Impedance measurements with a computer DAC interface unit

[stratotarts]

I am creating this thread to continue the sub-discussion at other thread and give it its own subject, because I believe it will continue to be "on the radar".
It concerns member ms's offsite posts Measuring pickup impedance with an A/D recording interface and Software for performing pickup analysis with a recording interface.

There are good reasons to pursue this approach. Mainly, by capturing a complete black box representation of the pickups behaviour by recording complex impedance at all frequencies, it may be possible to produce accurate bode plots for an endless variety of load situations, without any curve fitting or analysis (as might be required to interpret data recorded only as a bode plot). It would still be possible to perform such curve fitting or other analyses, but it becomes optional.

Member ms has suggested a simple test circuit that allows this to be done without any specialized amplifier circuits (such as the V5 integrator). There was some discussion about the effects of cable capacitance. I think that ms says it does not cause any problems of loading of the device under test (pickup). I do have my doubts about that, but I may be wrong. In any case, I have two suggestions to address that. One is to use the high impedance portion of the V5 as a buffer, omitting the integrator. Another is to introduce a compensating leg in the drive circuit. The idea is to allow the effects of capacitance in the two input channels to cancel, like this:



Honestly, I am not sure about this, it's just an idea, and I have no way to test it right now.

[antigua]

You spoke of the phase in the other thread, is this the sort of data you're going for?

[ms]

Dec 11, 2016 13:48:03 GMT -5 stratotarts said:

I am creating this thread to continue the sub-discussion at other thread and give it its own subject, because I believe it will continue to be "on the radar".
It concerns member ms's offsite posts Measuring pickup impedance with an A/D recording interface and Software for performing pickup analysis with a recording interface.

There are good reasons to pursue this approach. Mainly, by capturing a complete black box representation of the pickups behaviour by recording complex impedance at all frequencies, it may be possible to produce accurate bode plots for an endless variety of load situations, without any curve fitting or analysis (as might be required to interpret data recorded only as a bode plot). It would still be possible to perform such curve fitting or other analyses, but it becomes optional.

Member ms has suggested a simple test circuit that allows this to be done without any specialized amplifier circuits (such as the V5 integrator). There was some discussion about the effects of cable capacitance. I think that ms says it does not cause any problems of loading of the device under test (pickup). I do have my doubts about that, but I may be wrong. In any case, I have two suggestions to address that. One is to use the high impedance portion of the V5 as a buffer, omitting the integrator. Another is to introduce a compensating leg in the drive circuit. The idea is to allow the effects of capacitance in the two input channels to cancel, like this:



Honestly, I am not sure about this, it's just an idea, and I have no way to test it right now.

I agree that I do not have the necessary symmetry for high frequency gain difference cancelation due to cables and input capacitance since the output impedance of the line out on  the 2X2 is 110 ohms. I need to add about 900 ohms. (For some reason I though it was 1K until I read the manual again.)  However, I do not think it matters. With 1K as the highest impedance and the small capacitance from short cables, it does not seem to be an issue.

I do not think this is a device loading issue.  The voltage across the 1K resistor measures the current through the pickup very accurately, and the voltage across the series combination is used to derive the voltage across the pickup by subtracting the other sample from it.  The 1K resistor is very slightly loaded, but you can compensate for this if you want.

There is an over all gain matching issue, of course. This was easier with the Apogee Duet than the 2X2.

Of course yo do not have to make the channel gains the same; you can introduce a compensating factor in the software.  But you still have to get the gain right.

[stratotarts]

Dec 11, 2016 14:43:04 GMT -5 antigua said:

You spoke of the phase in the other thread, is this the sort of data you're going for?




Generally, yes. But this is the integrated signal. You need a different circuit to obtain Z. Basically you would use a polar to rectangular conversion (trig) to convert phase and magnitude to real and imaginary quantities. In electronics, the real term represents the resistance, and the imaginary term represents the reactance. Truthfully, people who are more familiar with the math can help better, especially because I'm kind of swamped with personal goings-on here so I don't have the time to hit the textbooks again.

