How to measure inductance and Q

[kayakerca]

Generally speaking, when making inductance measurements you want to stay well below any resonance peak, but choose a frequency high enough that the inductive reactance (the 'influence' of the inductance) is not completely swamped by coil resistance.

It is more complicated than that. . .

For me, some days it's like watching Suchitra Sebastian talk about new Superconductors. . . I just kinda gotta take what's being said on faith.

[LowNote]

Ok, so I think I jumped in too deep here. I understand some of it. Like what kayakerca said. " I just kinda gotta take what's being said on faith."

How many of you guys keep track of these numbers when making pickups? And are these numbers really that important?

LowNote

[Tony Bones]

LOL! Sorry if I took it too far. The short answer is that if you're measuring inductance, then do it 120 or 200 Hz or thereabouts. If your meter gives you Q, then great. If not then don't worry about it. The fact is, Q depends hugely on what's connected to the pup; as soon as you install it in a guitar and plug in a cable the Q and resonant frequency are going to change drastically.

I write down the numbers, but only because I'm a geek. I haven't actually found a good use for them. Maybe somebody else...

[kayakerca]

How many of you guys keep track of these numbers when making pickups? And are these numbers really that important?

I track every value my Extech LCR200 provides, both before and after the charged magnets are in place. It only takes a couple minutes and what readings I do not understand, well maybe I will some day and they will be there for me to reference. It also lets you see things like the impact on inductance that the magnets contribute to a wind, the effect of more turns on capacitance, and so on. And ya, I'm a little anal about stuff and only a hobbyist anyway.

[jack briggs]

I'd like to know how the capacitance is derived...

as would I......

[salvarsan]

The only thing with the EXTECH 380193 is no DCR. I have an $18 LCR and a EXTECH LCR200. The difference in LCR readings between the two is about 2 decimal places out. Totally insignificant for the purposes of measuring pickups, well, at least for my purposes.

I bought and returned the LCR200 a few years back
because the DCR readings were unstable and not
up to spec. A +/- 55 ohm bobble is ~33 ft of #42
wire and represents 65-80 winds.

This post explained the LCR200 inferior susceptibility
to damping factor D. The thread in which it resides
has more criticisms.

-drh

[kayakerca]

I bought and returned the LCR200 a few years back
because the DCR readings were unstable and not
up to spec. A +/- 55 ohm bobble is ~33 ft of #42
wire and represents 65-80 winds.

This post explained the LCR200 inferior susceptibility
to damping factor D. The thread in which it resides
has more criticisms.

-drh

Maybe they have made some improvements. . .



I'm definitely OK with my Extech LCR200 compared to my other meter.

[CheopisIV]

Are the numbers important.... no. Not really. It's just a way for us stats geeks to try to record and understand what's going on. The most important thing is how they sound and if you can repeat what you did.

Does it make sense? Sorta The more you do it, the more sense it seems to make. I've been at it for about 1-1/2 years and keeping as many records of everything I do for my own sense and understanding. I don't think my book would be a lot of use to anyone else, or maybe it would, who knows. I recently got an auto traverse machine that can give exact TPLs and am now doing up some test coils to measure against my hand wound coils. Here's one side of the test set, wound exactly to 5k on each with 80 TPL. The numbers per coil are quite different even though nothing was changed in the setup. Adding it all together gives some predictable results. Now I need to sit down and do up some hand guided coils to these specs and see what's going on.

LCR meter is the DER EE DE-5000 with alligator clips.


Top numbers are per coil, no magnets or metals, just leads.
Red Neck Screw/Slug are numbers with metals in and magnet in (A2) but still leads disconnected.
Last Red line is everything hooked up and taped off, ready to install
Last Black numbers is pickup left alone overnight to saturate and settle to room temperature.


Threw a label on for my records. I used to use a sharpie but it tends to rub off with too much handling.


It's interesting how much things change with the introduction of a magnet. I'll likely change the screws/slugs to different grades to see the measurable difference there as well as the magnet. None of this indicates exactly how the pickup will SOUND, although comparing to my notes I have an idea of how it should sound.

[Mike Sulzer]

Thanks Mike! I sometimes have a hard time integrating eddy currents into the whole picture. I don't always remember that, at least to first order, they are like a secondary winding with some resistance.

I'd like to know how the capacitance is derived...

OK. First, is it a reasonable number, 149pf? The measurement is of a single hum bucker coil. It you put two in series you get about 75pf which is a reasonable number for a hum bucker pickup, and so the derived measurement looks OK.

