Measuring AC Impedance with a LCR meter

[Steve Conner]

Well, that is kind of unfair. For a start, the relevant wavelength is a quarter wave: 4000 meters. Then, the length of interest is the total length of wire in the pickup, maybe a few kilometres.

Finally, the propagation velocity of "light" in the coil is not the same as if the wire were laid out in a straight line in free space. Inductive and capacitive coupling between turns makes it somewhat faster, but not anywhere near as fast that the characteristic dimension would be 3 inches instead of a kilometre.

I would argue that the self-resonance in a pickup coil is one of these transmission line phenomena that looks like a lumped one. If you go up into the ultrasonic region, you should find the 3/4 wave and higher resonances (the 1/2 is a zero) though another effect of coupling between turns is that the resonant modes are not harmonically related any more. They can be nowhere near 2x, 3x, etc.

I think mike meant, the Q measurement is the Q that the inductor would have if a suitable capacitor were used to make it resonant at the test frequency.

[Mike Sulzer]

Well, that is kind of unfair. For a start, the relevant wavelength is a quarter wave: 4000 meters. Then, the length of interest is the total length of wire in the pickup, maybe a few kilometres.

Finally, the propagation velocity of "light" in the coil is not the same as if the wire were laid out in a straight line in free space. Inductive and capacitive coupling between turns makes it somewhat faster, but not anywhere near as fast that the characteristic dimension would be 3 inches instead of a kilometre.

I would argue that the self-resonance in a pickup coil is one of these transmission line phenomena that looks like a lumped one. If you go up into the ultrasonic region, you should find the 3/4 wave and higher resonances (the 1/2 is a zero) though another effect of coupling between turns is that the resonant modes are not harmonically related any more. They can be nowhere near 2x, 3x, etc.

I think mike meant, the Q measurement is the Q that the inductor would have if a suitable capacitor were used to make it resonant at the test frequency.

I think that the inductive coupling between turns and the capacitance assure that the length of the wire is not relevant.

[Steve Conner]

Well then, how else can you explain that the resonant frequency of the device is so much lower than its dimensions and the speed of light would predict? It is because it has a long wire all coiled up in there. The length of the wire is very relevant, the relation is just not as simple as if the wire were laid out straight.

My experience is with single-layer coils. For Tesla coil design I've used a numerical simulation code that can calculate the first 5 resonant frequencies of an air-cored solenoid to within about 2%. But I bet that multi-layer ones with magnetic cores behave the same, just the code would be even harder to write, so nobody has ever bothered.

[Mike Sulzer]

Well then, how else can you explain that the resonant frequency of the device is so much lower than its dimensions and the speed of light would predict? It is because it has a long wire all coiled up in there. The length of the wire is very relevant, the relation is just not as simple as if the wire were laid out straight.

My own approach would be to use the law of magnetic induction, derived at low frequencies/small sizes from two of Maxwell's equations. How would you explain the fact that I can make a coil of equal inductance with much less wire with a properly enclosed high permeability core?

And if that did not work I would invoke Maxwell's demons.

Anyway, Joe's concern was coupling too nearby pieces of metal, not the coil.

[Steve Conner]

Well, I'd say that the magnetic core alters the characteristic impedance of the medium because of its high permeability, and that lowers the propagation velocity, which lowers the resonant frequency of the 1/4 wave mode.

It only works for the 1/4 wave mode, because the MMFs due to higher ones sum to zero in the core.

Talking of Maxwell's demons, I admit that I am playing devil's advocate. (A real cynic would also point out I am making hot air by rearranging microscopic bits of data. ) The lumped description is certainly by far the most useful one here. As you go up in frequency, the first problem you run into is that the self-capacitance of the coil is distributed, but as you mentioned earlier, the cable capacitance (another thing that looks perfectly lumped at audio frequencies, come to think of it) swamps it in use.

I did once manage to convince myself that humbuckers sounded slightly different depending on which order the coils were connected, but I could have imagined it.

