Measuring pickup impedance with an A/D recording interface

[Mike Sulzer]

If the operation of an instrument is complicated enough to encourage or require the use of a computer for the analysis of the data, then it is reasonable to put as much of the functionality as possible in software, and use hardware described by some or all of these conditions:
1. already available for a different purpose;
2. general purpose and thus relatively inexpensive due to the size of the market;
3. already owned by or at least familiar to the intended users of the new instrument.

If these conditions are met, then it is possible to make an instrument that uses minimal special hardware, and as for the software, once written, it can be distributed to anyone who wants it for free in its initial and updated forms.

The instrument under discussion here is a device for measuring the impedance of a pickup across frequency, presenting basic and derived quantities in a graphical form. The hardware is the A/D recording interface, available in many forms for recording music, but requiring only two channels for this application. This discussion describes the use of an example of this hardware, while using available software to demonstrate that the required functionality can be achieved, recognizing that convenient operation would require a custom program.

The minimal required user constructed hardware is a stand for holding the PUT with connectors for its leads and cables for connecting to the recording interface. This is something that is easy to make. The version used for these tests is shown here ().

The leads of the PUT are connected two the two terminals. Underneath, one terminal is connected to a 1K resistor which goes to ground; the other is connected to a random noise signal from the recording interface, in this case an Apogee Duet 2. Each terminal also is connected to one of the input channels of the Duet. The terminal connected to the resistor goes to a high input impedance instrument channel; the other one goes to a 4 DBU line input. The voltage across the resistor is a measure of the current through the PUT. The other signal is a measure of the voltage across the series combination. The impedance calculated from the ratio is the desired impedance plus 1K real, easily subtracted in the software. Thus there is no reason to build something like an analog current to voltage converter: this is simpler.

The Duet has a stereo head phone output and two speaker outputs. In the current perverse terminology, a speaker output drives an amplifier input, while a headphone output really does connect to head phones. Either could be used to drive the pickup with random noise. The headphone output has more leakage to the inputs, and so one speaker output is used instead, with the headphone amp muted.

The two voltages are measured across frequency by Electo Acoustics Toolbox running on a Mac. EAT performs the cross spectral analysis necessary to find the transfer function relating the two. This information is transferred to another program for computing the impedance and other quantities. Also the results can be displayed as graphs. Computing low noise results requires some integration; this is partly a result of the random nature of the signal, partly from additive noise present in any system. Because of the cross spectral analysis, the random signal contributes less noise than one might expect. Although the signal level at each frequency is random, the result is a ratio of the two inputs, and that is not random. It is still subject to some noise, however.

Integration is for less than one minute; the frequency resolution is 24Hz. The frequency response of the duet has some phase shift and a small amplitude change at the bottom and top. It is only differences that matter, and so one could do better in this regard by using the preamps on both channels. However, a calibration is necessary in any case, and it is possible to use a higher level into the pickup when skipping the preamp in the signal monitor channel.

The gain of the preamp is adjusted to give levels significantly below clipping, but high enough to avoid losing signal to noise ratio. A calibration is performed, and the preamp gain must be remembered so that it can be reset to that level in the future. (Or perform a new calibration.) The calibration consists of connecting a resistor across the terminal instead of a pickup. A value is chosen that gives a similar signal level that a typical pickup does. The integration is performed for ten times longer than for the PUT so that the calibration process introduces little random noise. The calibration data are transferred from EAT to the computation program, processed, stored, and applied to any PUT data that is input. The calibration is frequency by frequency and removes both amplitude an phase errors. Of course, these are audio amplifiers that are capacitor coupled, and so we cannot get information at dc, but we can see the limits as the frequency goes down.

A later post will present some results.

[Mike Sulzer]

This post discusses the measurement of the pickup impedance and the derivation of three simple parameters, the inductance of the coil, the resistance in the low frequency limit, and the coil capacitance. A later post will describe additional derived quantities.

By measurement, I mean both the raw amplitude and phase which come from EAT, and the smoother version that results from signal processing. The raw measurement has 24 Hz resolution, far greater than strictly necessary, but very useful for assuring that all details of the response are captured. For example, it is not possible to get meaningful measurements at dc with capacitor coupled amplifiers, and so it is useful to have measurements at as low a frequency as possible. It is also nice to have smooth curves for study, and so the raw measurement is processed to reduce the number of degrees of freedom to no more than necessary for the highest Q pickup coil one is likely to find (using high permeability ceramic [ferrite] cores).


The method used to make the smooth curves is cubic spline fitting. If you are familiar with cubic splines in signal processing work, it is probably the interpolation technique, where you have some data points of a curve and want good estimates of the ones in between. Fitting is sort of the opposite, where you have lots of points with some noise and want a few points with less noise. The second part of this process, generating the smooth curve from the fitted points, can be thought of as interpolation.

