Measuring AC Impedance with a LCR meter

[RedHouse]

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.

Wouldn't choosing a similar number (but an order of magnatude difference) be better for calculations?

ie; 120Hz - 1k2Hz

[salvarsan]

Wouldn't choosing a similar number (but an order of magnatude difference) be better for calculations?

ie; 120Hz - 1k2Hz

The two frequencies were chosen because of precedents that are roughly half a century old.

Right now, I'm thinkina plotting the differences between series RLC, parallel RLC, and series R + parallel LC bulk impedences, just to see how far much they differ. A quick test should be instructive.

Crap! Did I just talk myself into learning Spice software?

[Mike Sulzer]

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?

You want to see the red points on this plot http://www.naic.edu/~sulzer/fit8.png plotted against sqrt(f) rather than f. That is equivalent to moving the points on the plot to the left with higher frequency points moving farther to the left. You should be able to see that this causes a plot more like parabola than a line. If you cannot see this, I will plot it for you.

The f^2 dependence is a nice approximation for some situations; this is not one of them.

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.

We now have a physical model based on the physics and verified by comparison to measurement. The components tell us about the physical effects. At low frequencies, the impedance of Lm is small and we are dominated by resistive loss in Rp. As the frequency rises, the inductive reactance will rise faster than the resistance (this is above the frequency of the plots) and eventually the inductance dominates.

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.

When you go to a high enough frequency so that Lm dominates over Rp, then you have Lc and Lm in parallel and have reduced total inductance. This would be a pretty high frequency in this case, well above the the 2 KHz shown on the plots, and I suspect well above the useful range of the pickup. But I have not computed it.

The self resonance of this pickup is at about 13 KHz.

[Mike Sulzer]

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.

Thanks, Steve.

Well, I am not quite ready to give up on the usefulness of the Extech. Let's see if we can use it to get all of Rs, Lc, Lm, and Rp(1000). The last one is the value at 1000 Hz of the resistor in series with Lm. We assume that Lc is measured by the Extech at 120 Hz for reasons I gave above. This has somewhat limited accuracy, but maybe it is good enough to do what we need. We also have Rs, of course. Then we make the measurement at 1000 Hz, and turn the R and L back into real and imaginary parts and subtract Rs from the real part. Call the result Zp(1000) because it is the impedance at 1000 Hz of Lc in parallel with Rp in series with Lc. (Impedances in series add, so we can subtract off the value of Rs.) Now take the complex inverse of this to get Yp. Admittances in parallel add, and so no we want to subtract off the admittance of Lc. This is just -j2pi1000Lc. (Remember, we have Lc from the 120 Hz measurement. Also remember that we are subtracting off a negative number.) Now we have the admittance of Rp(1000) in series with Lm. We take the complex inversion of this and the real part is Rp(1000), and the imaginary part is the impedance of Lm at 1000 Hz, and so we get Lm also.

I do not need an Extech to test this since I have complex impedances at 120 and 1000 Hz. I do not think my measurements at 120 Hz are quite as good as the Extech, which is intended to work there, while I think I am starting to lose some sensitivity and accuracy there. But it is worth a try. The results are that the predicted value of Rp(1000) is a factor of two lower than the result from the fitting, while the predicted value of Lm is twice as high as the fitting. This is not great, but this is a sensitive measurement and calculation, and it might be that the Extech does enough better to make this a worthwhile measurement.

[Joe Gwinn]

Yes, but those noble souls need to think the problem worthwhile. The danger is that they will write the directions in partial differentials.

[Joe Gwinn]

You want to see the red points on this plot http://www.naic.edu/~sulzer/fit8.png plotted against sqrt(f) rather than f. That is equivalent to moving the points on the plot to the left with higher frequency points moving farther to the left. You should be able to see that this causes a plot more like parabola than a line. If you cannot see this, I will plot it for you.

The f^2 dependence is a nice approximation for some situations; this is not one of them.