[Mike Sulzer]

Well, I'd say that the magnetic core alters the characteristic impedance of the medium because of its high permeability, and that lowers the propagation velocity, which lowers the resonant frequency of the 1/4 wave mode.

It only works for the 1/4 wave mode, because the MMFs due to higher ones sum to zero in the core.

Talking of Maxwell's demons, I admit that I am playing devil's advocate. (A real cynic would also point out I am making hot air by rearranging microscopic bits of data. ) The lumped description is certainly by far the most useful one here. As you go up in frequency, the first problem you run into is that the self-capacitance of the coil is distributed, but as you mentioned earlier, the cable capacitance (another thing that looks perfectly lumped at audio frequencies, come to think of it) swamps it in use.

I did once manage to convince myself that humbuckers sounded slightly different depending on which order the coils were connected, but I could have imagined it.

I think you are right that the capacitor is not a simple one. But that does not throw out the lumped models. it just means that we might need several cpacitors and resistors.

[RedHouse]

Well, I'd say that the magnetic core alters the characteristic impedance of the medium because of its high permeability, and that lowers the propagation velocity, which lowers the resonant frequency of the 1/4 wave mode.

It only works for the 1/4 wave mode, because the MMFs due to higher ones sum to zero in the core.

Talking of Maxwell's demons, I admit that I am playing devil's advocate. (A real cynic would also point out I am making hot air by rearranging microscopic bits of data. ) The lumped description is certainly by far the most useful one here. As you go up in frequency, the first problem you run into is that the self-capacitance of the coil is distributed, but as you mentioned earlier, the cable capacitance (another thing that looks perfectly lumped at audio frequencies, come to think of it) swamps it in use.

I did once manage to convince myself that humbuckers sounded slightly different depending on which order the coils were connected, but I could have imagined it.

You didn't imagine it.

[Joe Gwinn]

You didn't imagine it.

But it may be due to differences in stray capacitance to ground.

[Steve Conner]

Yes, that was my point. If you agree that the effect is real, it proves that the simple LCR model is inadequate to model humbuckers: it needs a couple more capacitors somewhere to account for the audible effects. And also the frequency- dependent resistor for eddy currents, I'm sure, but that's a separate issue.

To me it seemed that one connection gave a slight midrange scoop, the other one a slight mid boost. The best explanation I could come up with was that the stray capacitances to ground might be different at the insides of the coils than the outsides. I'm no expert on pickup construction, so how does that work? Does the coil tap end up being two insides, or two outsides, or one of each?

[Mike Sulzer]

Yes, that was my point. If you agree that the effect is real, it proves that the simple LCR model is inadequate to model humbuckers: it needs a couple more capacitors somewhere to account for the audible effects. And also the frequency- dependent resistor for eddy currents, I'm sure, but that's a separate issue.

To me it seemed that one connection gave a slight midrange scoop, the other one a slight mid boost. The best explanation I could come up with was that the stray capacitances to ground might be different at the insides of the coils than the outsides. I'm no expert on pickup construction, so how does that work? Does the coil tap end up being two insides, or two outsides, or one of each?

Don't forget the leakage inductor inductor in series with the frequency dependent resistor.

Speaking of which, there is another possible interesting high frequency effect. You are all probably familiar with the kind of rf or if filter made with two coils placed near each other. The loose coupling between the coils results in a leakage flux represented by an inductor in series with one side (depending on how you want to represent it) large enough to be useful. This inductor is used as part of the filter circuit. The coupling between the two humbucker coils might cause a similiar effect.

[Joe Gwinn]

Speaking of which, there is another possible interesting high frequency effect. You are all probably familiar with the kind of rf or if filter made with two coils placed near each other. The loose coupling between the coils results in a leakage flux represented by an inductor in series with one side (depending on how you want to represent it) large enough to be useful. This inductor is used as part of the filter circuit. The coupling between the two humbucker coils might cause a similar effect.

Back in November 2004 I measured the coupling between the coils of a Seymour Duncan humbucker (label said "APH1B 0758 IDT72") with side-by-side coils. At 1 KHz, the coupling coefficient K= 0.17. I've tested other humbuckers, and gotten similar values of K.

