measuring inductance with a meat-and-potatoes DMM

[Joe Gwinn]

A measurement of complex impedance gives an amplitude and phase. Given that the loss is series, one can determine both the inductance and the resistance. Same for parallel. But not if you have both (unless they are both small, and so do not matter). If you have both you can measure at a sequence of frequencies and construct a model that matches the measurements. Two might do it in certain cases, but not in general, especially if you have no control over the two frequencies. If you disagree with this please show me how to get simultaneous series and parallel loss with the Extech. Maybe I am missing something.

Several things have become tangled together. Let's tease them apart:

1. I agree that in practical inductors, there can be both series and parallel resistance components, due to different physical effects, and that a two-frequency measurement of complex impedance cannot tease these apart except in unusual circumstances. However, in practical inductors, the parallel resistance is usually very large, and may be ignored, and the parallel capacitance (the self-capacitance) has no significant effect at 1000 Hz, given that self resonance is around 10 KHz. One measures self-capacitance most accurately by finding the self-resonant frequency with various external capacitors, and solves for the extra capacitance needed to make it all work out. (This method is very old, and I first saw it in Terman.)

2. Bringing a mass of non-magnetic electrical conductor, like brass, copper, or aluminum, near to a coil will reduce its inductance due to eddy currents counteracting coil currents.

A magnetic conductor such as steel will have permeability increase and eddy decrease in opposition, and things quickly become complex. Laminating the iron greatly reduces the eddy currents, causing the permeability effect to predominate, up to some frequency determined by the thickness of the laminations.

For a datapoint, variable-inductance RF coils can be ordered with a variety of core materials, including ferrite, powdered iron, or nonferrous (brass or aluminum). The ferrous cores increase the inductance, while the non-ferrous cores decrease the inductance.

Aside from eddy currents, the inherent permeability of most core materials varies with frequency, sometimes in complex ways.

3. Because eddy currents vary with frequency, so will the inductance of a coil with nearby metal, even if the geometry of coil and metal does not change.

What measurement do you want me to make?

Take an air core coil, hook it to an Extech LCR meter set to 1000 Hz, and bring a sheet or rod of brass or aluminum nearby or into the core hole. Observe how inductance and AC resistance react to the metal being brought near.

[jmaf]

For a handheld instrument costing less than $200 and measuring R, C, and L at 120 Hz and 1000 Hz, it's hard to beat the Extech LCR Meter 380193:

Extech Instruments: Specialty Meters: Specialty Meters: 380193

The next step up in capability costs thousands.

Thanks Joe. That is exactly what I was looking for.

[Mike Sulzer]

Several things have become tangled together. Let's tease them apart:

1. However, in practical inductors, the parallel resistance is usually very large, and may be ignored...

The humbucker pickup coil, with its steel cores, is an exception. Its impedance can not be modeled with just an L, C and series R. It is necessary to include the parallel loss from eddy currents induced in the cores, and furthermore it is necessary to account for the imperfect flux coupling to the cores with usual inductor in series with the parallel loss. Although an Extech is a useful tool for a pickup maker, it cannot do what I want.

2. Bringing a mass of non-magnetic electrical conductor, like brass, copper, or aluminum, near to a coil will reduce its inductance due to eddy currents counteracting coil currents.

But can the Extech measure this accurately? Not if the parallel loss caused by the eddy currents is significant and there is significant series loss. So if you see the inductance and ac resistance change, you cannot be sure either change is correct because you might simultaneous significant series and parallel loss.

Aside from eddy currents, the inherent permeability of most core materials varies with frequency, sometimes in complex ways.

Yes, and this might matter in a humbucker coil. I was recently reading a paper showing that steel (1018, I believe) shows a loss of permeability starting at about 1 KHz. The permeability is also complex; the induced magnetization lags the applied field.

3. Because eddy currents vary with frequency, so will the inductance of a coil with nearby metal, even if the geometry of coil and metal does not change.

But which is cause and which is effect? In the pickup model, the eddy currents decrease at high frequencies because the impedance of the inductor (in series with the loss resistor, included to account for the flux leakage) increases. It is not so simple in general.

Take an air core coil, hook it to an Extech LCR meter set to 1000 Hz, and bring a sheet or rod of brass or aluminum nearby or into the core hole. Observe how inductance and AC resistance react to the metal being brought near.

I do not own an Extech, but it does seem like a useful tool. It would be interesting to compare its measurements with the system I have.

[Joe Gwinn]

The humbucker pickup coil, with its steel cores, is an exception. Its impedance can not be modeled with just an L, C and series R. It is necessary to include the parallel loss from eddy currents induced in the cores, and furthermore it is necessary to account for the imperfect flux coupling to the cores with usual inductor in series with the parallel loss. Although an Extech is a useful tool for a pickup maker, it cannot do what I want.