The process:

1. Take the impedance measurements at just the higher frequencies. The capacitance dominates in this range and so this is the best range to use.
2. Construct a mathematical model of the pickup impedance including two eddy current parameters. The eddy current model was derived as part of one of those discussions some time ago.
3. Construct a function which finds the difference between the model results (for some assumed set of parameters, C, eddy current params) and the measured impedances. Rcoil and Lcoil are fixed parameters in this function, already measured accurately.
4. Use a least squares optimization routine to find the parameters (C, eddy current params) that minimize the summed squared differences between the model and the measurements.

5. Compute what the measurements would have been if the resulting capacitance C were not there (Green and yellow lines).

This is done by some Python code in the software that executes the impedance measurement (using a recording interface connected to a computer).

The routines that code calls are:


# Routine to make pu imp with the two ec parms
# and the pickup cap free. Lcoil and Rcoil are globals,
# as well as Rcap, a resistor in series with the cap
# l is k**2, k and Rse being the usual ec params
def model(w, Rse, l, C):
Znc = Rcoil + j*w*Lcoil + ((w*Lcoil)**2)*l/(j*w*Lcoil + Rse*np.sqrt(w)/np.sqrt(w[-1]))
Zcap = Rcap + 1./(j*w*C)
Zp = 1./(1./Znc + 1./Zcap)
return Zp

Note: Rcap is set to zero in actual use, a good approximation.


def residuals(params, w, Z):
Rse, l, C = params
diff = model(w, Rse, l, C) - Z
d1d = np.zeros(Z.size*2, dtype = np.float64)
d1d[0:d1d.size:2] = diff.real
d1d[1:d1d.size:2] = diff.imag
return d1d


# Routine to find the pickup capacitance, the two eddy
# current parameters, Rse and k (actually, l = k**2,
def fCkRse(obj):
global Rcoil, Lcoil, Rcap, realMax
Rcoil = obj.pdict['Rcoil']
Lcoil = obj.pdict['Lcoil']
Rcap = 0.
nfit = 100
floc = obj.freqs.size - nfit - (obj.freqs[-1] - 20000.)/obj.freqs[1]
w = obj.freqs[floc:floc + nfit]*2.*np.pi
Z = np.zeros(nfit, dtype = np.complex128)
Z.real = obj.Zr[floc:floc + nfit]
Z.imag = obj.Zi[floc:floc + nfit]
p_guess = 1.e5, .2, 1./((obj.freqs[realMax]*2.*np.pi)**2*obj.pdict['Lcoil'])
print(p_guess)
params, cov = optimize.leastsq(residuals, p_guess, args=(w,Z))
return w, Z, params, cov


# Function to remove the impedance of the parallel capacitance
# of the pickup after it has been found with fCkRse
def unparZc(obj):
Zc = np.zeros(obj.freqsb.size, dtype = np.complex128)
Zc.imag = -1./(2.*np.pi*obj.freqsb*obj.pdict['C'])
Z = np.zeros(obj.freqsb.size, dtype = np.complex128)
Z.real = obj.Zr
Z.imag = obj.Zi
return unparZ(Z, Zc)



# Function to "unpar" Zp and Zb to give Za
def unparZ(Zp, Zb):
return Zp*Zb/(Zb - Zp)


The last function is the "inverse" of this one:



# Function to return Zp, Za and Zb in parallel
def parZ(Za, Zb):
return Za*Zb/(Za + Zb)

[Tony Bones]

The process:

1. Take the impedance measurements at just the higher frequencies. The capacitance dominates in this range and so this is the best range to use.
2. Construct a mathematical model of the pickup impedance including two eddy current parameters. The eddy current model was derived as part of one of those discussions some time ago.
3. Construct a function which finds the difference between the model results (for some assumed set of parameters, C, eddy current params) and the measured impedances. Rcoil and Lcoil are fixed parameters in this function, already measured accurately.
4. Use a least squares optimization routine to find the parameters (C, eddy current params) that minimize the summed squared differences between the model and the measurements.

Thanks. I will read the code more carefully after I understand the basic process, or at least figure out what I don't understand. This is all fascinating to me and is crucial to the whole topic of making meaningful LCR scans or even just single frequency measurements.

At the moment I'm lucky to have access to big $, high precision LCR meters (not that that means I know how to correctly interpret that measurements.) But I do think I could get useful results with a good sound card, a relatively small amount of electronics hardware, and a bunch of software. But that's a different thread!

[Joe Gwinn]

Ok, so I think I jumped in too deep here. I understand some of it. Like what kayakerca said. " I just kinda gotta take what's being said on faith."

How many of you guys keep track of these numbers when making pickups? And are these numbers really that important?

The industry standard test frequency for audio components is 1 KHz. This choice is arbitrary, but it is nonetheless the standard.

