Measurement of Coil Self Capacitance - Terman's method

[Joe Gwinn]

How to measure the self-capacitance of pickup coils comes up from time to time, and I've posted on the subject from time to time, often in response to attempted use of an Extech LCR meter set to measure C, sometimes in attempts to measure inductance at 100 KHz (which some LCR meters offer).

First of all, no LCR meter can measure self-capacitance (versus total capacitance), because inductance and capacitance are opposites, and one in effect measures their difference. At frequencies well below resonance, the inductance dominates and the total capacitance serves only to slightly reduce the measured inductance. At frequencies well above resonance, the total capacitance dominates, and the inductance causes a slight reduction in measured capacitance. At resonance, inductance and capacitance exactly balance.

LCR meters set to measure inductance and then used well above resonance (like 100 KHz for a 10 KHz resonant frequency) will be completely baffled. If one sets the LCR meter to measure capacitance, one will get a value for the total capacitance, but this value will include all manner of parasitic effects due to the fact that the pickup was not designed to operate anywhere near that frequency.

If there is a metallic core in the coil, things will be even more complicated because of the effects of eddy currents, again far away from the design range.

First conclusion is that one must measure more or less in the operating range to get useful data.

Total capacitance is that of the coil self-capacitance plus everything else, including cables et al, so we need a way to separate that out.

Terman published in ("Radio Engineers' Handbook, Terman, 1943, section 13, paragraph 10, starting on page 922) the standard way to make self-capacitance measurements of radio coils (think megahertz), reacting to all of the above problems, summarizing approaches developed in the 1920's on. For best accuracy, especially with low-Q inductors like pickup coils, the resonant frequencies are the zero-phase points, not the peak amplitude points. Here is the relevant part of Terman's book:

Terman on Measurement of Self-Capacitance 1943.pdf

[bbsailor]

How to measure the self-capacitance of pickup coils comes up from time to time, and I've posted on the subject from time to time, often in response to attempted use of an Extech LCR meter set to measure C, sometimes in attempts to measure inductance at 100 KHz (which some LCR meters offer).

First of all, no LCR meter can measure self-capacitance (versus total capacitance), because inductance and capacitance are opposites, and one in effect measures their difference. At frequencies well below resonance, the inductance dominates and the total capacitance serves only to slightly reduce the measured inductance. At frequencies well above resonance, the total capacitance dominates, and the inductance causes a slight reduction in measured capacitance. At resonance, inductance and capacitance exactly balance.

LCR meters set to measure inductance and then used well above resonance (like 100 KHz for a 10 KHz resonant frequency) will be completely baffled. If one sets the LCR meter to measure capacitance, one will get a values for the total capacitance, but this value will include all manner of parasitic effects due to the fact that the pickup was not designed to operate anywhere near to that frequency.

If there is a metallic core in the coil, things will be even more complicated because of the effects of eddy currents, again far away from the design range.

First conclusion is that one must measure more or less in the operating range to get useful data.

Total capacitance is that of the coil self-capacitance plus everything else, including cables et al, so we need a way to separate that out.

Terman published i("Radio Engineers' Handbook, Terman, 1943, section 13, paragraph 10, starting on page 922) the standard way to make self-capacitance measurements of radio coils (think megahertz), reacting to all of the above problems, summarizing approaches developed in the 1920's on. For best accuracy, especially with low-Q inductors like pickup coils, the resonant frequencies are the zero-phase points, not the peak amplitude points. Here is the relevant part of Terman's book:

[ATTACH]28787[/ATTACH]

Joe G.

One thing I discovered is that it is very difficult to accurately calculate distributed capacitance, as it is better to measure it. See my article: http://www.geotech1.com/pages/metdet...s/FastCoil.pdf. When placing a shield around the coil, the full capacitance measured between one coil wire end and the fully isolated shield, is not fully imposed on the resulting coil resonance. Only about 20 percent of the coil to shield capacitance is added to lower the coil resonant frequency. When near the 1MHz range the 1pf series capacitor helps lower the effect of probe capacitance loading, however at audio frequencies (near 10KHz) using a 10X probe should not impose too much of a load on the measured circuit. I did notice that the wire insulation dielectric constant had a very big influence on the resonant frequency with only about 20 coil turns in the 1Mhz range (for a pulse induction metal detector 300 microhenry coil) but a 2H to 3H guitar pickup with 7,000 to 10,000 turns will create a significant resonance in the audio range where the ear is most sensitive and where other things may be happening.