[stratotarts]

Dec 11, 2016 18:10:27 GMT -5 ms said:

Dec 11, 2016 13:48:03 GMT -5 stratotarts said:

I am creating this thread to continue the sub-discussion at other thread and give it its own subject, because I believe it will continue to be "on the radar".
It concerns member ms's offsite posts Measuring pickup impedance with an A/D recording interface and Software for performing pickup analysis with a recording interface.

There are good reasons to pursue this approach. Mainly, by capturing a complete black box representation of the pickups behaviour by recording complex impedance at all frequencies, it may be possible to produce accurate bode plots for an endless variety of load situations, without any curve fitting or analysis (as might be required to interpret data recorded only as a bode plot). It would still be possible to perform such curve fitting or other analyses, but it becomes optional.

Member ms has suggested a simple test circuit that allows this to be done without any specialized amplifier circuits (such as the V5 integrator). There was some discussion about the effects of cable capacitance. I think that ms says it does not cause any problems of loading of the device under test (pickup). I do have my doubts about that, but I may be wrong. In any case, I have two suggestions to address that. One is to use the high impedance portion of the V5 as a buffer, omitting the integrator. Another is to introduce a compensating leg in the drive circuit. The idea is to allow the effects of capacitance in the two input channels to cancel, like this:



Honestly, I am not sure about this, it's just an idea, and I have no way to test it right now.

I agree that I do not have the necessary symmetry for high frequency gain difference cancelation due to cables and input capacitance since the output impedance of the line out on  the 2X2 is 110 ohms. I need to add about 900 ohms. (For some reason I though it was 1K until I read the manual again.)  However, I do not think it matters. With 1K as the highest impedance and the small capacitance from short cables, it does not seem to be an issue.

I do not think this is a device loading issue.  The voltage across the 1K resistor measures the current through the pickup very accurately, and the voltage across the series combination is used to derive the voltage across the pickup by subtracting the other sample from it.  The 1K resistor is very slightly loaded, but you can compensate for this if you want.

There is an over all gain matching issue, of course. This was easier with the Apogee Duet than the 2X2.

Of course yo do not have to make the channel gains the same; you can introduce a compensating factor in the software.  But you still have to get the gain right.

Okay, then. For a lower output impedance you could use the headphone jack, if it matters. To deal with gain, I suggest some kind of calibration procedure. Edit - for example, you would insert some test load (resistor?) into the fixture, and run a calibration routine. It would adjust levels and save a gain constant in a file. The test routine would read the calibration constant stored in the file, and incorporate it in the calculations.

[ms]

Dec 11, 2016 18:58:40 GMT -5 stratotarts said:

Dec 11, 2016 18:10:27 GMT -5 ms said:

I agree that I do not have the necessary symmetry for high frequency gain difference cancelation due to cables and input capacitance since the output impedance of the line out on  the 2X2 is 110 ohms. I need to add about 900 ohms. (For some reason I though it was 1K until I read the manual again.)  However, I do not think it matters. With 1K as the highest impedance and the small capacitance from short cables, it does not seem to be an issue.

I do not think this is a device loading issue.  The voltage across the 1K resistor measures the current through the pickup very accurately, and the voltage across the series combination is used to derive the voltage across the pickup by subtracting the other sample from it.  The 1K resistor is very slightly loaded, but you can compensate for this if you want.

There is an over all gain matching issue, of course. This was easier with the Apogee Duet than the 2X2.

Of course yo do not have to make the channel gains the same; you can introduce a compensating factor in the software.  But you still have to get the gain right.

Okay, then. For a lower output impedance you could use the headphone jack, if it matters. To deal with gain, I suggest some kind of calibration procedure. Edit - for example, you would insert some test load (resistor?) into the fixture, and run a calibration routine. It would adjust levels and save a gain constant in a file. The test routine would read the calibration constant stored in the file, and incorporate it in the calculations.

