step 4) Connect the extra probe to "Channel 1", and then connect it's lead and ground to the pickup being tested.
This is how the full setup will look:
Setting up the software
I'll presume you're using the Velleman PCSGU250. Any USB oscilloscope will work as long as it provides built in bode plotting against a function generator, and it's settings will be similar.
Looking at the main screen:
- Make sure both probes have "x10" highlighted, and make sure that the little switch on the actual probes are set to "x10" as well.
- Make note of the voltage slider on the far right. This is where you can adjust the amount of voltage that is sent to the driver coil.
- Click "Circuit Analyzer"
Looking at the Circuit Analyzer screen:
- Click "Options", select "Show Multiple Traces"
- Click "Options" again, select "Automatic Voltage Scale", this will automatically increase resolution as the voltage input decreases.
- Click "View", select "Markers f & V", and "Audio Range 30kHz"
- Under "Vertical Scale", select "5db/div". This can be set to 1dB/div if it's determined that the pickup has a low Q factor, and it will yield a higher resolution.
- Under "Frequency Range", select 30khz
- Under "Frequency Start", select 100Hz
- Uncheck "Log. Freq. Steps"
Finally, place the driver coil over the pickup and attempt to create a bode plot. Click the "Start" button to fire off the process.
When you measure a humbucking pickup (even single-coil sized rails humbuckers), you must position the driver coil on it's side, as shown below. This is because the current runs in opposite directions within the two coils, and by laying the driver coil on its side, the coils will receive magnetic flux that is of the correct polarity for each coil.
Using the setup above, I created a plot for Fender NoCaster, and a Donlis Chinese humbucker:
From the plot above, a few things can be learned a) the specific resonant peak of NoCaster Bridge and the Donlis humbucker, and the relative Q factor of the pickups can be compared. It's clear that the NoCaster bridge has a much higher Q (steeper peak) than the Donlis, as evidenced by the more pointy plot line it created.
This effectively becomes a metallurgical analysis, because when you see the steepness of a peak drop, it means that you are seeing eddy current losses caused by the metal used in the construction of the pickup. The reason the Donlis has a lower peak than the Tele bridge pickup is because the steel used in the humbucker has a higher conductivity and permeability than the AlNiCo in the Tele bridge, and higher permeability and/or conductivity means more eddy current losses. This method therefore allows you compare the qualities of various metals used in the construction of pickups. A high DC resistance in a pickup will also reduce the Q factor somewhat, but if the DC resistances of two pickups are within, say 25% of each other, and you see an obvious difference in Q factor, the cause in this case will be the eddy currents in the metal parts. A counter example, would be two pickups that are alike but have very different DC resistances, for exmaple an Seymour Duncan SSL-1 has a DC resistance of 6.5k, while the SSL-5 has a DC resistance of about 14k, but both pickups have all the same parts otherwise, the SSL-5 has a lower Q factor because it's DC resistance is more than twice that of the SSL-1. Eddy current losses and DC resistances have a similar, but not exactly the same, effect upon the Q factor.
Note that AlNiCo magnets are metal, and therefore subject to the same qualities of permeability and conductivity as the rest of the metal used in the pickup (mostly steel). Ceramic and neodymium magnets are special in that they are neither permeable, nor conductive, and so they are like air, in terms of their electrical effects. AlNiCo has a much lower permeability and slightly conductivity than steel, so if you take a Strat pickup, remove the AlNiCo pole pieces and replace them with steel pole pieces, the pickup's inductance increases by about 50%, and the Q factor also drops by about 50%, and this largely what sets AlNiCo Strat pickups apart from AlNiCo Strat pickups, not the ceramic magnet underneath, as is generally assumed.
When a pickup has a lower resonant peak frequency, as the Fender Tele bridge appears to have based on the plot, it must mean that it has a higher amount of inductance and/or capacitance. If you purchase a good LCR meter, such as the DE-5000 (set it to measure "L" with series losses "SER" mode, and the lowest test frequency possible, 100Hz or 120Hz), you can determine the inductance of the pickup separately, then it's easy to work out the capacitance specifically with an online calculator, by entering the resonant peak and the inductance value. Similarly, an LCR meter like the DE-5000 with a very high test frequency (a minimum of 100kHz is recommended), the capacitance can be measured (set to measure "C", assuming parallel losses "PAR" mode, and the highest test frequency available), and then from that L and C you can determine the resonant peak with the same online calculator.
