Measuring AC Impedance with a LCR meter

[Mike Sulzer]

If there was a niche for a kit, I'd say a LR meter that worked at 100Hz where the capacitances are negligible.

The Extech measures at 120 Hz. At this frequency the effects of eddy currents are small. The measurement there gives the inductance from the coil and the permeability of the core. Measurements at other frequencies can be used to deduce the additional circuit elements that describe the effects of the currents. More about this soon.

Capacitive effects are still pretty small at 1 KHz: 100 pf ==> 1.5 million ohms, while the magnitude of the impedance of the pickup is about 30,000 ohms. It is the eddy current effects that are the dominate error, although it is still typically only about 10% or so.

[salvarsan]

Capacitive effects are still pretty small at 1 KHz: 100 pf ==> 1.5 million ohms.

Minor quibble over the capacitive reactance figure.

1/(2 * PI * freq * C) = 1591 ohms.

You may have entered microFarads instead of picoFarads.

Correction: I entered nanoFarads instead of picoFarads.

Nevermind.

[salvarsan]

Must have missed my point, go figure. I was making a point (sarchasm) about all the fuss and churn about silly crap that goes on here and yet we can't... as a group... make a simple kit to address one of the most fundamental parts of this hobby/interest/business. The Eleopro reference was just to highlight how many are actually willing, and able, to build a kit because you had said "few people...", again debugging isn't the point but never mind, I see we're back to the 1% accuracy notion again.(emphasis added)

Y'know, this kind of discussion crops up a lot.

Over on a science forum, some folks argued the merits of a shoebox-sized NMR for workaday quality control in industry. It costs 1/10 what a research-grade NMR does, and although low-rez, is extremely easy to use.

The industrial chemists (a majority) think it's a desirable product.
The research chemists (a noisy minority) think it sucks because they are used to large expensive high-rez NMR.

The Perfect is the enemy of the good (or "good enough").

I've argued that a lot but am chagrined to find myself in the perfectionist camp this time.

Here's the money shot:
What would make an inexpensive inductance tester good enough for pickup builders?

• Inexpensive.
• Convenient/ease of use.
• Adequate accuracy. 5.0% maybe?

Can this be done using a microcontroller and one of Joe's or Mike's VI interface daughterboards?

[RedHouse]

....the real parameters of a pickup are too complicated for the internal assumptions made by these meters...

Aye, they're nae good, gonn'ae-no trust 'em.

It's just that reason why it begs a purpose-specific build, but I'll digress, it's not gonna happen.

Y'know, this kind of discussion crops up a lot.

...

Here's the money shot:
What would make an inexpensive inductance tester good enough for pickup builders?

• Inexpensive.
• Convenient/ease of use.
• Adequate accuracy. 5.0% maybe?

Can this be done using a microcontroller and one of Joe's or Mike's VI interface daughterboards?

Yes exactly.

I see it much like the difference between using a go-gauge or a digital caliper in the fabrication shop, both will get the job done, one works much quicker, is less expensive, both are appropriate for the job, both fit the function, but one is left on the toolbox 90% of the time. Those who don't use their hands as much as their intellect unsually find it tought to grasp why people might need a lesser tool, or a tool which has a acceptance of a lesser standard.

Think about how many people use those $4.99 Harbor Freight DMM's which well do the job they are designed for, even as well as a $499 Fluke, we can dismiss that and revel in how cool and exacting our Fluke's are, but it doesn't make our DCR reading any better if that +/- 1-digit accuracy is telling us we have a 3k652 coil or a 3k656 coil so most don't bother with extreme accuracy.

A couple of years ago when helping with a teach-in type thing for a youth group with the goal of trying to get kids interested in entry-level electronics (simple circuits, blink-the-LED etc) and we bought several of those Harbor Freight cheepies when the $4.99 ones were on sale at like $1.99 so we could demonstrate stuff in a hands-on kinda way. Before the class my friend and I decided to check them against my mid-level meter and his high-end Flukes and see just how bad $1.99 got us, we were surprised to see that all were working accurately and all were within reasonable spec (+/- 1-digit). Needless to say we felt like one of "those geeks" in the crowd with the fancy-schmancy-super-duper-thingy-ma-bober-jobber doing the exact same thing as the low budget workin'-man's Radio Shack or Harbor Freight special.