But can the Extech measure this accurately? Not if the parallel loss caused by the eddy currents is significant and there is significant series loss. So if you see the inductance and ac resistance change, you cannot be sure either change is correct because you might simultaneous significant series and parallel loss.

Yes, and this might matter in a humbucker coil. I was recently reading a paper showing that steel (1018, I believe) shows a loss of permeability starting at about 1 KHz. The permeability is also complex; the induced magnetization lags the applied field.

But which is cause and which is effect? In the pickup model, the eddy currents decrease at high frequencies because the impedance of the inductor (in series with the loss resistor, included to account for the flux leakage) increases. It is not so simple in general.

This all reminds me of my first attempt to design a one-transistor amplifier in the early 1970s, when the ink on my EE degree was still damp. Despite taking all the usual and necessary courses, I couldn't design that damn amplifier. For one thing, my textbooks wanted ten or twenty device parameters, but the datasheet for the ten-cent jellybean transistors everybody used specified only two or three parameters, and yet life went on and amplifiers were built. Without angst. Very perplexing. And embarrassing. So I quietly scuttled over and looked at the books the electronics technicians were using, and borrowed a copy. Then it became clear. All but a very few of those parameters were for minor effects, and could be ignored in safety. It also became clear that my professor had never built anything, and didn't know big from small.

I do not own an Extech, but it does seem like a useful tool. It would be interesting to compare its measurements with the system I have.

I would recommend that you buy one. Failing that, the maxwell wein impedance bridge (look here) will duplicate the Extech results to within 0.1% (or the accuracy that you can measure R and C values, whichever is worse). The Extech is a lot faster, but operates at only two frequencies. The bridge is slow, but will work at any frequency, although the answers get strange as resonance is approached.

[Mike Sulzer]

For a humbucker coil, these effects are large, not small. That is why I have taken the trouble to put together a system that collects enough information so that one can model them. The evidence is in the earlier thread.

This all reminds me of my first attempt to design a one-transistor amplifier in the early 1970s, when the ink on my EE degree was still damp. Despite taking all the usual and necessary courses, I couldn't design that damn amplifier. For one thing, my textbooks wanted ten or twenty device parameters, but the datasheet for the ten-cent jellybean transistors everybody used specified only two or three parameters, and yet life went on and amplifiers were built. Without angst. Very perplexing. And embarrassing. So I quietly scuttled over and looked at the books the electronics technicians were using, and borrowed a copy. Then it became clear. All but a very few of those parameters were for minor effects, and could be ignored in safety. It also became clear that my professor had never built anything, and didn't know big from small.

I would recommend that you buy one. Failing that, the maxwell wein impedance bridge (look here) will duplicate the Extech results to within 0.1% (or the accuracy that you can measure R and C values, whichever is worse). The Extech is a lot faster, but operates at only two frequencies. The bridge is slow, but will work at any frequency, although the answers get strange as resonance is approached.

[Joe Gwinn]

For a humbucker coil, these effects are large, not small. That is why I have taken the trouble to put together a system that collects enough information so that one can model them. The evidence is in the earlier thread.

Ahh, well, make the measurement. Only measurement will allow us to sort this out.

[Mike Sulzer]

Ahh, well, make the measurement. Only measurement will allow us to sort this out.

Rather than make a measurement, let's analyze what happens when one first measures the impedance of a coil with some series resistance with the Extech, and then adds some parallel resistance, that is, loss from eddy currents induced in some metal.

The ac resistance R and the inductance L are found from a measurement of the impedance magnitude Z and phase angle phi by these equations:

R = Z/(sqrt(1 + tan(phi)))

and

L = Z/(2*pi*(sqrt((tan^2(phi))/(1 + tan^2(phi))))).

Let us assume that we are measuring at 1 KHz where the inductive reactance is significantly greater than the series resistance in a typical pickup coil. Adding the resistance in parallel with the coil lowers both Z and phi. This lowers the apparent reading of L using the equation above. This is totally fallacious. The inductance has not changed, but the meter reading indicates that it has.

[Joe Gwinn]

Rather than make a measurement, let's analyze what happens when one first measures the impedance of a coil with some series resistance with the Extech, and then adds some parallel resistance, that is, loss from eddy currents induced in some metal.

The ac resistance R and the inductance L are found from a measurement of the impedance magnitude Z and phase angle phi by these equations:

R = Z/(sqrt(1 + tan(phi)))

and

L = Z/(2*pi*(sqrt((tan^2(phi))/(1 + tan^2(phi))))).

Let us assume that we are measuring at 1 KHz where the inductive reactance is significantly greater than the series resistance in a typical pickup coil. Adding the resistance in parallel with the coil lowers both Z and phi. This lowers the apparent reading of L using the equation above. This is totally fallacious. The inductance has not changed, but the meter reading indicates that it has.