The basic measurement has 2001 points, covering a 48KHz bandwidth (96Ksamples/sec). The highest two hundred points are discarded since they are contaminated by the anti-aliasing filter. The dc point is discarded also, and so 1800 remain. These are used to fit to 81 uniformly space points. This number can be chosen as necessary, and for most pickups, it need not be so high. The cubic spline fit constructs a third power polynomial between each pair of the 81 points. Two polynomials meet at each of the 81 points (except the ends), and the values, slopes and curvatures are continuous across the two polynomials. This gives a very smooth curve that has enough flexibility to match nearly any function. The fit within an interval minimizes the differences between the data points and the polynomial in a least squares sense.

The magnitude calibration waveform () used for the humbucker measurements shown later is here. This plot is in db. The combination of the hardware and processing is flat to better than 0.01 db over nearly all of the frequency range. Although not shown on the plot, the point at 24 Hz is 2.75 db down. It is necessary to do the calibration in order for the low frequency limits to be useful.

Thee phase calibration waveform () is also necessary for useful low frequency limits. The slope across the rest of the useful range is actually a time delay through the Duet preamp. It is a positive rather than negative slope because the signal that uses the preamp is in the denominator of the ratio that makes the transfer function.

The real and imaginary parts of the impedance of a Japanese humbucker bought from All Parts some years ago is shown here. (There is no cover and the base plate has been replaced with one made of nickel silver.) The plot () shows the raw data, the 81 points of the fit, and the smooth curve. The raw data are not easily visible, and so a blow up of part of the plot is shown here ().

The coil inductance and resistance can be derived from one of the low frequency measurements. I use 72 Hz. Some comparisons with the Extech (120Hz) and DVM are:
humBucker pickup: pickupmeter: 4.807H, 8.712 K
Extech: 4.816H DVM: 8.77K
tele bridge*: pickupmeter: 2.142H, 7.041K
Extech: 2.159 H, DVM: 7.008K
coil with ferrite cores: pickup meter: 1.77H, 4.693K
Extech: 1.803H , DVM: 4.69K

These seem accurate enough for pickup work.

One of the advantages of measuring the frequency to 43 KHz is that the impedance at the high frequencies is more a function of the coil capacitance, and less of the inductance. It is not high enough to ignore the inductance completely, though. One can try different values of inductance until finding one that gives the most consistent capacitance measurement over a range of high frequencies. This gives 38.1 pf; this algorithm might need some more work before passing to general use. The inductance that is found is significantly less than the inductance of the coil, as expected for the high frequency limit of eddy current effects.

A later post will describe more derived parameters, concentrating those relevant to eddy currents.



* Stew mac parts, #43 wound to 7K, no baseplate

[Mike Sulzer]

The purpose of this post is to describe a way of comparing the effects of eddy currents on different pickups across about 10KHz of frequency range. It is not necessary to go any higher since the response of whole electric guitar system falls quickly above 5KHz.

First review the effect of eddy currents on the humbucker pickup,measured with no cover. Using the results found in the post about the basic measurement, the effect of the coil capacitance is removed from the measured impedance. In this plot () the impedance of the inductance of the coil is the black line. The red line is the measurement of the imaginary part, with the effect of the coil capacitance removed. At low frequencies, it follows the coil inductance, but diverges with increasing frequency. The green line is the coil resistance; it is just a number and has no variation with frequency. The blue line is the measured real part, also showing a divergence, rising above the coil resistance with increasing frequency.

This suggests the following method for quantifying the effects of eddy currents:
At each frequency, subtract the coil impedance (Rc + 2pi*f*Lc*j) from the measured complex impedance (with the effect of the C removed), compute the magnitude squared, and divide by the magnitude squared of the coil impedance. Then put the whole thing in db by taking the base ten logarithm and multiplying by 10. The resulting numbers will be negative, more negative for larger effects from eddy currents. Various results are shown in this graph: (). Removing the cover, and then the base plate both reduce the effects, but the dominant effect is from the cores since the other two pickups show much smaller effects. The Alnico magnets in the tele bridge pickup conduct much less than the steel cores of the humbucker, the ferrite cores of the other pickup even less so.

[RedHouse]

Ladies and Gentlemen, fasten your seatbelts, 'cause here we go with the eddy currents ....again.

[Steve Conner]

Well, it's interesting! The eddy currents probably account for a lot of the tonal difference between an actual pickup and the crude second-order lowpass model.

Mike's results remind me of the graphs of complex permeability vs. frequency that I see in ferrite core data sheets. Complex permeability is an extension of the concept of permeability, to cope with lossy materials. The real part of it affects the inductance of the coil, the imaginary part appears as a loss resistance. I think Mike is basically measuring the complex permeability of the magnetic circuits in his pickups.

[Mike Sulzer]

Some attachments seem to have gone missing. They are here:

[ScottA]

Mike,

Great stuff.

I'd still like to talk to you off-line if you have any interest. If you want to contact me, please use the email on our website. I'm still getting malware warnings from this site at home so I hesitate to come here on my home computer.

I've got two responses:

1) The Chevy Chase response:

"It's so simple, maybe you need a refresher course. It's all eddy currents these days"

2) The Captain Kirk response:

"Eddy currents.

Ed-dy Cur-rents!"