Anyway, enough of my rambling. Resistance is high doing anything productive/definative for our environment, or I should say what's been done, is what's gonna get done.

They should re do that Apollo 13 movie to show those engineers over thinking and over shooting the time line when they were told to figure out how to make a carbon dioxide scrubber out of spare space gear. They need to show them locked in pie-in-sky debate over how the scubber doesn do things perfectly, re-defining the needs of the common man etc and show the crew of the 13 fading into oblivion waiting for the brain-trust to get over themselves, that would be more like what happens in most cases.
(dang dood thing the NASA guy's walk-the-walk while they talk-the-talk)

I would sugest the list read:

• Inexpensive, between $50-$100
• Convenient/easy & quick to use and read a reasonable effective result
• Accuracy 5.0% (goal) better if possible as long as it doesn inhibit meeting bullet point-1 above

PIC, Arduino, AVR whatever, PIC would be better IMHO because it's more of a basic start and can bring the cost down not needing a pre-built module as an initial buy-in. If it was PIC then I would suggest using the 18F as it offers more mem and options like USB or SD-card support so one could save/export the data in a format modern PC/Mac users can deal with (as opposed to simple in-device EEPROM storage) and their is already support in PICBasic and MicroC for those.
(two of the most user-friendly, and affordable, PIC dev platforms)

As long as it's an open-source project. Interested parties should be able to download code-or-bits (both really) for those who would want to either learn, or just use the gear.

Can't speak for others, but nothing pisses me off more when doing a DIY project (Elektor, EPE, Nuts-n-Volts, Silicon Chip etc) and they have a nice article about some thing/device I might want to build (Hardware/Software solution) and when it comes down to the code that gets the job done, they skip right over the jucy bits and offer you a hex file, shweeet. Sometimes there is a nice flow-chart to give one the idea of how they do but no discussion about what was done in code to accomplish the task at hand, no modules/function/classes/lib's to learn from etc. So what does a guy learn? well pretty much how to solder up a PCB and download somebody's code and wheeeeee ...there you have it... oh that's right, we already know how to populate and solder PCB's, oh and BTW they'll do it double-sided SMT and then you have to buy a PCB their reader service dept for $20+ship, wheeee!.

We now return to your regularly scheduled program....

[Mike Sulzer]

Minor quibble over the capacitive reactance figure.

1/(2 * PI * freq * C) = 1591 ohms.

You may have entered microFarads instead of picoFarads.

Well, it is Monday, and I do things like that, but I keep getting my answer. I just multiplied it out in my calculator program, but this:Capacitive Reactance Calculator seems to agree with me as does the chart in the back of may Radio Engineers Handbook.

Just to check, it is for 1000 Hz ( that is, 1 KHz), 100 pf.

[bbsailor]

Well, it is Monday, and I do things like that, but I keep getting my answer. I just multiplied it out in my calculator program, but this:Capacitive Reactance Calculator seems to agree with me as does the chart in the back of may Radio Engineers Handbook.

Just to check, it is for 1000 Hz ( that is, 1 KHz), 100 pf.

Gentlemen,

The first point that needs agreement is whether the Extech LCR meter is capable of producing a reasonably accurate pickup profile with the collection of the following measured data.

1. DC Resistance
2. AC Resistance at 120 Hz and 1KHz
3. AC Resistance at 120 Hz and 1KHz
4. Inductance at 120 Hz and 1KHz
5. Q at 120 Hz and 1KHz
6. D at 120 Hz and 1KHz
7. Self resonance measured from the end of a 10 ft guitar cable using a signal generator and oscilloscope

Salvarsan (Daniel) You have some nice pickup related tools on your web site. Here is a related idea that could help put this issue to rest for good.

Devise a program or use an Excel template that accepts web inputs from items 1 through 7 above and then creates a graphic profile of the pickup under test. Allow users to copy the graphed output data so that people can share and compare results to determine if the results from testing the same pickup produces a reasonably acceptable profile to enable objective comparisons.

If there is not enough valid data using items 1 through 7 above then discussions can evolve to identify what additional data would be helpful or recognize that the Extech LCR does not generate enough relevant data (with other simple measurements in items 1 and 7 above), or has too wide a variance in output to be helpful in graphically profiling a pickup under test to enable productive conversations on this forum.