No, I do not see any need for lower output impedance; I was just thinking of matching it to the 1K of the resistor, although this is not really necessary.  One calibration procedure is to measure the dc resistance of the pickup independently, and then make fine adjustments on one of the channel gain controls until you match it.  Then the other parameters should be correct as well.  But it is more convenient to have a piece of equipment quantized accurate gain adjustment, well matched between channels.

[ms]

Consider two diagrams for measuring pickup impedance by dividing the voltage across the pickup by the current through it.

Diagram A appears simpler, but it has the disadvantage that the finite impedance of the voltmeter is across the pickup, a high impedance device over some frequency range.  It also has the disadvantage that a computer controlled floating input high impedance voltmeter and a computer controlled ammeter are expensive.  Diagram B can be realized with inexpensive hardware.  The resistor can have a low value and so loading by the voltmeter is not as much of an issue.  The voltage across the pickup is found by subtraction of the lower sample from the upper, and so there is no loading, while the current through the pickup is the lower sample divided by the resistor.  So it is preferred for at least two practical reasons.

[antigua]

Forgive me for being slow, but is diagram B depicting what I had done here guitarnuts2.proboards.com/thread/7775/pickups-resonant-peak-usb-oscilliscope ? 

[ms]

Dec 16, 2016 23:45:20 GMT -5 antigua said:

Forgive me for being slow, but is diagram B depicting what I had done here guitarnuts2.proboards.com/thread/7775/pickups-resonant-peak-usb-oscilliscope ? 

There are some similarities, but the intent and the results are very different.  In the setup you show using a 1M resistor (an improvement over the sys comp diagram using a 56K resistor; is that a typo?), you are just driving a pickup from a high impedance and measuring the voltage across it to get the resonant frequency.  The Q is limited by the resistor and the scope input impedance.

Diagram B drives a pickup in series with a small resistor with a voltage source.  This voltage is measured; also the voltage across the resistor is measured.  The loading on the small resistor is either negligible or easily corrected.  The voltage across the pickup is found by subtracting the two samples.  It can be affected by the small stray capacitance across the pickup, but you could look at this part of the measurement since you always have some with the pickup in the instrument also.  This voltage also could be affected by cross coupling in the channels in the measuring instrument, but that is small.  The current through the pickup is found from Ohm's law using the voltage across it.  This voltage is not huge, but you are using a measurement device intended to keep noise low, gain flat, and have good cross talk rejection.  So the idea of the processing is to divide the current through the pickup into the voltage across it resulting in the impedance.  All frequencies are obtained at once by using an appropriate waveform, and results are averaged long enough to get quiet measurements.

[stratotarts]

Curious. In "B" you measure the voltage across the voltage source. Don't you already know the value, since you defined it and it's not affected by the load because the load is in parallel with it?

[ms]

Dec 17, 2016 8:31:13 GMT -5 stratotarts said:

Curious. In "B" you measure the voltage across the voltage source. Don't you already know the value, since you defined it and it's not affected by the load because the load is in parallel with it?

1. It is not a perfect voltage source (zero output impedance) just because I drew it that way for simplicity.  It must have some impedance.

2. Even if it had zero output impedance, that does not mean that you know the frequency response  or amplitude perfectly.

I use a digital waveform, a so called code, that by its very nature does not have equal response at all frequencies.  Since this response can be modified by the D/A and the analog amplifier, it is better to measure what you actually have, than to try to predict it.  This way the ratio is very close to correct at all frequencies of interest

[ms]

In this post I would like to discuss the waveform used in the measurement outlined in diagram B in a post above.

The idea is to measure the impedance at many frequencies, and for simplicity, to use a single waveform that contains all the frequencies. (But this single waveform is repeated many times to overcome the effects of random noise.)

Since the measurement involves taking a ratio of voltage to current at each frequency, it is not necessary that the waveform contain equal amounts of power at all frequencies: the ratio is independent of the actual value since both the voltage and current are affected by the same factor.  However, it is not good if it contains too little power at some frequencies because the measurements at such frequencies have a a poorer signal to noise ratio than you would like.