LCR meters are best for comparative measurements - knowing that the inductance is 6 Henreys tells you little about how it will sound.

One very useful use of LCR meters in production is to detect shorted coils - look at the series AC resistance, which goes up substantially if there is a shorted turn or coil.

[Mike Sulzer]

The industry standard test frequency for audio components is 1 KHz.

The inductance of the pickup coil is properly measured at a lower frequency. The value measured with a meter at 1KHz is low, often not by enough to matter for most purposes, but why would you even think about getting the wrong number in order to adhere to an irrelevant standard?

[Joe Gwinn]

The inductance of the pickup coil is properly measured at a lower frequency. The value measured with a meter at 1KHz is low, often not by enough to matter for most purposes, but why would you even think about getting the wrong number in order to adhere to an irrelevant standard?

As I said, the choice is somewhat arbitrary, but a single frequency is needed so people can compare results, and entries in catalogs can be compared.

The telephone industry went through just this debate starting in 1876, and settled on 1 KHz. I bet the number was chosen by A. G. Bell, who also invented the twisted pair.

The telephone industry preceded the audio industry by some 40 years, and set the standard. Early audio wasn't all that much better than telephones.

Why 1 KHz? It's determined by human hearing and the standard telephone system passband, 300 Hz to 3 KHz. This is the most critical part of the audio spectrum. The geometric mean of 300 and 3000 is 948.7 Hz, call it 1 KHz. Done.

The 100 Hz and 120 Hz test frequencies are standard for power supply components, simply because these are the ripple frequencies of full-rave rectified single-phase 50 Hz or 60 Hz AC power systems.

[Tony Bones]

As I said, the choice is somewhat arbitrary, but a single frequency is needed so people can compare results, and entries in catalogs can be compared.

I have no trouble comparing results so long as I can believe the measurements are reasonably accurate. Suppose I'm comparing pickups of substantially different designs such that each needs to have inductance measured at a different frequency to be accurate. I won't be able to make a useful comparison if we force them both to use the same frequency. At least one of them will have errors, but I'll have no idea which or how much!

I'd rather let everyone measure at whatever frequency they need to to get accurate results. The fact is, for any given DUT and instrumentation there usually will be a broad window of frequencies where accurate measurements can be made. It's conceivable that there might be some common frequency where all the windows overlap for everybody, every pickup, every LCR meter, every day from now until eternity. Or maybe not. I don't know. I do know that forcing everyone to use the same frequency can, best case, buy us no advantage whatsoever. Worst case it will make comparisons difficult or impossible, which is exactly the opposite of what is intended.

[Mike Sulzer]

As I said, the choice is somewhat arbitrary, but a single frequency is needed so people can compare results, and entries in catalogs can be compared.

There are two aspects to this issue of allowing people to make comparisons. The first considers the pickup as a circuit, and for this aspect the comparison people can make is between the values assigned to the components of the circuit in different pickups. The second is operational; perhaps the most basic such comparison that could be made is the resonant frequencies that would be obtained when using different cable capacitances.


First aspect, circuit. The circuit model of the pickup has inductance, a series resistance, a parallel capacitance, and a least two parameters associated with the eddy current losses. If we want to specify the inductance of a pickup, the value in the model is the only one that makes any sense across a range of pickups because it is independent of the other parameters in the model. That is, it has a specific definition, it can be measured, and this value can be communicated to other people. The value measured at low frequencies (say 100 to 200 Hz) with a good meter is the model value: for good accuracy, the series resistance is measured at the same time, and the frequency is too low for there to be a significant effect from the capacitance or from eddy currents.


On the other hand, the value at 1000Hz is somewhat affected by eddy currents, although not that much usually. But none the less, a comparison across many pickups of the inductance measured at 1000Hz is less definite than such a comparison of values measured at 100 Hz because different pickups have different eddy current effects, and so the values measured a 1000Hz differ from the true model values by different amounts.


Second aspect, operational. Suppose you want to be able to predict the resonant frequencies of some pickups in some external circuits, including, for example, various cable capacitances. There is no single number that lets you do this with reasonable accuracy because the eddy current losses are a function of frequency. One possible approach would be to derive an effective inductance at each frequency of interest from, for example, the yellow line in the plot I included below, the imaginary part of the impedance with the effect of the capacitance removed. Then you could do the computations for the response as a function of frequency including the variable effective inductance and see where the peak is for a given set of external components.


The eddy current effect is significant: at 5KHz the effective inductance is almost 30% lower than the model (coil) inductance (the gray dashed line gives its impedance versus frequency).


Thus I think that if one wants to specify a single number it has to be the model inductance. If you want to compute some practical effects, it takes a function, or a sequence of numbers, and it is not simple to do.