Depends on your level of modesty.

As I said, we will have a mixture, and f^2 is a bounding case.

We now have a physical model based on the physics and verified by comparison to measurement. The components tell us about the physical effects. At low frequencies, the impedance of Lm is small and we are dominated by resistive loss in Rp. As the frequency rises, the inductive reactance will rise faster than the resistance (this is above the frequency of the plots) and eventually the inductance dominates.


When you go to a high enough frequency so that Lm dominates over Rp, then you have Lc and Lm in parallel and have reduced total inductance. This would be a pretty high frequency in this case, well above the the 2 KHz shown on the plots, and I suspect well above the useful range of the pickup. But I have not computed it.

The self resonance of this pickup is at about 13 KHz.

The various log plot combos may be more informative. More than likely is that more than one thing is going on at once.

[Joe Gwinn]

The two frequencies were chosen because of precedents that are roughly half a century old.

Yep.

Right now, I'm thinkina plotting the differences between series RLC, parallel RLC, and series R + parallel LC bulk impedences, just to see how far much they differ. A quick test should be instructive.

Crap! Did I just talk myself into learning Spice software?

The Extech manual is actually quite explicit about their assumed circuit models: they give the assumed circuit schematics, which are dead simple.

[salvarsan]

The Extech manual is actually quite explicit about their assumed circuit models: they give the assumed circuit schematics, which are dead simple.

They are indeed explicit, but there are no schemata in either the current manual or the datasheet or the instruction set dox.

For guitar pickups, I advise against the parallel test mode at 120Hz.

[Joe Gwinn]

They are indeed explicit, but there are no schemata in either the current manual or the datasheet or the instruction set dox.

Hmm. I looked at my original users manual (received in 2005, copyright 2003) and there are no schematics, so I don't know where I got the scematics from. However, they are standard across the industry:

There are exactly two components, an AC resistance and a reactance (be it inductive or capacitive).

In parallel (PAR) mode, the AC resistance is in parallel with the reactive component.

In series (SER) mode, the AC resistance is in series with the reactive component.

That's all there is to it.

For guitar pickups, I advise against the parallel test mode at 120Hz.

Yes. Parallel mode is most useful for testing non-electrolytic capacitors.

[Mike Sulzer]

Hmm. I looked at my original users manual (received in 2005, copyright 2003) and there are no schematics, so I don't know where I got the scematics from. However, they are standard across the industry:

There are exactly two components, an AC resistance and a reactance (be it inductive or capacitive).

In parallel (PAR) mode, the AC resistance is in parallel with the reactive component.

In series (SER) mode, the AC resistance is in series with the reactive component.

That's all there is to it.




Yes. Parallel mode is most useful for testing non-electrolytic capacitors.

But let's be very clear what ac resistance means: If the circuit under test really is a resistance in series with a reactance, then the ac resistance is the value of that resistor measured at that frequency. If the circuit under test really is a resistance in parallel with a reactance, then the ac resistance is the value of that resistor measured at that frequency.

If the circuit is something else, then the meaning is unclear unless you have an established and verified procedure to relate the parameters of the circuit to the measurement.

For example, in my response to Steve yesterday, I have proposed a procedure for using measurements at both frequencies, measured with the Extech, to determine the values of the components in this particular pickup model. It remains to be seen how well it works in general.

[Joe Gwinn]

But let's be very clear what ac resistance means: If the circuit under test really is a resistance in series with a reactance, then the ac resistance is the value of that resistor measured at that frequency. If the circuit under test really is a resistance in parallel with a reactance, then the ac resistance is the value of that resistor measured at that frequency.

If the circuit is something else, then the meaning is unclear unless you have an established and verified procedure to relate the parameters of the circuit to the measurement.

The question was how the Extech works, in particular what the PAR and SER buttons do. Nothing more.

If you disagree with how Extech built their meter, we cannot help; you would need to take it up with Extech.