Generally, the bulk of fundamental guitar notes (less harmonics) are covered between 120 Hz and 1Khz with the slope being extended down to 82 Hz and projected up to the pickup self resonant point.

I believe that a community generated tool like I descibe above will enhance technical discussions and further pickup innovation and idea sharing.

I hope this stimulates some more ideas?

Joseph Rogowski

[Joe Gwinn]

Here's the money shot:
What would make an inexpensive inductance tester good enough for pickup builders?

• Inexpensive.
• Convenient/ease of use.
• Adequate accuracy. 5.0% maybe?

Can this be done using a microcontroller and one of Joe's or Mike's VI interface daughterboards?

Sure it can. A soundcard with V-I interface and some software could work well too.

The software can then make measurements at a large number of frequencies, and fit the data to anyone's favorite circuit (or physics) model.

More generally, the effort is not worth it if it yields a $100 kit to replace a $200 Extech, but replacing a $5,000 multifrequency lab LCR meter could well be worthwhile, and oddly is probably less trouble than the microcontroller circuit so long as one's accuracy requirements are modest.

And one can always use the soundcard as a soundcard.

[Mike Sulzer]

The purpose of this post is to show how to derive pickup parameters from multiple frequency measurements* of the magnitude and phase of the impedance. (Actually, the real and imaginary part are used. Think of drawing a line from the origin of an x-y coordinate system. The magnitude is the length of the line. The angle is measured counterclockwise from the x-axis. The real and imaginary parts are the projections of the line onto the x and y axes.) In the series mode, the Extech meter interprets the imaginary part as 2*pi*f*L. The real part is interpreted directly as R. The Extech does this at 120 and 1000 Hz. The system I am using does this at many frequencies across the audio band simultaneously.

Let's look at the L and R values derived in this way. The pickup is a humbucker made in Japan that I use for testing. The cover has been removed, and the brass baseplate replaced with a n-s from all parts. The unknown magnet has been replace with an A8 from Mojo for this measurement. The graph for inductance, derived as described in the previous paragraph is here: http://www.naic.edu/~sulzer/L8.png. The measurement is shown only to 2 KHz since we want to work with a low frequency model for now. The measurements are bad at very low frequencies. There are two reasons for this:
1. The impedance of an inductor drops as frequency decreases. At very low frequencies, there is little voltage across it and the resistance dominates, leading to a poor measurement.
2. My A/D converters are ac coupled, and so the sensitivity of the measurement drops at low frequencies.

The inductance apparently drops as frequency increases. The problem with this is discussed above.

The real part, interpreted as a resistance, is here: http://www.naic.edu/~sulzer/R8.png. It rises with frequency. This curve cannot be interpreted as an actual resistance. It is the result of a more complicated circuit, as is the decreasing inductance.

It is believed that this behavior is explained as inductive coupling to various metal parts. If it were the cores alone, a model of a poorly coupled transformer would work very well. Since the pickup has other metal parts as well, it could be more complicated, but possibly these other metal parts do not change things all that much.

The model proposed to explain the measurements consists of a coil inductance, Lc, with a series resistance, Rs. Another inductor, Lm, with a resistor, Rp, in series, connect in parallel across Lc. Rp is frequency dependent since the skin effect comes into play due to the high permeability and conductivity of the steel cores. The function Rp(f) is described by two parameters, Rp0, a multiplicative scale factor, and f0, which determines the shape of the function. Th function starts at zero frequency with some value and rises curving upward; it then bends over and takes on the square root of frequency variation typical os the skin effect. f0 is the approximate frequency at which the variation makes a transition from curving up to straightening out before bending over. Since this is a low frequency model, we do not expect very much variation.

The mathematical method used to adjust the values of the parameters is non-linear least squares fitting. The mathematical model of the function (with a schematic of the model) and the partial derivatives used by the fitting program to determine how to change the parameters in order to iteratively arrive at the best fit are described in this pdf file: http://www.naic.edu/~sulzer/fitting.pdf.