The whole point of measuring is to allow one to sort the theory out, so more theory isn't the answer.

If you don't believe the Extech, resonate an air coil with a capacitor, and observe how the resonant frequency behaves as pieces of brass are brought near. A brass slug is standard way to tune an RF coil.

[Mike Sulzer]

The whole point of measuring is to allow one to sort the theory out, so more theory isn't the answer.

If you don't believe the Extech, resonate an air coil with a capacitor, and observe how the resonant frequency behaves as pieces of brass are brought near. A brass slug is standard way to tune an RF coil.

Why would that make me believe the Extech? Both these statements are true:
1. A piece of metal near a coil affects the inductance of the circuit.
2. Introducing a loss in a coil due to eddy currents is misinterpreted by the Extech in the situation I described above as a change in inductance.

Statement one cannot be used to disprove two.

Measurement and theory are used together to find a consistent and believable model of the physical situation.

[Joe Gwinn]

Why would that make me believe the Extech?

It won't. It's an independent way to measure, one that is simpler than an Extech, and known in full detail. One can also use a bridge.

More generally, one way to be sure that some effect is real is to measure it in multiple ways, and see how well the answers agree. In Science, this is called replication of experiments, or just replication.

Both these statements are true:
1. A piece of metal near a coil affects the inductance of the circuit.
2. Introducing a loss in a coil due to eddy currents is misinterpreted by the Extech in the situation I described above as a change in inductance.

Statement one cannot be used to disprove two.

Item 2 is not correct. In fact, the Extech does distinguish added loss from changed inductance, as it measures inductance and AC resistance independently. The Extech directly measures the complex impedance of the component under test, yielding both real and imaginary values, and does not assume that either real or imaginary part is dominant.

As I mentioned before, the Extech gives exactly the same answer as a Maxwell-Wein bridge. Such bridges were the gold standard in impedance measurement for at least a century, until displaced by the rise of digital techniques.

Measurement and theory are used together to find a consistent and believable model of the physical situation.

Agree. All that's missing is the measurement.

[David Schwab]

In fact, the Extech does distinguish added loss from changed inductance, as it measures inductance and AC resistance independently.

Don't eddy currents increase the AC resistance? That would explain why eddy current loss increases with frequency, which is what (I think) you've been saying all along.

[Mike Sulzer]

Item 2 is not correct. In fact, the Extech does distinguish added loss from changed inductance, as it measures inductance and AC resistance independently. The Extech directly measures the complex impedance of the component under test, yielding both real and imaginary values, and does not assume that either real or imaginary part is dominant.

Any single measurement of of complex impedance, Extech, wien bridge, op amp circuit, or whatever, can give a correct measurement when the type of loss is known to be series or parallel, but not when it is an unknown mixture of both.

The post above with the equations shows this. If you measure a coil with series resistance, the Extech measures the amplitude and phase of the impedance (or the real and imaginary part, I do not know the details), and then uses a process, involving something like the equations above, to derive the inductance and resistance.

If we add a resistor in parallel with the coil under the conditions described above, the magnitude of the impedance (Z) drops, and the angle drops. The equation (that is correct for finding the inductance when there is only series resistance) incorrectly indicates a decrease in inductance when none has occurred. You can see that the inductance is proportional to Z in the equation. The angle (phi) response is more complicated, but if you examine it, you will see that it also results in a drop in L, although less of one under the stated conditions. Therefore, a drop inductance from the addition of a parallel resistance is indicated, and this is not correct.

Please notice that I am not saying that bringing a piece of metal close to a coil does not cause the inductance of the circuit to be different from the coil alone. I am only saying that you cannot accurately measure this with a single frequency measurement of complex impedance if you have to allow for series loss as well. And this is the case with a pickup coil.

[Joe Gwinn]

Don't eddy currents increase the AC resistance?

Yes, they do.

That would explain why eddy current loss increases with frequency, which is what (I think) you've been saying all along.

No, the argument is if the inductance also changes (decreases to be specific).

[Joe Gwinn]

Single-frequency measurement of low-Q inductances

Any single measurement of of complex impedance, Extech, wien bridge, op amp circuit, or whatever, can give a correct measurement when the type of loss is known to be series or parallel, but not when it is an unknown mixture of both.

The measurement is correct in all these cases. It's the interpretation of the measurement that's in dispute.

The post above with the equations shows this. If you measure a coil with series resistance, the Extech measures the amplitude and phase of the impedance (or the real and imaginary part, I do not know the details), and then uses a process, involving something like the equations above, to derive the inductance and resistance.