Here is one question that I have been wrestling with for many years since I have been making low impedance pickups. Is there any coil characteristic, other than the self-resonance point, that affects our perception of a pickup's sound?

Thanks for the technical reference.

Joseph Rogowski

[Rick Turner]

Joe, the 3D interface between the coil, magnetic field, and strings is of utmost importance, and I think this is one of the things missing from a lot of low Z pickup designs. There's such a focus on getting self-resonance out of the audio picture than other issues are missed. Forest and trees effect, I'm afraid.

[Mike Sulzer]

Joe G.

Here is one question that I have been wrestling with for many years since I have been making low impedance pickups. Is there any coil characteristic, other than the self-resonance point, that affects our perception of a pickup's sound?
Joseph Rogowski

The width of the resonance matters, not just its location. This is easy to demonstrate. In general, anything that affects the frequency response matters. For example the location(s) of the string that are sampled. For example, the standard humbucker with about one inch spacing between the coils has a different sound than a single coil that samples a single narrow region, at least in the bass strings.

[Mike Sulzer]

Joe, the 3D interface between the coil, magnetic field, and strings is of utmost importance, and I think this is one of the things missing from a lot of low Z pickup designs. There's such a focus on getting self-resonance out of the audio picture than other issues are missed. Forest and trees effect, I'm afraid.

Not sure I see what you mean, but this seems to cover various geometrical effects, such as the location of sampling the string. But this would seem to have nothing to do with coil impedance directly since a set of coils with identical shape can be wound with an arbitrary number of turns, and thus impedance, by adjusting the wire size.

[Mike Sulzer]

Why would you want to measure the capacirance of a guitar pickup coil coil by a method 70 years old intended for measuring that of an rf coil? If you are really interested in measuring pickup parameters accurately, especially for many pickups, it would seem easier and more accurate to use the software I have written using a recording interface as the hardware analyzer to measure the impedance over the entire audio range. The capacitance is then computed in the software.

By the way, Terman's method is not always totally accurate with steel cores, because the imepdance is more complicated than just an L and a distributed C. However, I would expect it to be good enough for most purposes.

How to measure the self-capacitance of pickup coils comes up from time to time, and I've posted on the subject from time to time, often in response to attempted use of an Extech LCR meter set to measure C, sometimes in attempts to measure inductance at 100 KHz (which some LCR meters offer).

First of all, no LCR meter can measure self-capacitance (versus total capacitance), because inductance and capacitance are opposites, and one in effect measures their difference. At frequencies well below resonance, the inductance dominates and the total capacitance serves only to slightly reduce the measured inductance. At frequencies well above resonance, the total capacitance dominates, and the inductance causes a slight reduction in measured capacitance. At resonance, inductance and capacitance exactly balance.

LCR meters set to measure inductance and then used well above resonance (like 100 KHz for a 10 KHz resonant frequency) will be completely baffled. If one sets the LCR meter to measure capacitance, one will get a values for the total capacitance, but this value will include all manner of parasitic effects due to the fact that the pickup was not designed to operate anywhere near to that frequency.

If there is a metallic core in the coil, things will be even more complicated because of the effects of eddy currents, again far away from the design range.

First conclusion is that one must measure more or less in the operating range to get useful data.

Total capacitance is that of the coil self-capacitance plus everything else, including cables et al, so we need a way to separate that out.