The results of the fitting are shown here: http://www.naic.edu/~sulzer/fit8.png. The small circles are the measurements, and the solid lines are the model. The red circles with the black line on top are the real part, while the blue circles with the green line are the imaginary part. The fit is very good, although not perfect. The values of the parameters are shown on top of the plot. The function Rp(f) corresponding to the parameters Rp0 and f0 is here: http://www.naic.edu/~sulzer/Rp8.png. The resistance increases by about 50% between 0 and 2000 Hz.

It is interesting that the value of Lc is very nearly the same as the low frequency limit of the imaginary part of the measured impedance. This suggests that the 120 Hz measurement of the Extech is Lc to a good approximation. Possibly Lm and Rp(1000) can be obtained from the Extech 1000 Hz measurement.

*I do not look at this as a practical way to make everyday measurements, but rather as a research tool that could point the way to easier measurements.

[Steve Conner]

Great work Mike, thanks for sharing it.

To me this simply says that there is no point in spending money on an accurate LCR meter for pickup work. It will never give an answer accurate to 1% if its internal model doesn't agree with the equivalent circuit of the pickup to 1%. So I think one of the cheap kits would be fine.

The reason to own an Extech would be if it was a de facto standard. If most pickup makers own one, at least they all operate off the same wrong assumptions, so the data can be compared. This also suggests an open source initiative would flop if it wasn't backwards compatible with the Extech.

[RedHouse]

...A soundcard with V-I interface and some software could work well too.

The software can then make measurements at a large number of frequencies, and fit the data to anyone's favorite circuit (or physics) model....

The effort is not "worth it" by replacing a $200 meter with $200 worth of Soundcard/Software/Kit either.

So you're saying the on-board sound chip and some freebie software is going to get one there? that's going to make a pickup-specific test platform. That's the only way that notion would be a cheap alternative.

Decent sound cards start at right around $100 and the minimum shareware is $35, oh wait, maybe you mean we can all buy a Mac and use the free software, that would bring the cost right down, woohooo!
(rampant sarcasm there)

...the effort is not worth it if it yields a $100 kit to replace a $200 Extech...

Wow, there's an economic epiphany.

We all shop around for cheaper gas, food, clothes, hardware, software, everything. Many times with a difference of just a dollar or two, or in the case of gasoline ...a few cents.

But in your opinion, building a kit for $100 isn't worth the effort if one saves $100? with all due respect, you really need to get out more Joe.

...

Meanwhile Lovell, Swigert and Haise are looking pale, air's get'in thin...

[Joe Gwinn]

Let's look at the L and R values derived in this way. The pickup is a humbucker made in Japan that I use for testing. The cover has been removed, and the brass baseplate replaced with a n-s from all parts. The unknown magnet has been replace with an A8 from Mojo for this measurement. The graph for inductance, derived as described in the previous paragraph is here: http://www.naic.edu/~sulzer/L8.png. The measurement is shown only to 2 KHz since we want to work with a low frequency model for now. ...

The inductance apparently drops as frequency increases. The problem with this is discussed above.

The real part, interpreted as a resistance, is here: http://www.naic.edu/~sulzer/R8.png. It rises with frequency. This curve cannot be interpreted as an actual resistance. It is the result of a more complicated circuit, as is the decreasing inductance.

It is believed that this behavior is explained as inductive coupling to various metal parts. If it were the cores alone, a model of a poorly coupled transformer would work very well. Since the pickup has other metal parts as well, it could be more complicated, but possibly these other metal parts do not change things all that much.

Eddy current loading varies in proportion to the square of frequency, so it would be illuminating to plot the AC resistance data against the square root of frequency - do we get a reasonably straight line?

We may not see pure frequency-squared behavior because the f^2 dependence assumes thin sheets (no eddy-current variation across the thickness) while the skin depth varies as sqrt[f], and pickup components vary in their thickness expressed in multiples of the skin depth in the various materials from which those components are made.

Eddy current - Wikipedia

More generally, if we plot in log-log, log-linear, and linear-log formats and look for piecewise linear plots, comparing the effect as parts of the unit under test are changed, we may get clues to the dominant physical mechanisms underlying the various straight-line segments.

As for inductance reduction, eddy currents can do this, as has been discussed at length, and ferrous materials can increase inductance in opposition to the effect of eddy currents. Another effect is seen as one approaches self-resonance, where the self-capacitance of the coil (and cables, if present) cancels more and more of the self-inductance, but from your description of the unit under test, resonance is probably well above the 2 KHz max test frequency shown.