K is the mutual inductance divided by the square root of the product of the individual inductances of the two coils. One can measure K using an Extech, but it's a multi-step process.

The self inductance of each coil of the Duncan was about 2 Hy, and the inductance when they were connected in series aiding was about 4.8 Hy.

[Mike Sulzer]

These two files (http://www.naic.edu/~sulzer/airCore1SimpleR.png, http://www.naic.edu/~sulzer/aircore1SimpleL.png) are graphs of the inductance and resistance of a humbucker coil with the slugs removed. This is the simple L and R, that is, computed from the model R + j2pi*f*L as the Extech does, but at many frequencies up to about 2 KHz. The coil is about 3.9K #43. The coil is three inches from the nearest metal, a thin sheet of aluminum about 4.5 by 7.5 inches, that comes with a Radio Shack plastic box. There is no significant variation; this is what you get without any significant eddy currents. There is no need to fit for values; this is the simple case when the Extech can get the correct values at 1000 Hz.

The coil is placed on the aluminum plate. The simple R and L, computed as above, are shown here: http://www.naic.edu/~sulzer/airCore2SimpleR.png, http://www.naic.edu/~sulzer/aircore2SimpleL.png. There is a significant variation of the apparent parameter values with frequency. We need to fit, but is the same model used for the pickup with cores valid? In order to find out, I wrote software that allows fixing any number of the parameters to arbitrary values, fitting just to the others. The object was to check to see if both Rp and Lm (the series L and R that go across the core) could fit the data alone. It was not possible to get a good fit without both parameters. And the fit is good as shown in this plot: http://www.naic.edu/~sulzer/airCore2Fit.png.

So the conclusion is that this model with Rp and Lm in series across the coil is valid for a highly conductive sheet. To understand why draw a set of imaginary closed curves on the aluminum sheet. Each has the shape of the coil and is centered on the coil, but they start small and increase in size. A small curve has only part of the downward directed flux passing through it. It has an inductance associated with it since there is leakage flux. As the curves get bigger, they contain more flux, and these curves are associated with a low value of leakage flux. As the curves continue to increase in size, they contain return flux going back up that cancels some of the down going flux and there is an increasing leakage inductance. The net effect is the sum of all. We do not know how the current is distributed among the various loops; that would be difficult to solve for, but it is still clear how it works on an intuitive level.

[salvarsan]

These two files (http://www.naic.edu/~sulzer/airCore1SimpleR.png, http://www.naic.edu/~sulzer/aircore1SimpleL.png) are graphs of the inductance and resistance of a humbucker coil with the slugs removed. This is the simple L and R, that is, computed from the model R + j2pi*f*L as the Extech does, but at many frequencies up to about 2 KHz. The coil is about 3.9K #43. The coil is three inches from the nearest metal, a thin sheet of aluminum about 4.5 by 7.5 inches, that comes with a Radio Shack plastic box. There is no significant variation; this is what you get without any significant eddy currents. There is no need to fit for values; this is the simple case when the Extech can get the correct values at 1000 Hz.

Mike,

I think your work is very important.

Could you please walk the rest of us through it starting with the schematic?
I will be happy to help if embedding schematics is difficult from Arecibo.

-drh

[Mike Sulzer]

Mike,

I think your work is very important.

Could you please walk the rest of us through it starting with the schematic?
I will be happy to help if embedding schematics is difficult from Arecibo.

-drh

Thanks. Sure will. The schematic needs a little bit of updating and a few comments.

[hasan hadi]

LCR meter model 380193

i having device LCR meter model 380193 but i founding some proplem
1- how working this device
2- this device measuring impeadance(Z) or not measuring
3-when using key PAL\SER and key FREQ 120HZ and 1KHZ
4- When key FREQ 120HZ the reading is diffreance when using key 1KHZ
5-at working device display all symbols in the screen this symbols all active or some symbols is active example somple Z is apear in screen but not founding in keys
6- how measuring off angle
please i wanted answer of this equation