Terman published i("Radio Engineers' Handbook, Terman, 1943, section 13, paragraph 10, starting on page 922) the standard way to make self-capacitance measurements of radio coils (think megahertz), reacting to all of the above problems, summarizing approaches developed in the 1920's on. For best accuracy, especially with low-Q inductors like pickup coils, the resonant frequencies are the zero-phase points, not the peak amplitude points. Here is the relevant part of Terman's book:

[ATTACH]28787[/ATTACH]

[Joe Gwinn]

One thing I discovered is that it is very difficult to accurately calculate distributed capacitance, as it is better to measure it. ... When placing a shield around the coil, the full capacitance measured between one coil wire end and the fully isolated shield, is not fully imposed on the resulting coil resonance. Only about 20 percent of the coil to shield capacitance is added to lower the coil resonant frequency. When near the 1MHz range the 1pf series capacitor helps lower the effect of probe capacitance loading, however at audio frequencies (near 10KHz) using a 10X probe should not impose too much of a load on the measured circuit. I did notice that the wire insulation dielectric constant had a very big influence on the resonant frequency with only about 20 coil turns in the 1Mhz range (for a pulse induction metal detector 300 microhenry coil) but a 2H to 3H guitar pickup with 7,000 to 10,000 turns will create a significant resonance in the audio range where the ear is most sensitive and where other things may be happening.

It's true that computation of self-capacitance is hard to do accurately. The theory is best used to compare winding arrangements and find optimums on a common basis, and quickly (compared to making and testing 1000 different variations).

Here is one question that I have been wrestling with for many years since I have been making low impedance pickups. Is there any coil characteristic, other than the self-resonance point, that affects our perception of a pickup's sound?

There are several: The 3D shapes of the magnetic fields and of the pickup coil sensing changes in that field, as mentioned by Rick Turner. The Q of the coil, which controls the shape of the resonance curve, as mentioned by Mike Sulzer. Then there is the location of the coil along the strings (bridge versus neck and all between, and the length of string (the aperture) that is sensed by the pickup. The plane of string vibration: Ordinary pickups sense mainly up-down vibration, and ignore side-to-side vibration, and yet picking is mostly in the horizontal direction. (The energy from a pluck rapidly distributes into all the string modes, so the debate hinges on the importance of sensing things before this equipartition happens during the attack transient.) Not to mention the resonances of the body. Etc.

What saves us is that these effects are largely independent of one another, so we can consider each effect in isolation, and in some sense "sum" their results. (Mathematically, the combination is really some kind of product of the individual effects, but these effects are individually linear or N-linear, which in practice means that one does not get a lot of cross-product terms.)

[Joe Gwinn]

Why would you want to measure the capacitance of a guitar pickup coil coil by a method 70 years old intended for measuring that of an rf coil?

Hmm. Newton's Principia was published in 1687, almost 330 years ago, and Maxwell's Equations were published in 1861 and 1862, 150 years ago. Are these theories too old?

As for RF, why does that prevent the method from working at audio frequencies?

If you are really interested in measuring pickup parameters accurately, especially for many pickups, it would seem easier and more accurate to use the software I have written using a recording interface as the hardware analyzer to measure the impedance over the entire audio range. The capacitance is then computed in the software.

Actually, this will measure only total capacitance. If you use your setup and method with various film capacitors in parallel with the coil under test, the self-capacitance of the coil may be computed.

By the way, Terman's method is not always totally accurate with steel cores, because the impedance is more complicated than just an L and a distributed C. However, I would expect it to be good enough for most purposes.

It's them damn eddy currents for sure.

[Mike Sulzer]

Hmm. Newton's Principia was published in 1687, almost 330 years ago, and Maxwell's Equations were published in 1861 and 1862, 150 years ago. Are these theories too old?

Measurements depend on technology, which changes quickly. Theories evolve, but the old ones still remain valid within a certain range of applicability. Why would one not want to use recent technology, making it easier to make measurements?

As for RF, why does that prevent the method from working at audio frequencies?

Prevent, no, not what I said. It is a matter of technology. The lower frequency of audio wrt rf means that a different technological solution is applicable and convenient.

Actually, this will measure only total capacitance. If you use your setup and method with various film capacitors in parallel with the coil under test, the self-capacitance of the coil may be computed.