[RedHouse]

...The first point that needs agreement is whether the Extech LCR meter is capable of producing a reasonably accurate pickup profile with the collection of the following measured data.

1. DC Resistance
2. AC Resistance at 120 Hz and 1KHz
3. AC Resistance at 120 Hz and 1KHz
4. Inductance at 120 Hz and 1KHz
5. Q at 120 Hz and 1KHz
6. D at 120 Hz and 1KHz
7. Self resonance measured from the end of a 10 ft guitar cable using a signal generator and oscilloscope

After several posts about how the Extech doesn't really do the job (but is better than the others) why would you want to base a project on the Extech as the baseline?

Of course a "spec" would need to be developed/discussed but that could be independant of what an Extech is doing.

...Devise a program or use an Excel template that accepts web inputs from items 1 through 7 above and then creates a graphic profile of the pickup under test. Allow users to copy the graphed output data so that people can share and compare results to determine if the results from testing the same pickup produces a reasonably acceptable profile to enable objective comparisons....

The Excell import idea is very good, that would allow further data display and calculation, but I'd stay away from the webserver notion.

That brings in more expense (another $40 module to buy and configure) it's enough to have a device log data into a file format and save it on an SD card and have some connectivity ability such as USB which the 18F series PIC.
(and a generic USB stack is free from Microchip)

...I believe that a community generated tool like I descibe above will enhance technical discussions and further pickup innovation and idea sharing.

I hope this stimulates some more ideas?

I don't believe you're describing anything that hasn't already been suggested here and in past threads, am I missing something?

[Joe Gwinn]

The effort is not "worth it" by replacing a $200 meter with $200 worth of Soundcard/Software/Kit either.

....

Wow, there's an economic epiphany.

We all shop around for cheaper gas, food, clothes, hardware, software, everything. Many times with a difference of just a dollar or two, or in the case of gasoline ...a few cents.

But in your opinion, building a kit for $100 isn't worth the effort if one saves $100? with all due respect, you really need to get out more Joe.

Don't forget to include labor, especially the labor of those who would develop the design that could later be turned into a kit, and write the software to run the kit hardware.

And if those noble souls are in their labs developing hardware and software, they really won't be getting out much.

[RedHouse]

Don't forget to include labor, especially the labor of those who would develop the design that could later be turned into a kit, and write the software to run the kit hardware.

And if those noble souls are in their labs developing hardware and software, they really won't be getting out much.

Noble souls? noble would be contributing wouldn't it?

The labor issue wouldn't effect you Joe, you've made it clear you're not interested in contributing to something like this. Other people do things for the sake of interest, community, enlightenment, challenge and many other reasons besides weighing the cost against the gain.

I've contributed to forum-community efforts in the past, the project I put together after many weeks of work (see the ForumVibe project) is free to the forum members, I require no compensation unless of couse they want to sell them for profit, then they need to deal. Maybe it's just easier for me, I also volunteer at the local Food Lifeline and Union Gospel Mission with effort, time, and resources without consideration of the cost/gain/loss of the efforts, so maybe it's just a natural transition to participate in forum (community) efforts contributing time or whatever I can pitch-in for zero compensation. Not to mention the original gauss meter group-buy, it was quite a bit of cost and labor. The parts, bags, ordering, sorting, packaging the kits, making the PCB's, shipping the packages. I didn't add a penny onto the cost, it was a "community project" not for profit.
(Elepro got paid, but then it was not offered as an open-source project anyway)

Point is, things can be done, for fun, for interest, for other reasons than if it's "worth it". Check out Sourceforge and other websites where people do open-source development.

[salvarsan]

...about the Extech

Bbsailor's idea of an excel spreadsheet seemed good, expecially since it makes my life so much easier in analytical chemistry data analysis.

After running some numbers, I suspect the Extech uses "pure" serial and parallel RLC models in its computations.

Whenever it generates a Q factor, it assumes that the inductor is at resonance at the test frequency.

For a reported R,L,C, and Q, your calculations give you the ExTech test frequencies, 122.x Hz and 1000Hz +/-4.

In short, the Extech makes a few ideal assumptions that are problematic for something as non-ideal as a guitar pickup.