A short pulse, that is with width something like one over the bandwidth we want to cover, contains all frequencies in that range.  However, we cannot repeat the pulse too often, something like one over the frequency resolution we want, and so a short pulse makes very poor use of the average power capability of the amplifier that creates the waveform.  Thus the SNR would be poor, and we would have to repeat the waveform many many times to get good results.  Such a waveform can be said to have "low duty cycle", and we would like to use a waveform with high duty cycle.

One way to get high duty cycle is to use a waveform that has only two values, the positive and negative maxima that the amplifier can produce, or at least near to those values.  But how do we get the bandwidth?  That comes from some appropriate time pattern of changes between + and -.  There is no pattern that gives perfectly distributed frequency values.  How do I know?  This is a very well researched problem because radars are a very important tool.  Suppose you have a radar that emits rf pulses.  You often want a short pulse to give good range resolution, that is, to allow to close targets to be easily seen.  However, you also want to transmit high power to get good sensitivity.  It turns out that radar transmitters usually can achieve their full average power output only by transmitting a pulse longer than you want.  That is, the peak power is not really as high as you would like.  Can you make a long pulse act like a short one?  Yes, under some useful conditions.  You need to make the long pulse have a spectrum  that is wider like a short pulse.  You do this by modulating the pulse, often with the two value waveform that gives high duty cycle.  Then you have to do some special processing in the receiver, but that is another matter.

So how do you find such waveforms? You can search for them.   One way is to do a computer search over billions of waveforms until you get one that is good enough.  Or you can do a literature search. That is, you look for a paper where someone else shows what good codes they have found.  That is the easier way.

The top plot in the attachment shows the code of the length I wanted found by literature search.  It is in arbitrary time units.  The next plot down shows the spectrum in arbitrary frequency units.  The bottom two plots show a randomly selected code.  The spectrum dips much deeper, and so it is not nearly as good.

[ms]

What wave form to use?  A bit of an aha! moment:  Golay complementary sequences, used for radars sometimes, but I had not thought about them for some time (decades).  For purposes here, these are a pair of sequences of +1 and -1 such that if you add the two power spectra, the result is flat, that is independent of frequency, even though individually they are not flat.   We do not really need perfectly flat, but it is convenient, and these codes come in all powers of two. Also, they are generated by a simple recursive algorithm:

# Complementary codes
# l is the length (must be power of two)
def ccode(l):
    lc = 2
    c0 = np.array([1,1])
    c1 = np.array([1,-1])
    cs0 = c0
    cs1 = c1
    lc *= 2
    while lc <= l:
        c0 = np.append(cs0, cs1)
        c1 = np.append(cs0, -cs1)
        cs0 = c0
        cs1 = c1
        lc *= 2
return c0, c1

The attachment () shows a small part of the measurement stream, about one code pair.  The codes (blue) have passed through the anti aliasing filter after the DAC, and so they are no longer constant amplitude.  The red shows the voltage across the sensing resistor, that is, proportional to the current, and it has greatly reduced high frequencies since the impedance of a pickup increases with frequency.  The codes have 512 samples and are separated by another 512 samples.  This is to allow the correlation introduced by the pickup to die down.  This condition is not met at very low frequencies, of course, and so a ripple is introduced in the spectra, but this does not hurt the measurement because it involves taking the ratio.

[stratotarts]

Jan 6, 2017 12:30:46 GMT -5 ms said:

What wave form to use?

I find what you're doing with these signals very interesting, but what is the reason to consider using them vs. the common swept sine wave?

[ms]

Now look at some results.  This test pickup is an old tele bridge (no base plate) I wound sometime ago with #43 wire, loose and scattered, giving low capacitance. The attachment shows the results.  The measurement required about 3.5 seconds of integration.  The instrument was calibrated (at Stratotart's suggestion), and the following means was used:
1.  The pickup is measured with the Extech (120 Hz), and the resulting series resistance is input to the software.

2. The inductance is also input for comparison with the results.

3.  When the measurement integration is complete, lines are fit to the low frequency real and imaginary parts, and results are evaluated at 120 Hz.