There are many other uses for this pickup testing technique:
*** You can compare two or more pickups to find which pickup is hotter than another, determine if pickups that should be alike are in fact alike, or if you buy a new set of pickups, and you want to see how they differ from the old pickups on a technical level, this plot will elucidate that difference.
*** You can determine how much of an effect a particular part of a pickup has on it's Q factor and resonant peak. For example, you can plot a humbucker, the remove all the screws, or anything you want, then plot it again, and you will be able to determine the contribution of thsoe component by comparing the difference with and without those parts included. Of if you bought a bunch of pickup arts on eBay and you are unsure of their quality or consistency, this method will reveal any unwanted deviations immediately. Or do as I have recently, measure the difference a steel "base plate" makes on the underside of a Fender pickup, and conclude what I concluded; not much.
Generally speaking, when the the resonant frequency decreases, it means the metallic component you have added has increased the inductance of the pickup, due to its having a higher permeability. If the resonant frequency increases, they the opposite is true, so you will find that as you remove slugs, screws, spacers, etc. that the resonant peak frequency increases.
Generally speaking, when the resonant peak amplitude decreases in amplitude, which is to say, "the Q factor has dropped" or "the mountain has become a hill", it means the metallic component is imposing eddy current losses, or resistance upon the pickup, meaning the metal is conductive. Higher permeability will also increase the eddy current resistance, but it is only necessary that the metal be conductive. The more conductive and permeable the metal, the greater the eddy current resistance, and the shorter the mountain" will be. This is especially useful for testing the quality of cheap brass versus better nickel silver covers, and figuring out if an eBay seller has screwed you or not. Also note that any kind of series resistance in the circuit, and not just eddy current resistance, will also lower the Q factor. Resistance that is parallel to the pickup also lowers the Q factor, but in that case, a lower resistance lowers the Q factor, and higher resistance increases it.
*** You can even perform this test with the pickup still in your guitar, and see the resonant peak and Q factor with the pickup(s) loaded down by the tone and volume posts. You can see how the resonant peak changes when you tweak the knobs on your guitar, or combine pickups. You can compare one guitar to another, one pickup to another, and on and on.
Taking things further, you could plug your guitar cable into the guitar, then plot the result from the end of the guitar cable, and witness how much the resonant peak drops on account of the guitar cable, and find out which guitar cables are higher quality than others. I've done some guitar cable testing here using an LCR meter guitarnuts2.proboards.com/thread/7725/capacitive-coupling-various-guitar-parts
In order to better understand the physics involved, it's worth reading up on how core materials effect inductors, by aiding their performance with permeability, and detracting from it through hysteresis and eddy current losses, though only the latter will audibly effect guitar pickups powerelectronics.com/content/inductor-core-material-heart-inductor due to the relatively low frequencies involved. One notable difference is that inductors and often utilize ferrite cores, and transformers utilize steel laminations to achieve a very high Q factor, but as a high Q factor is not generally desirable in a guitar pickup, these techniques are dispensed with. In fact, the parallel circuit resistance of the tone and volume pot lower the Q factor of a pickup, and this is generally considered a good thing. To deliberately retain a higher Q factor, you can use 1 meg or no-load control pots.
Producing plots that are more "realistic"
One small problem with the absolute resonant peak frequency is that a small amount of capacitance can cause it to change by a lot. Pickups only feature about 100pF to 200pF capacitance inherently, and this can cause the resonant peak to shift by several kilohertz. In practice, your guitar cable adds 500 to 1,000pF capacitance, driving the resonant peak way down, and this is how we hear pickups; through guitar cables.
Therefore, it helps to test pickups with a "dummy load", which is arbitrary values of capacitance and resistance that are meant to stand in for a guitar cable and the volume and tone pots. In this tiny community of guitar pickup testing, some of us had decided upon 470pF capacitance, and 200k ohms resistance across the pickup. This value simulates a 10' to 15' guitar cable, and potentiometer values that fall somewhere between a Strat and a Les Paul.
The resonant plots you create with a dummy load will be more indicative of how the pickup actually performs in real life. You should also find that pickups that might seem very different at first glance are actually very similar in the context of the dummy load. Strat pickups tend to end up with resonant peaks near 4kHz, while humbuckers have peaks that are between 2.5kHz and 3kHz. I hope that should you measure pickups and wish to share the data, that you will also measure the pickups with 470pF and 200k ohm dummy loads so that we will also have this additional data point to use for comparing and contrasting.