[Mike Sulzer]

The question was how the Extech works, in particular what the PAR and SER buttons do. Nothing more.

If you disagree with how Extech built their meter, we cannot help; you would need to take it up with Extech.

How the Extech works? It measures the complex impedance at 120 Hz and 1 KHz. It interprets that information in various ways, and it is up to the user to determine the validity of the interpretations. That is the difficult part. In particular, the term "ac resistance" could be confusing. It is not well defined in the manual. Do you disagree with my attempt at defining it?

I do not see how you arrived at the idea that I disagree with how Extech built its meter. And if I did, I would not be asking for your help or that of whoever is included in "we". I would indeed take it up with Extech!

[Steve Conner]

Yes, it is all about the interpretation. If you understand how the equipment works, you understand how to interpret the results.

For instance, no "true RMS" meter is actually true RMS, because they don't include the DC component of the waveform. But every EE I know interprets this correctly without even thinking about it, and would get confused (My meter is broken! It can read DC on its AC ranges!) if the meter makers suddenly "fixed" it. This is an example of a "wrong" implementation that works perfectly well because it's consistent.

Some high-end Tektronix models had an "AC+DC RMS" position on the mode switch for this reason. Angus Young had one and liked it so much he named the band after it.

[Joe Gwinn]

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

Almost. It does R, RL, or RC, but not RLC.

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

No, because the Extech cannot know resonance as the Extech assumes either L or C at any time, never LC, and tests at a single frequency.

Said another way, a complex impedance contains two independent numbers, which allows one to solve algebraically for the values of no more than two components. To solve for three components requires measurements at two or more frequencies.

What the Extech reports as Q is the reactance divided by the AC resistance, at the test frequency. (The Q/D/R button changes only the computation, presenting the complex impedance in one of three equivalent ways. The measurement is always the same.)

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

The Extech measures the actual test frequency it generates, so frequency error does not cause measurement error, so long as the parameters of the practical components being measured don't vary much with frequency.

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

Yes and no. All single-frequency LCR meters make the same basic assumptions, fitting a measured complex impedance to one of five circuits (R, RL parallel, RL series, RC parallel, RC series) where the RLC components are assumed to be ideal and lumped. No real component can live up to these assumptions, but some get pretty close.

Pickups are not in this hallowed group. The biggest issue has been that the Q of pickup coils can be pretty low, and many handheld LCR meters cannot accurately measure the inductance of such a coil. This problem is what led us to the Extech, which was far more able to deal with non-ideal components than most other $200 instruments.

But even with the Extech (or a real impedance bridge) the L and R components are not really lumped, largely because of eddy currents in nearby pieces of metal, and to the self-capacitance of the coil itself. Although we represent the self capacitance as a ideal lumped capacitor across the coil, in fact the capacitance is distributed. But we ignore that, because the error thus committed isn't often important.

[Mike Sulzer]

But even with the Extech (or a real impedance bridge) the L and R components are not really lumped, largely because of eddy currents in nearby pieces of metal, and to the self-capacitance of the coil itself. Although we represent the self capacitance as a ideal lumped capacitor across the coil, in fact the capacitance is distributed. But we ignore that, because the error thus committed isn't often important.

See this about lumped elements: Lumped element model - Wikipedia, the free encyclopedia.

A relevant quote:

The lumped element model is valid whenever , where Lc denotes the circuit's characteristic length, and λ denotes the circuit's operating wavelength. Otherwise, when the circuit length is on the order of a wavelength, we must consider more general models, such as the distributed element model (including transmission lines), whose dynamic behaviour is described by the Maxwell equations.

For pickups:
Lc = 3 inches
Shortest wave length in audio range: 15,000 meters
validity of lumped element model: unsurpassed

I think you mean something else, but I do not know what. Remember, we are not computing the effect of eddy currents, which would require PDEs. The purpose here is to establish the correctness, or not, of a model of the behavior and measure useful parameters.