4. A scale factor is derived so that the measured real part at 120 becomes equal to that of the Extech.

5.  The scale factor is saved and printed, and it is used in further measurements instead of a value from the Extech.



There are 513 points in the spectra, with about 256 independent points, and so the smoothness of the measurement is a result of low noise, not digital post processing.
The value of the resonant frequency is derived by fitting a line in the neighborhood of the zero crossing of the imaginary part.  Not only is this consistent with the formal definition of resonance, it is more accurate than looking using the peak of the real part.

I will discuss how the value of C is derived some time in the future, but for now it is easy to verify that the value is accurate.  The green and yellowish lines are the impedance with the C "unparalleled".  The purpose of these lines is to show the effect of eddy currents, by comparison to the gray dashed and dot dashed lines, which are the case for no eddy currents.  Eddy currents are low in this pickup because there is little deviation from those lines, as a result of alnico magnets.  However, the main point here is that there is no sign of the peak in the yellowish and green curves, and therefore an accurate value of C was removed.

A sequence of measurements was made in order to look at noise on the measurements and at drifting, a result of temperature change affecting both the pickup and the instrument.  This attachment shows three parameters on a zoomed in scale so that changes are easily seen:



The inductance differs from the Extech value by about .16%.  I was hoping for better, but I guess it will do. The noise is dominated by mH size spikes; I do not know the cause, but speculate some kind of transient magnetic noise.

The resistance is very close because that is what we are calibrating to.  The value decreases as the temperature increases in the morning.  The standard deviation is way under 1 ohm, better than needed.

The frequency shows a more complicated drift, apparently because there are multiple factors involved.  The standard deviation is less than 1 Hz, also more than good enough.

[ms]

Jan 6, 2017 12:37:09 GMT -5 stratotarts said:

Jan 6, 2017 12:30:46 GMT -5 ms said:

What wave form to use?

I find what you're doing with these signals very interesting, but what is the reason to consider using them vs. the common swept sine wave?

Thanks for your interest! Measuring all the parameters at once avoids various small problems that arise in non-simultaneous measurements, and also, when information is used in a near optimum fashion, results in very fast complete measurements, done before any conditions can change.  Also one thing I do professionally is radar coding techniques, and there is that old thing about everything looking like a nail to a hammer.

[ms]

An interesting effect appears when you measure a humbucker.  In this case, we measure one coil with the other coil open.  This is an SD pickup; the sticker on the bottom reads "SH1N Neck".  This is the so called PAF replacement that does not carry the SD label on top.  Here are the measurements:




Of course the peak is lower and broader as expected, compared to the tele pickup, but it also has a funny shape above the peak.  Apparently the open second coil, which resonates with its own capacitance, is stealing some energy from the coil under measurement.  This is quite high in frequency and should have no practical effect, but it does suggest that there could be even more coupling when both coils are connect together.

[ms]

Here are the impedance measurements for the SN1 Neck connected as a normal humbucker.


With the two coils in series, the inductance is higher, and, with the high capacitance connecting cable, the resonance frequency comes down a lot.  The funny coupling effects at the top are even more apparent.

[JohnH]

Jan 6, 2017 15:04:13 GMT -5 ms said:

Here are the impedance measurements for the SN1 Neck connected as a normal humbucker.


With the two coils in series, the inductance is higher, and, with the high capacitance connecting cable, the resonance frequency comes down a lot.  The funny coupling effects at the top are even more apparent.

Here's something I found interesting. I took one of the 6-part theoretical models, and extracted impedance results in the same form as in your tests. This one is for a 8.04k 4.83H uncovered '57 Classic (recently tweaked as in previous posts.)

Compared to SD '59's, these seem to be slightly less lively, but the form of the graphs are very similar indeed, up to above 10khZ where your measured results start to show extra wiggles. You can see the low frequency reactance aligning to the gradient of the Lcoil impedance, and also it has a similar effect whereby the imaginary impedance sneaks slightly above the Lcoil impedance, before reaching a maximum and then dropping.

Encouraging I think.