This is the "dummy load" I use. I tried a lot of resistors and capacitors to ensure that I arrived at exactly 470pF and 200k ohms, and then I attached alligator clips for convenience:
An even better way to plot frequency responses...
The plots above are sufficient to make a variety of determinations about guitar pickups, but there is a way they can be presented that makes them even more useful.
The reason why these plots look like "mountains" is because, as frequency rises with a constant current in the driver coil, so the rate of change of flux increases. According to Faraday's law, as the rate of flux change increases, induced voltage also increases, and it does so at a rate of 6dB per octave.
Since an actual, working guitar pickup exhibits this same +6dB/octave slope, these mountain shapes graphs are an honest representation of how a guitar pickup performs, but for the sake of comparison, it is helpful to isolate just the RLC properties of the pickup, with the +6dB/octave component deliberately neglected. It makes the aspects that separate one guitar pickup from another more obvious to the naked eye, and it aids in taking measurements, such as the Q factor, the rise in decibels at resonance, and to generally observe how a pickup deviates from a "flat" response curve.
Below is a graph showing the "mountain" shaped plot in red, the sort that were created above, and an integrated plot in green, which has a -6dB/octave attenuation:
The green plot line, -6dB/octave slope, exposes the RLC characteristics of the pickup, where you have a 0dB slope ahead of the resonant peak, and a -12dB/octave slope beyond the resonant peak, on account of the inductor in series (the coil itself), and the capacitance in parallel (the parasitic capacitance of the coil).
Here is an example of how the -6dB/octave bode plot makes eddy current losses more apparent. This diagram, borrowed from Helmuth Lemme's site linked above, shows the expected loss in voltage transfer as a result of eddy currents:
Offsetting the reactances with a -6dB bias makes that eddy loss easy to visually spot, and measure, in an actual bode plot:
The device needed to accomplish is called an integrator, and it would be placed in between the guitar pickup and the input interface. Ken Willmott, who's blog is linked to above, designed an created several integrator circuits. You can either make one with a breadboard by following one of his schematics, or inquire with him about receiving an complete PCB version. His blog contains a contact form:kenwillmott.com/blog/archives/152
Once you've created a plot using the integrator, it becomes very easy to measure the dB increase at the resonance by selecting "View" -> "Marker f & dV", which will place two horizontal guides onto the grid, which you can position at the base and the crest of the peak. The distance between the two horizontal markers will indicate the gain in decibels, which is shown below the grid:
Here is the integrator I use in the setup:
Inside if a hand made version of the integrator circuit, generously provided to me by Ken Willmott.
Determining a pickup's inductance
The inductance of the pickup essentially tells you the overall output of the pickup. The resonant peak is great and all, but when it comes to how loud a pickup is, or how hard it will push an amplifier, we're talking almost exclusively about inductance. If you know the flux density at the pole tops, which is described in the next section, you can make an educated guess as to the amount of generated current that will be produced between the strings and the pickup, and the generated current in conjunction with the inductance will determine the actual output voltage of the pickup.
If two pickups are physically alike, and are known to use the exact same magnets, say AlNiCo 5, then you can presume that the generated current will be the same, and therefore the inductance will tell you the entirely of the difference in output. This makes comparing the output of, say, several Strat pickups, or PAF style humbuckers, using only the inductance as your data point, very effective.
You need a good quality LCR meter in order to measure the inductance of a pickup on account of the fact that they produce an uncommonly high inductance and low Q factor, compared to more inductors that are used in electrical applications. The Extech 380193 LCR Meter appears to be the favored LCR meter among pickup people. It costs $220 from most retailers www.amazon.com/Extech-380193-Passive-Component-Meter/dp/B00023RTYU Make sure the Extech is set to "SER", or series mode, when measuring guitar pickups in order to get an accurate inductance measurement. Helmuth Lemme suggests that 120Hz is the optimal testing frequency, and that this same meter goes by the name "PeakTech PKT-2165" and "Voltcraft 4080", so be sure to search for all these various re-seller designations in order to find the best price.