The fundamental measurement is of complex impedance at the specified frequency. There is a button marked SER/PAL (drawing in manual is wrong) that allows the user to specify which of two equivalent circuits to assume while computing inductance or capacitance and AC resistance.


I found the circuit diagram of the Extech (under a different brand name) on the web. For the record, it measures in the following way:

The 1000 Hz (or 120 Hz) oscillator has two outputs, one at 0 degrees (I) and one at 90 degrees (Q) phase shift. The 0 degrees output is amplified and imposed on the unit under test (UUT), a pickup in this case. Both 0 and 90 degree outputs are fed to a pair of synchronous demodulators, as will be discussed later.

The voltage across the UUT is sensed by one opamp circuit, and the current through the UUT is sensed by another opamp circuit, yielding two voltage signals, one proportional to UUT voltage and the other to UUT current.

These two voltages are fed one at a time to to the pair of synchronous demodulators, yielding a pair of complex numbers.

The first complex number consists of the I (real) and Q (imaginary) values of the UUT voltage, and the second complex number consists of the I and Q values of the UUT current.

The complex impedance (I and Q) is the UUT voltage (I and Q) divided by the UUT current (I and Q).

If we add a resistor in parallel with the coil under the conditions described above, the magnitude of the impedance (Z) drops, and the angle drops. The equation (that is correct for finding the inductance when there is only series resistance) incorrectly indicates a decrease in inductance when none has occurred. You can see that the inductance is proportional to Z in the equation. The angle (phi) response is more complicated, but if you examine it, you will see that it also results in a drop in L, although less of one under the stated conditions. Therefore, a drop inductance from the addition of a parallel resistance is indicated, and this is not correct.

Here is the key misunderstanding. The inductance is not proportional to either the magnitude or to the argument (the angle) of the complex impedance Z, it is instead proportional to the imaginary (quadrature) component of Z alone.

The Extech and the Maxwell-Wein bridge measure the in-phase (follows the signal generator) and quadrature (leading or lagging by 90 degrees) components independently of one another, yielding two signed real numbers. This works over a very wide range of resistance (in phase) and inductance or capacitance (quadrature) in the equivalent circuit.

Most handheld LCR meters measure only the magnitude of Z, and so are useful only for inductors and capacitors with little parasitic resistance. This is why such LCR meters are useless for guitar pickups.

Whenever someone comes up with a possible LCR meter and asks if it will work with pickups, I suggest that they wire a relatively pure multi-henry inductor (such as a choke or audio transformer winding) in series with a 50K pot and try to measure the inductance of the series string while varying the pot setting. If the indicated inductance varies more than a percent or two, the LCR meter will prove useless for pickups. What is being tested is the ability of the meter to accurately and independently measure both I and Q components of the UUT's impedance.

Please notice that I am not saying that bringing a piece of metal close to a coil does not cause the inductance of the circuit to be different from the coil alone. I am only saying that you cannot accurately measure this with a single frequency measurement of complex impedance if you have to allow for series loss as well. And this is the case with a pickup coil.

Actually, as described above, one can measure at a single frequency the inductance or capacitance component while ignoring the resistance component, so long as the resistance doesn't totally swamp the reactance (due to capacitance or inductance).

The Extech will achieve full accuracy if the inductive reactance exceeds the AC resistance by a factor of at least two.

[Mike Sulzer]

The measurement is correct in all these cases. It's the interpretation of the measurement that's in dispute.

In the case of series and parallel resistance, a correct interpretation is not possible. You have misunderstood my explanation.

Here is the key misunderstanding.

There is no misunderstanding on my part. Those two equations are derived from the impedance, R + 2*pi*j*L. Why go to the trouble to put this complex equation in the form of two real equations for Z and tan(phi)? Two reasons:
1. More people are familiar with the concepts of amplitude and phase than with complex algebra.
2. Putting them is this form allows one to easily see what the effects are of violations of series only resistance.

In this case one sees that the apparent value of L is a function of two variables, the magnitude of Z, and the phase. Since putting a resistor in parallel with L decreases both variables, and reducing either reduces the apparent value of L, an upper bound on the change in L can be deduced from the change in magnitude only. Since this relationship is one of proportionality, it is a large effect, unless the resistance is significantly larger than the reactance, when the usual square root of the sum of squares makes it small.

Actually, as described above, one can measure at a single frequency the inductance or capacitance component while ignoring the resistance component, so long as the resistance doesn't totally swamp the reactance (due to capacitance or inductance).

Actually, if you are in the series mode and a parallel resistor is added with a resistance equal to the reactance of the inductor, the apparent (and totally wrong) change in the inductance will be at least just under 30%.

The Extech will achieve full accuracy if the inductive reactance exceeds the AC resistance by a factor of at least two.

Not in the series mode if there is a parallel resistor present.