You neither understood my setup and method, nor bothered to look at the capacitance values I measured, which are for a coil, not for a coil with cables, etc. Also the resonant frequencies are certaonly the result of the coil capacitance, except where I have added additional C. The technique: A small resistor is placed in series with the pickup coil. A voltage is applied across the series combination, and this voltage is measured. The voltage across the resistor is measured, and the small effect of cable capacitance across this small resistor is compensated for in order to make very precise measurements. The voltage across the coil and current through it are computed, with the impedance derived from the ratio. There is no capacitance added across the coil to modify the measurement.

This is what you do with modern technology: combine general purpose hardware with software to make high quality, convenient measurements. The 17th, 18th, 19th and 20th centuries are history.

It's them damn eddy currents for sure.

From your tone, I assume you disagree with what I wrote. You are wrong on this as well.

[Rick Turner]

re. lateral vs. vertical string vibration...I think this may be one of the reasons why magnetic pickups are considered "slower" than piezos, especially piezos designed to transduce lateral vibrations...like those made by Richard McLish and myself. This "speed" can be a good thing, especially for synth guitar systems, and if coupled with high headroom electronics is pretty amazing. Done poorly, it leads to piezo "quack", though, which is a combination of first stage half and first full cycle clipping and the sense that the event is happening too phase perfectly...too fast. DSP can take care of that.

It is certainly possible to design hex magnetic pickups that are more sensitive to lateral string vibrations, but it takes having pole pieces in between the strings which may or may not be acceptable to players.

[rjb]

Silly question

For a six-string guitar, wouldn't you want a "hept" pickup? (Five "in between" and two "outer" pole pieces)

It is certainly possible to design hex magnetic pickups that are more sensitive to lateral string vibrations, but it takes having pole pieces in between the strings which may or may not be acceptable to players.

[Joe Gwinn]

Measurements depend on technology, which changes quickly. Theories evolve, but the old ones still remain valid within a certain range of applicability. Why would one not want to use recent technology, making it easier to make measurements? ... Prevent, no, not what I said. It is a matter of technology. The lower frequency of audio wrt rf means that a different technological solution is applicable and convenient.

Well, Terman was solving a problem: Most RF coils are designed to have self-resonant frequencies well above the operational frequency, to suppress various parasitic effects, especially if the coil has a core. For this reason, a test using signals in the operational band was needed, so the coil under test was paralleled with capacitors such that the resonance fell in or near the operational band.

With pickups, the self-resonant frequency isn't usually as far from the operational band as for RF coils, but the principle is the same.

You neither understood my setup and method, nor bothered to look at the capacitance values I measured, which are for a coil, not for a coil with cables, etc. Also the resonant frequencies are certaonly the result of the coil capacitance, except where I have added additional C. The technique: A small resistor is placed in series with the pickup coil. A voltage is applied across the series combination, and this voltage is measured. The voltage across the resistor is measured, and the small effect of cable capacitance across this small resistor is compensated for in order to make very precise measurements. The voltage across the coil and current through it are computed, with the impedance derived from the ratio. There is no capacitance added across the coil to modify the measurement.

I do understand your method. It measures the self-resonant frequency of the coil under test, and uses this to compute the self capacitance. There is no intentional added capacitance. The problem with this and any approach using a single resonance frequency measurement is that the apparent inductance of the coil varies with frequency, causing errors in the computed self-capacitance. This variation of inductance with frequency cannot be detected and quantified without loading the coil with various capacitors and measuring the resulting resonant frequencies.

If one plots the results with added capacitance on the X-axis and the square of resonant frequency on the Y-axis, one will get a straight line (if the apparent inductance is constant) or a curve (if the apparent inductance varies with frequency).

This is what you do with modern technology: combine general purpose hardware with software to make high quality, convenient measurements. The 17th, 18th, 19th and 20th centuries are history.

True enough. I'm pretty sure that Lemme's Pickup Analyzer automates Terman's method.

From your tone, I assume you disagree with what I wrote [on eddy currents]. You are wrong on this as well.

I'm not sure how to interpret this, but my point was that eddy currents cause the apparent inductance to vary with frequency. As mentioned above, one can see this effect in the f^2 versus added C plot.

[Mike Sulzer]

I do understand your method. It measures the self-resonant frequency of the coil under test, and uses this to compute the self capacitance. There is no intentional added capacitance. The problem with this and any approach using a single resonance frequency measurement is that the apparent inductance of the coil varies with frequency, causing errors in the computed self-capacitance. This variation of inductance with frequency cannot be detected and quantified without loading the coil with various capacitors and measuring the resulting resonant frequencies.

No. The complex impedance vs frequency is used over a range of the higher frequencies (above the resonance). Thus information is used at a number of frequencies, similar to Terman's method, but this is better. A model of the impedance with eddy current effects and the C is constructed. It uses the equations I derived that you are familiar with. A least squares fit is performed to derive three parameters, one of which is the C. You can see the advantage of working above the resonance: the inductive reactance is larger than the capacitive reactance, and so the former does not have to be known as accurately for a given accuracy in the C. Thus the eddy current model only needs to be approximately correct.

If one plots the results with added capacitance on the X-axis and the square of resonant frequency on the Y-axis, one will get a straight line (if the apparent inductance is constant) or a curve (if the apparent inductance varies with frequency).

With eddy currents effects, I believe that this involves extrapolating a curved line to an axis. Those who extrapolate "straight" lines put their lives at risk. Those who bet their lives on extrapolating curved lines die.

The Terman method allows measuring the apparent inductance as a function of frequency below the resonance, using these measurements to predict the inductance at the resonance. Of course, the same information is available from the measurements of complex impedance. I tried using it, but gave it up in favor of this, which is statistically better.

[Joe Gwinn]

No. The complex impedance vs frequency is used over a range of the higher frequencies (above the resonance). Thus information is used at a number of frequencies, similar to Terman's method, but this is better. A model of the impedance with eddy current effects and the C is constructed. It uses the equations I derived that you are familiar with. A least squares fit is performed to derive three parameters, one of which is the C. You can see the advantage of working above the resonance: the inductive reactance is larger than the capacitive reactance, and so the former does not have to be known as accurately for a given accuracy in the C. Thus the eddy current model only needs to be approximately correct.

We've been down this road before, maybe twice, and I don't have the energy to do it again.

At resonance (as measured by zero phase), the impedance is not complex -- the imaginary term is zero.

An assertion of "better" needs to be supported by a formal definition of "better", and an A-vs-B comparison. I would venture that people have various definitions.

With eddy currents effects, I believe that this involves extrapolating a curved line to an axis. Those who extrapolate "straight" lines put their lives at risk. Those who bet their lives on extrapolating curved lines die.

Whoa! It's only our guitars that are at risk. And people extrapolate curved lines all the time. All it takes is a curve fit.

But the curve is in fact how it works, so we have to deal with them. Those curves don't deviate all that much from straight lines, but they do curve.

As I recall, we had a long thread on such things. Which I do not wish to relive.

The Terman method allows measuring the apparent inductance as a function of frequency below the resonance, using these measurements to predict the inductance at the resonance. Of course, the same information is available from the measurements of complex impedance. I tried using it, but gave it up in favor of this, which is statistically better.

OK. Others may differ.

[Mike Sulzer]

We've been down this road before, maybe twice, and I don't have the energy to do it again.

If we had been down this particular road before, why did you not remember how I am measuring the C? I had to tell you twice before you now, apparently, recognize that I am not just computing the C from the resonant frequency as you thought. No, as far as I remember, we have not discussed the details of how I do this measurement.

At resonance (as measured by zero phase), the impedance is not complex -- the imaginary term is zero.

I am not sure why you have written this here, but I can give you a proof that measurement of the complex impedance contains the information used in the Terman method. Consider the the complex impedance at a particular frequency. From the negative of the imaginary part one can derive the value of the C that would give the zero phase resonance. One can do this over a range of frequencies and construct the plot made in the Terman method. But why would you do this if you have more information?

An assertion of "better" needs to be supported by a formal definition of "better", and an A-vs-B comparison. I would venture that people have various definitions.

Well go right ahead. Certainly the technique that uses less information and a poor numerical technique is the one that needs the support.

And people extrapolate curved lines all the time. All it takes is a curve fit.

Nobody with any sense does simple extrapolation if there is a better technique available, one using more information and incorporating a model of the process if possible. Take for example the stock market....