The DER-EE-DE-5000 is also a well reviewed LCR meter, it costs less and features more test frequencies than the Extech: www.deree.com.tw/de-5000.html
Here is the Extech reporting that the NoCaster bridge produces 3.7 henries inductance.
You can also use the Extech 380193 to measure the capacitance of various guitar parts and accessories in order to determine the extent to which each component degrades high end response, as seen in this thread: www.tdpri.com/threads/a-double-cream-humbucker-set-that-isnt-dimarzio-and-costs-only-25.666998/page-4#post-7165576
Determining a pickup's inductance without a meter
I find that using the Extech saves me a ton of time and hassle, but if you want to find the inductance of a pickup without a meter, you can also determine the inductance if you A) have a capacitor on hand that is of a much higher value than that of the pickup (pickups contain roughly 100pF capacitance on average), and B) a way to measure the resonant peak of the pickup.
A variety of capacitor values can be used in theory. The trick is to choose a value that will combine with the pickup in parallel which will result in a low resonant peak, and one that is easy to identify. I'd recommend using a capacitor that results in a resonant peak near 1kHz, and a 10 nanofarad capacitor should accomplish that, though I would keep slightly lower and higher value capacitors on hand, just in case.
When you're ready to test, you put the 10 nanofarad capacitor in parallel with the pickup, and you measure the resonant peak, using the USB oscilloscope and the driver coil as described above. Let's suppose you find that the resonant peak is only 1kHz, and that's a very low resonant peak for a pickup, but the 10nF of capacitance drives the frequency down that far.
Now you take your values, 10nF capacitance and 1kHz resonant peak, and you plug them into a calculator that solves for inductance, such as this one: www.sengpielaudio.com/calculator-XLC.htm You enter the capacitance in terms of "microfarads", so 10nF becomes "0.01uF", and you enter the frequency in terms of hertz, so 1kHz becomes "1000Hz". You enter those values into the calculator, and you press "calculate", and you get a calculated inductance of 2533.03 millihenries, or 2.533 henries. Due to the lack of precision involved with this method, it is probably best to round off to the first decimal place, and call it 2.5 henries, or 2.5H. Be sure to make it known that you have determined a "calculated inductance".
Ken Willmott told me about this method, though his method included a few extra steps for added accuracy. I just call it "capacitance swamping", as I don't know the more technical term, if there is one.
Determining a pickup's capacitance
You get capacitance any time two conductors in the same circuit are nearby each other. The close and larger the conductors are, the higher the capacitance. Guitar cables have capacitance, because the lead wire and the shielding represent to such conductors that are large (by way of length) and very close together. A guitar cable also has a lot of capacitance, owing to the windings of the coils being very close together.
In order to measure the capacitance of a pickup, an LCR meter must be used that features a very high test frequency, because pickups are only purely capacitive at frequencies beyond their resonance. The Extech 380193 has a max test frequency of 10kHz, which is too close the resonant frequency of a guitar pickup to determine its capacitive value, but an LCR meter such as the DE-5000 has a test frequency of 100kHz, which is about ten times greater than the resonant frequency of a typical guitar pickup, and therefore is suitable. To do this, you set the meter to the highest test frequency, 100kHz or higher, and set the meter to measure "C" capacitance in "PAR" parallel mode.
Another, possibly more reliable way to determine the capacitance of the coil, is to calculate "C" based on the inductance and the resonant peak. Both of these values can be acquired using the methods above, using the bode plot and the LCR meter. Online calculators such as this one allow you to easily calculate the capacitance www.sengpielaudio.com/calculator-XLC.htm . For example, suppose you have a NoCaster bridge pickup with an inductance of 3.821 henries and a resonant peak of 6.81kHz, you would type in 3821 millihenries and 6810 hertz into the calculator, hit "calculate", and it return 0.000143 uF (microfarads), which we convert to picofarads, since that's a more practical unit at this scale, 0.000143uF = 143 pF (picofarads).
That's not quite the end of the story, though. Some of that 143 picofarad capacitance didn't come from the guitar pickup, it came from the BNC oscilloscope probe. All you have to do is figure out what the capacitance is of that proble, and subtract it from your measurement. Therefore, if your probe has a capacitance of 20pF, you can subtract 20pF from your measurement, and conclude that the pickup contains 123pF (143 - 20) picofarads of capacitance caused by the windings of the coil. Additionally most humbuckers feature shielded hookup wire, and this hookup wire will generally add about 70pF capacitance for every twelve inches in length. I usually don't measure the capacitance without the lead wire, since removing it for the sake of testing is quite a chore.