[antigua]

Jan 6, 2017 13:57:41 GMT -5 ms said:

An interesting effect appears when you measure a humbucker.  In this case, we measure one coil with the other coil open.  This is an SD pickup; the sticker on the bottom reads "SH1N Neck".  This is the so called PAF replacement that does not carry the SD label on top.  Here are the measurements:




Of course the peak is lower and broader as expected, compared to the tele pickup, but it also has a funny shape above the peak.  Apparently the open second coil, which resonates with its own capacitance, is stealing some energy from the coil under measurement.  This is quite high in frequency and should have no practical effect, but it does suggest that there could be even more coupling when both coils are connect together.

I had a thread on this topic a few months ago guitarnuts2.proboards.com/thread/7769/damping-caused-unused-splitting-humbucker   The unused coil sucks from the active coil different depending on whether it's open or closed. If it's closed, it's an inductive load, if it's open, it's faintly capacitive. 

Another thing to note about 4 conductor humbuckers is that there is a 40pF capacitance, give or take, between the series coils as a result of the two way run through the shielded hookup wire. If the shield is left disconnected, usually an braided wire with not insulator, that capacitance mostly goes away.  

[ms]

Jan 6, 2017 15:52:28 GMT -5 JohnH said:

Jan 6, 2017 15:04:13 GMT -5 ms said:

Here are the impedance measurements for the SN1 Neck connected as a normal humbucker.


With the two coils in series, the inductance is higher, and, with the high capacitance connecting cable, the resonance frequency comes down a lot.  The funny coupling effects at the top are even more apparent.

Here's something I found interesting. I took one of the 6-part theoretical models, and extracted impedance results in the same form as in your tests. This one is for a 8.04k 4.83H uncovered '57 Classic (recently tweaked as in previous posts.)

Compared to SD '59's, these seem to be slightly less lively, but the form of the graphs are very similar indeed, up to above 10khZ where your measured results start to show extra wiggles. You can see the low frequency reactance aligning to the gradient of the Lcoil impedance, and also it has a similar effect whereby the imaginary impedance sneaks slightly above the Lcoil impedance, before reaching a maximum and then dropping.

Encouraging I think.

Yes, it is. It might be interesting to 'unparallel' the C and see how the eddy current effects show up.

[ms]

Jan 6, 2017 16:38:43 GMT -5 antigua said:

Jan 6, 2017 13:57:41 GMT -5 ms said:

An interesting effect appears when you measure a humbucker.  In this case, we measure one coil with the other coil open.  This is an SD pickup; the sticker on the bottom reads "SH1N Neck".  This is the so called PAF replacement that does not carry the SD label on top.  Here are the measurements:




Of course the peak is lower and broader as expected, compared to the tele pickup, but it also has a funny shape above the peak.  Apparently the open second coil, which resonates with its own capacitance, is stealing some energy from the coil under measurement.  This is quite high in frequency and should have no practical effect, but it does suggest that there could be even more coupling when both coils are connect together.

I had a thread on this topic a few months ago guitarnuts2.proboards.com/thread/7769/damping-caused-unused-splitting-humbucker   The unused coil sucks from the active coil different depending on whether it's open or closed. If it's closed, it's an inductive load, if it's open, it's faintly capacitive. 

Another thing to note about 4 conductor humbuckers is that there is a 40pF capacitance, give or take, between the series coils as a result of the two way run through the shielded hookup wire. If the shield is left disconnected, usually an braided wire with not insulator, that capacitance mostly goes away.  

Interesting, this is a mutual inductance effect, related to eddy currents, not sure how the term should be used technically.  This brings up again the possibility of "shaping" the resonant peak by the use of an extra coil with a particular kind of loading.  It need not have a lot of turns if the right size wire and load are used.  It would be most conveniently put around the main coil like a transformer secondary.

[ms]

Here are some results from a coil using ferrite cores. It is low resistance and inductance, but surprisingly high capacitance. (must be wound very tight and evenly, I do not remember)  The ferrite material is the highest permeability commonly available, about 3000, I believe.  It is thus high loss for a ferrite. It appears that this loss can be measured at the top of the audio range, but it is a lot less than alnico.



I suspect that the method for finding the coil inductance needs a bit of work.

[ms]

Here is a block diagram of the current setup:



It works better with the signal into input 2 attenuated; also the level controls should be adjusted well back from where the overload indicators come on.  Both inputs are set up for instrument, not line.

[JohnH]

Jan 7, 2017 8:06:12 GMT -5 ms said:

Yes, it is. It might be interesting to 'unparallel' the C and see how the eddy current effects show up.

Easily done, here it is, with the same colours as your tests:

The plots with C removed look to have the similar tendencies as those from the tests, up to around 10khz or so, including their general curvature and the way they merge into the plots with C at low frequency.



The differences above 10khz are interesting because they might relate to why often a model that works well below that frequency tends to deviate above the highest peak, often not falling quite so steeply.  These are the loaded and unloaded outputs for the tests and the model:



You can see there, where the solid green line from the unloaded model declines slightly less steeply at 9khz and above compared to the dashed lines traced from Antigua's test. At these high frequencies, such deviations are of theoretical interest but not really of practical significance.

[ashcatlt]

Jan 6, 2017 16:38:43 GMT -5 antigua said:

I had a thread on this topic a few months ago guitarnuts2.proboards.com/thread/7769/damping-caused-unused-splitting-humbucker   The unused coil sucks from the active coil different depending on whether it's open or closed. If it's closed, it's an inductive load, if it's open, it's faintly capacitive. 

This is not new to the nuthouse, but it's the closest to real definitive numbers that we've seen.

The fun part of this is that we're talking about a whole lot of things that don't make much difference on their own.

[ms]

Jan 7, 2017 15:24:28 GMT -5 JohnH said:

Jan 7, 2017 8:06:12 GMT -5 ms said:

Yes, it is. It might be interesting to 'unparallel' the C and see how the eddy current effects show up.

Easily done, here it is, with the same colours as your tests:

The plots with C removed look to have the similar tendencies as those from the tests, up to around 10khz or so, including their general curvature and the way they merge into the plots with C at low frequency.



The differences above 10khz are interesting because they might relate to why often a model that works well below that frequency tends to deviate above the highest peak, often not falling quite so steeply.  These are the loaded and unloaded outputs for the tests and the model:



You can see there, where the solid green line from the unloaded model declines slightly less steeply at 9khz and above compared to the dashed lines traced from Antigua's test. At these high frequencies, such deviations are of theoretical interest but not really of practical significance.

That's good.  I think now I have to run the eddy current model (time permitting) to see if it is possible to use just one parameter in the range of values normally encountered with pickups. (I mentioned in that other discussion that it is hard to fit for both parameters at once.  That might mean that one parameter, set up in some way to be determined, would be enough.)  Of course, even if one parameter is enough, that does not mean that one real component would be enough to make your model work well.  We are dealing with mutual induction; it is a bit special.  Who knows? it might be convenient to invent a mutual inductistor with some useful characteristic.

[antigua]

Jan 7, 2017 8:12:11 GMT -5 ms said:

Jan 6, 2017 16:38:43 GMT -5 antigua said:

I had a thread on this topic a few months ago guitarnuts2.proboards.com/thread/7769/damping-caused-unused-splitting-humbucker   The unused coil sucks from the active coil different depending on whether it's open or closed. If it's closed, it's an inductive load, if it's open, it's faintly capacitive. 

Another thing to note about 4 conductor humbuckers is that there is a 40pF capacitance, give or take, between the series coils as a result of the two way run through the shielded hookup wire. If the shield is left disconnected, usually an braided wire with not insulator, that capacitance mostly goes away.  

Interesting, this is a mutual inductance effect, related to eddy currents, not sure how the term should be used technically.  This brings up again the possibility of "shaping" the resonant peak by the use of an extra coil with a particular kind of loading.  It need not have a lot of turns if the right size wire and load are used.  It would be most conveniently put around the main coil like a transformer secondary.

What was a surprise to me is that the open coil had any effect at all, as I figured open circuit = no current, but the capacitive coupling of the coil windings makes the secondary a closed circuit no matter what. 

[JohnH]

Jan 8, 2017 14:04:45 GMT -5 ms said:

That's good.  I think now I have to run the eddy current model (time permitting) to see if it is possible to use just one parameter in the range of values normally encountered with pickups. (I mentioned in that other discussion that it is hard to fit for both parameters at once.  That might mean that one parameter, set up in some way to be determined, would be enough.)  Of course, even if one parameter is enough, that does not mean that one real component would be enough to make your model work well.  We are dealing with mutual induction; it is a bit special.  Who knows? it might be convenient to invent a mutual inductistor with some useful characteristic.

Looking at the test plots with C removed, they seem to suggest some secondary resonance effect at around 12kHz, due to the way the real part rises and falls and the imaginary goes up then down. But very muted, no sharp peaks. To me, that suggests an addional branch with some capacitive (ie negative) reactance plus some resistance, and that this is interacting with inductance.

One way to investigate might be to try modelling such an element in a few places to find out where to put it that creates the right tendencies, then to find some credible values. Having arrived at 'ball-park' values, it may then be possible to figure out if or when the extra branch is significant at lower frequencies and if it can usually be ignored for modelling.

[ms]

The purpose of this post is to describe how the impedance is computed from the raw measurements. A pickup with a resistor in series, connected as in diagram B above, is a linear filter.  So what we need to do is compute the relationship between the output and the input, as a function of frequency, and then combine the various results of that process to get the impedance.

One way to think of what a linear filter does is this: at each frequency of interest it scales the amplitude of the input signal and shifts the phase.  (Of course you can think of this in terms of real and imaginary parts also.)  One way to measure this is to use cross spectral analysis.  To implement this, we divide the samples from the two inputs into convenient size sections and compute the fft of each.  We add up the magnitudes squared (versus frequency) of all the sections from channel 1 and channel 2, but also we take the cross product.  That is, we multiply channel 1 times the complex conjugate of channel 2 for each section and sum up the results.  This latter result is an estimate of the cross spectrum; it is a complex quantity, which means that it has an amplitude and a phase.  By taking the complex conjugate before multiplying, we are subtracting the phases, and so the phase of the cross spectrum is the phase shift introduced by the filter, averaged to reduce the effect of noise.

In addition to the signal we want, the measurements have additive random noise.  The relationship between the signals at the input and output can be thought of as coherent: there is a definite relationship between both the magnitude and phase.  The noise, on the other hand, is thought of as incoherent since the noise at each frequency is not so related to the signal.  There is a quantity called the coherence (or actually the squared coherency spectrum) which measures this relationship; it is near one at frequencies where noise is small and much smaller where noise dominates.  This quantity is found by dividing the magnitude squared of the cross spectrum by the product of the two individual spectra.  Here is a typical coherence measurement from this instrument:



It is minimum at the frequency where the pickup self-resonates.  This is because the pickup has a maximum in its impedance at this frequency, and so the voltage across the resistor is smallest, and so the effect of noise the greatest.  However the coherence is still quite high, and we expect the measurement to be useful across the band.  However, the ripples in the coherence are interesting; they imply small periodic changes in the SNR as a function of frequency.  To see where this is coming from we look at the spectrum of the signal applied to the pickup:




The response of the complementary codes is flat, and so we look at the rest of the system to see what this ripple is.  I think it must be the antialiasing filter on the line output; I missed this at first, having misread the specs. It appeared that they were stating how flat the response of the system is across the band. Actually, they state the response at 20KHz.  Sure enough, the figure shows that the response at 20KHz is just about between the extremes of the ripple.  Of course, the +/- 1 db is not an issue since we take a ratio, and the coherence shows that the effect on the SNR of the measurement is small.

The measured cross spectrum is the average of the product of the two voltages; we want the ratio of the voltage applied to the current through the resistor.  We have the voltage squared, the self spectrum of the voltage across the resistor, and so we divide by that. Then we just have to multiply by the resistor to get the impedance of the pickup plus the resistance. So we subtract the resistance to complete the process.