The reason why capacitance is higher or lower in a pickup depends on a number of factors, such as the shape of the coil, the magnet wire insulation thickness, and grounded metal parts (mostly shielding) that cause capacitive coupling between the hot and ground sides of the circuit. If you have two pickups that are otherwise alike, it can be interesting to see how near or far their capacitive values are, and try to determine why they differ, if they do.
Determining flux density at the poles and strings
One major aspect of a guitar's function that is not addressed by the driver coil is the amount of flux change / voltage the pickup is able to acquire from the moving guitar strings. The more powerfully the pickup can charge the strings, the more flux change will occur within the coils, and the more voltage will be generated. Certain grades of AlNiCo, as well as certain magnetic assemblies made out of steel (PAF humbucker) will produce more or less flux density at the strings. Aside from voltage output, another reason to observe the flux density of a pickup is to determine how much magnetic pull can be expected between the pickup and the guitar strings. For example, AlNiCo 5 pole pieces in Strat pickup usually measure a very high strength of ~1050 Gauss, and these pickups are known to cause unpoleasent sounds when they are set too close to the guitar strings, especially the thicker wound strings.
In order to determine how much flux density the pickup has to offer the guitar strings at the pole tops, you need a magnetometer. The Spin Doctor magnetometer is commonly used by pickup testers gravitastech.weebly.com/spin-doctor.html , and costs just under $100. This type of magnetometer exploits a Hall effect sensor in order to measure flux density. The Spin Doctor is no longer being produced, but there are similarly priced alternatives, such as the WT10A , which shows values in milliteslas. To convert milliteslas to Gauss, just multiple the value by 10. 100mT = 1000G.
Also make note that twice the flux density, as might be seen between AlNiCo 2 and AlNiCo 5, does not mean twice the generated voltage, since there is not a linear relationship between voltage and remnant flux density, but rather the voltage owes to the rate of flux change through the coil, as the string moves, and these two things don't have a linear relationship. Doubling the magnetic flux might only increase the voltage by about 15%, based on observational data. The voltage output will also increase if the pickup's pole pieces have a higher permeability, because this higher permeability increases the overall flux change as well. Therefore, a pickup with a strong AlNiCo pole piece may generate less voltage than a pickup with steel pole pieces and a weaker overall magnetic field, because the permeability of the steel pole pieces nevertheless increases the overall flux change as the guitar string moves nearer and further.
As mentioned in the first paragraph, a more useful take away might be how the pickup's magnetic pull effects the guitar string. At it's most extreme, it can cause "Stratitus", or "wolf tones" which is an easily audible inter-modulation and beating of two frequencies that are close together, but even at the non extremes, experiment shows that even minor changes in magnetic pull changes the output waveform as the guitar string's energy decays, and in my opinion, when the differences between magnets are discussed, it's the difference in how the magnet pulls upon the guitar string that is being spoken of.
In conclusion...
In order measure resonant peaks, f, and Q factor losses as described here, you need a USB oscilloscope with function generator and bode plotting capabilities, costing in the area of $160. Ken Willmott is a proponent of creating voltage-by-frequency response plots using the RightMark audio software in conjunction with an audio interface. This setup can potentially cost you nothing, and he describes this setup at his blog kenwillmott.com/blog/archives/152
In order to measure the inductance L, you'd want a quality LCR meter, costing about $120, or use the capacitor swamping method described above. When you know the resonant peak and the inductance, you can then calculate the capacitance C, or you can also attempt to determine C with an LCR meter with a test frequency that is at least ten times the resonant frequency of the pickup (~100kHz). A simple $10 multi-meter can tell you the resistance R.
Finally, you can measure the flux density B with a Spin Doctor magnetometer or the WT10A, costing about $110 om Amazon.
This accumulation of these data points will leave little, if any, mystery remaining as to how a pickup will perform, and how it will compare to other pickups. This data can be directly applied to the electrical modelling of guitar pickups, such as is seen with the GuitarFreak interactive spreadsheet guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator , from which you can virtually design and analyze a pickup, or the wiring of an entire guitar, without every breaking out the soldering iron or a multi-meter.
Here is a reference chart I made generalizing the tonal consequences of differences that arise in the bode plots:
