A couple Q's about parasitic capacitance in an inductor

[Landru]

First question; I was measuring capacitance in various guitar pickup coils that have the same diameter of wire with an Extech LCR Meter, and it seemed to be that the more winds, the higher the inductance as expected, but I would get lower capacitance readings, too, both at 120 kHZ and 1k Hz. Could there actually less capacitance for more turns of wire, or is this an error in measurement?

Second question; in a normal capacitor, the dielectric has a big impact on the degree of capacitance, but I haven't found much information on how the different insulator materials between the coil windings would serve to act as a dielectric and alter the amount of parasitic capacitance. Is the effect of the insulator material negligible, or otherwise unimportant?

 

[nlantz]

To address your first question: We have to remember that capacitance and inductance cancel each other out in the complex plane. You can almost think of them as opposites of the same thing (Just don't tell a physicist i said that) like add and subtract , or multiply and divide. I found this image on here that helps explain the phasor relationship.

If you increase the amount of turns you will increase the inductance. You can also think of this as subtracting a -j/wC vector (reducing the capacitance).
Remember, you can't have something that is both capacitive and inductive at a single frequency.

To address your second question, capacitance is given by the following (for a parallel plate capacitor, I am abstracting a bit):

C = k*E0*A/D

Where:
K = relative permittivity
E0 = permittivity of free space
A = Area of the plate
D = distance between plates

As you can from the equation, the material properties are equally as important as all other inputs.

 

[berkeman]

Yeah, you need a vector impedance analyzer to measure the parasitic capacitance of most inductors. If you're close to Silicon Valley, you can stop by my work and I'll help you make the measurement...

 

[Landru]

To address your first question: We have to remember that capacitance and inductance cancel each other out in the complex plane.

Thanks for the explanation! Just to make sure I'm not mistaken, is this true for cases were the inductance and capacitance is in parallel with each other, as well as in series?

 

[berkeman]

Thanks for the explanation! Just to make sure I'm not mistaken, is this true for cases were the inductance and capacitance is in parallel with each other, as well as in series?

Series LC cancel at resonance, giving a near-zero series impedance. Parallel LC at resonance is a very high impedance.

Are you familiar with the complex notation shown in Landru's post? You can do the math yourself to see the behavior of the magnitude and phase of Z versus frequency...

 

[The Electrician]

First question; I was measuring capacitance in various guitar pickup coils that have the same diameter of wire with an Extech LCR Meter, and it seemed to be that the more winds, the higher the inductance as expected, but I would get lower capacitance readings, too, both at 120 kHZ and 1k Hz. Could there actually less capacitance for more turns of wire, or is this an error in measurement?

What values do you get for the measurement of inductance and capacitance for one particular coil, measured at 120 Hz (I assume your mention of a measurement at 120 kHz was a typo).

 

[Averagesupernova]

nlantz pretty much hit the nail on the head saying that you cannot have both inductive reactance and capacitive reactance at the same frequency. The method that it is measured will determine the displayed result on the measuring equipment.
-
In high school physics our teacher hung a heavy chain link from a thread and tied the same sized thread to the bottom of the link and allowed it to hang below. He asked us if he pulled on the lower thread which thread would break. We said the top. He gave it a quick pull and broke the bottom one. Then set the experiment up again and pulled on it slowly and broke the top one. Not really an analogy but it shows that the method of testing will determine the result.
-
In my opinion a simple LCR meter should never give you a result if it is able to sense DC continuity when testing a capacitor. It is misleading.

 

[Landru]

What values do you get for the measurement of inductance and capacitance for one particular coil, measured at 120 Hz (I assume your mention of a measurement at 120 kHz was a typo).

So I have two single coil pickups, both wound with the same gauge of wire, both feature six AlNiCo 5 pole pieces. This is what I measured:

"Cooler" Pickup A:
DC Resistance: 6.33 k ohms
L @ 120 Hz: 25.52 H
L @ 1 kHz: 3.070 H
C @ 120 Hz: 65.7 nF
C @ 1 kHz: 8.231 nF

"Hotter" Pickup B:
DC Resistance: 8.20k k ohms
L @ 120 Hz: 33.52 H
L @ 1 kHz: 4.050 H
C @ 120 Hz: 50.1 nF
C @ 1 kHz: 6.23 nF

 

[The Electrician]

OK. Your numbers show me what's going on. You are simply changing the setting of the LCR meter to read either inductance or capacitance with the same component (one of your pickups) connected to the meter. If you look closely you should see a minus sign in front of the reading when you're in capacitance measuring mode.

LCR meters show a negative capacitance when an inductor is the component you're measuring. Similarly, they show a negative inductance when the component you're measuring is a capacitor.

For example, if you have a 1 uF capacitor (something other than an elecrolytic) and measure it at 1 kHz with your LCR meter in inductance mode, it will measure about -25.33 millihenries.

The upshot of this is, you can't measure the parasitic capacitance the way you're doing it.

There's a much earlier thread in this forum that may be of help: https://www.physicsforums.com/threads/how-to-measure-parasitic-capacitance-of-inductor.81881/

Also, have a look at this: http://www.qsl.net/in3otd/inductors.html

Edit: Here's another page with more details on measuring parasitic capacitance than you could ever want! http://www.cliftonlaboratories.com/measuring_distributed_capacitance.htm

 

[Landru]

OK. Your numbers show me what's going on. You are simply changing the setting of the LCR meter to read either inductance or capacitance with the same component (one of your pickups) connected to the meter. If you look closely you should see a minus sign in front of the reading when you're in capacitance measuring mode.

LCR meters show a negative capacitance when an inductor is the component you're measuring. Similarly, they show a negative inductance when the component you're measuring is a capacitor.

For example, if you have a 1 uF capacitor (something other than an elecrolytic) and measure it at 1 kHz with your LCR meter in inductance mode, it will measure about -25.33 millihenries.

The upshot of this is, you can't measure the parasitic capacitance the way you're doing it.

There's a much earlier thread in this forum that may be of help: https://www.physicsforums.com/threads/how-to-measure-parasitic-capacitance-of-inductor.81881/

Also, have a look at this: http://www.qsl.net/in3otd/inductors.html

Edit: Here's another page with more details on measuring parasitic capacitance than you could ever want! http://www.cliftonlaboratories.com/measuring_distributed_capacitance.htm

Thanks for the links. It's clear to me now after rereading your, and some of the earlier posts, that this meter was never measuring parasitic capacitance, and that it can instead be worked out from the resonant peak of the coil.

The Extech 380193 LCR meter doesn't show a negative sign when measuring for C, is the negative sign implied?

 

[The Electrician]

The Extech 380193 LCR meter doesn't show a negative sign when measuring for C, is the negative sign implied?

Well, I've learned something from your thread. I was under the impression that all LCR meters, even the low-cost portable ones read a negative capacitance when measuring an inductance. For example, here's the reading shown by my B&K LCR meter when measuring a nominal 1 H inductor:

You can see the prominent minus sign. However, I checked the same measurement with a DER DE-5000, and to my surprise it looks just like your meter--it shows the right value but no minus sign. This is too bad. The minus sign is a good indication that the measurement is being made on a wrong setting.

 

[sophiecentaur]

Yeah, you need a vector impedance analyzer to measure the parasitic capacitance of most inductors.

We used to have an old Marconi Q meter, which would find the self resonant frequency of an inductor. Of course, there was a limit to the frequency range. At the time, we did stuff without Mathematica and the Internet, too. haha

 

[Landru]

Hello again, I've come back around to my own post while doing Google searches; I could use some clarification, so I have an addendum question:

Is it fair to say that the reason you can't measure the capacitance of an inductor directly is because, unlike a capacitor by itself, an inductor has inductance and capacitance in parallel with one another?

Is the purpose of solving for capacitance from the inductance and resonant peak of a coil to effectively remove the parallel inductor from the equation, leaving only the capacitance to be observed?

 

[nlantz]

Lets look at this from a different direction. Capacitance and inductance are mathematically... weird. They are differential equations and they hurt to look at. But I think it will help if you stick with me for a second. Let's look at Capacative and Inducive Impedance (just a slightly more complex flavor of resistance).

Z_L = jwL
Z_C = -j/(wC)

Ok so that j is a complex number. We can think about it as a direction, or more accurately as a "unit vector." It means that it only plays with numbers that also have a j in them and has no impact on non complex numbers.

The w is a frequency, L is inductance, and C is capacitance. All of these are positive numbers.
OK so lest do something crazy. Let's assume that our frequency, inductance ans capacitance are all fixed numbers, and let's replace them with constants tomake it easier to look at.

K_L for all of our inductive junk ( K_L = wL) and
K_C for all of our capacitive junk ( K_C = 1/wC )

Our equations then become Z_L = j*K_L
Z_C = -j*K_C

Now remember that j is nothing more than a direction. You'll notice that our inductive junk is contributing the system in a positive direction and the capacitive junk is contributing to the system in a negative direction.

The result of this is, when you add them, you will always end up with one specific impedance. It might be somewhere +j or it might be -j but you will always get one number (don't tell a mathematician I said that but for our purposes it's true).

So let's say your Z_L and Z_C are equal. you will end up at the 0 point on the j line. The is a special point at which resonance happens.

So now that we have the background out of the way, let me address your specific questions.

Is it fair to say that the reason you can't measure the capacitance of an inductor directly is because, unlike a capacitor by itself, an inductor has inductance and capacitance in parallel with one another?

I don't think you can really say this. The reason you cannot measure the paracitic capacitance directly is because they are not really separate things. You can only measure where your component is on the j axis. remember its only one number.

Its also not safe to say that the capacitors do not have parasitic inductance. In fact, if you increase the frequency enough, a capacitor will become an inductor (you will increase w enough that you cross the 0 point on the j axis)

Is the purpose of solving for capacitance from the inductance and resonant peak of a coil to effectively remove the parallel inductor from the equation, leaving only the capacitance to be observed?

This is just a math trick. You are not removing the capacitance or inductance. Remember these values are determined only by the geometry of the coil. What your doing there is finding the frequency (w) at which the effect of the Inductance and capacitance cancel each other out. You are finding the 0 point on the j axis. You then set the Impedances equal to one another. and solve for C.

Z_L = Z_C

Skipping the details you will end up with this.

wiggle it around to solve for C

Now you know f, and L, you can solve for your parasitic capacitance.
I think the confusion is coming from the lumped element model. Remember circuit diagrams are only models. They are just tools and no tool is perfect. Even though the circuit might show parasitic capacitance as a separate component in the circuit, that is really just a work around to make the math correct. It's a fix for a model only includes ideal components.

 

[anorlunda]

One can have (very small) series capacitance between windings in a coil, and capacitance between the coil and ground.

Given any circuit element from point A to point B, one can make measurements from A to ground, B to ground, and A to B. In general, all three should give different readings. In discussions like those in this thread, it would be important to specify which of the three we're talking about.

I'm a bit fuzzy myself on the definition of parasitic capacitance. I suspect that it means all the above, but I'm not sure.

 

[Jeff Rosenbury]

BTW, the various parasitic capacitances Anorlunda mentioned will vary with areas (wire diameter/shape), distances between windings (insulator thickness) and dielectric (insulator type). So they will probably vary for the same inductor made by different manufacturers or possibly even by the same company with different job lots.

 

[Landru]

I don't think you can really say this. The reason you cannot measure the paracitic capacitance directly is because they are not really separate things...
I think the confusion is coming from the lumped element model. Remember circuit diagrams are only models. They are just tools and no tool is perfect. Even though the circuit might show parasitic capacitance as a separate component in the circuit, that is really just a work around to make the math correct. It's a fix for a model only includes ideal components.

Thanks for your detailed reply, but I still have an acute point of confusion: it's said that the parasitic capacitance of a coil owes to the windings being nearby one another, as if there were an infinite number of little capacitors in parallel with the coil, along it's entire length. In that respect, it seems to me like there is a real capacitor there, and not just capacitance from a perspective of mathematical convenience.

 

[Averagesupernova]

It is real but the method of measurement will determine the results. Take a capacitor and inductor in parallel. Hook a resistor in series with that network and drive with an AC generator and measure the current, phase angle, etc. Very the frequency up and down and you will see the changes. At resonance there will be virtually no current. Above resonance current will go up and the majority of it will be passing through the capacitor. Below resonance the majority of current will go through the inductor. Landru, I am assuming that this is not all that difficult for you to understand. So why should it be difficult to understand if you cannot see a physical capacitor actually hooked to the inductor?

 

[Landru]

It is real but the method of measurement will determine the results. Take a capacitor and inductor in parallel. Hook a resistor in series with that network and drive with an AC generator and measure the current, phase angle, etc. Very the frequency up and down and you will see the changes. At resonance there will be virtually no current. Above resonance current will go up and the majority of it will be passing through the capacitor. Below resonance the majority of current will go through the inductor. Landru, I am assuming that this is not all that difficult for you to understand. So why should it be difficult to understand if you cannot see a physical capacitor actually hooked to the inductor?

Well you are stating intuitively as I understand it, but it seems to be at odds with what nlantz, who says "The reason you cannot measure the parasitic capacitance directly is because they are not really separate things." The way you describe is as if they really are two separate things that happens to entangled due to the physical fact of the coil windings being close enough together to exhibit many tiny parallel capacitances.

I've seen it repeatedly said that an ideal inductor would have no parasitic capacitance, which again, asserts that L and parasitic C are more like two different coins, rather than two sides of the same coin.

 

[Averagesupernova]

Is it any different than a black box with a capacitor and inductor wired in parallel inside with only 2 terminals on the outside and you cannot gain access to the inside of said black box?

 

[Landru]

Is it any different than a black box with a capacitor and inductor wired in parallel inside with only 2 terminals on the outside and you cannot gain access to the inside of said black box?

I has asked a few posts above:

"Is it fair to say that the reason you can't measure the capacitance of an inductor directly is because, unlike a capacitor by itself, an inductor has inductance and capacitance in parallel with one another?"

to which nlantz says "I don't think you can really say this. The reason you cannot measure the paracitic capacitance directly is because they are not really separate things."

But it sounds like you are saying my assertion was correct, that the capacitance can't be measured directly because rather than having a capacitor by itself, you have a "black box" wherein the parallel inductor will interfere with attempts to analyze the parasitic capacitive portion by itself.

I really do have to get a better grasp of complex numbers and how they work, I'll admit that. That's probably where I'm headed next.

 

[sophiecentaur]

Is it any different than a black box with a capacitor and inductor wired in parallel inside with only 2 terminals on the outside and you cannot gain access to the inside of said black box?

If you do your measurement at only one frequency then you could expect to mimic the coil but a real black box with real components couldn't be relied on to mimic the coil over a whole range of frequencies because of the parasitics of the two 'equivalent' components in your black box.

Another way of looking at this problem is that real 'things' have an Impedance at any given frequency and some 'things' have an impedance that's the same as an ideal C or L over a certain range. They make Inductors (Capacitors and resistors) so that the parasitics are small enough over the desired operating frequency range. Its in the nature of things that components for high frequency operation tend to have low C and L values and so are the values of their parasitics. (For instance, you are unlikely to want a 100mH Inductor that could have a large parasitic C in a 500MHz circuit.)

 

[berkeman]

When using a vector impedance analyzer to measure parasitic capacitance of an inductor (like the HP 4194 that I posted about earlier in this thread), you can use the Equivalent Circuit feature to calculate what the various parts of the impedance are, like the DCR of the inductor, its inductance, and the parasitic capacitance. Here is a picture of the Equivalent Circuit menu on our HP 4194 (please pardon the white T-shirt reflection in the screen...):

And here is an equivalent circuit from a National Instruments discussion of parasitic capacitance and inductors:

https://awrcorp.com/download/faq/english/docs/Elements/images/indqp_fig1.png

And here is the NI page that discusses the various parts of this Equivalent Circuit:

https://awrcorp.com/download/faq/english/docs/Elements/indqp.htm

It's just hard to measure the parasitic capacitance of an inductor with a hand-held meter. The method that Averagesupernova describes is a good alternative.

 

[Averagesupernova]

If you do your measurement at only one frequency then you could expect to mimic the coil but a real black box with real components couldn't be relied on to mimic the coil over a whole range of frequencies because of the parasitics of the two 'equivalent' components in your black box.

Another way of looking at this problem is that real 'things' have an Impedance at any given frequency and some 'things' have an impedance that's the same as an ideal C or L over a certain range. They make Inductors (Capacitors and resistors) so that the parasitics are small enough over the desired operating frequency range. Its in the nature of things that components for high frequency operation tend to have low C and L values and so are the values of their parasitics. (For instance, you are unlikely to want a 100mH Inductor that could have a large parasitic C in a 500MHz circuit.)

Yes. We should not forget that a real world black box will have what I described plus the parasitics of real world components.
-
On a somewhat related subject, long ago I had a subwoofer mounted in a sealed box. Dimensions of the box put resonance in the neighborhood of 50 hertz give or take. So, I wanted to test this. Just put a series resistor in and drive the network with a signal generator and watch the voltage, current, and phase shift. The sub would go through electrical resonance at about the predicted frequency based on the box size. You could watch the phase shift from leading to lagging. It seemed strange to me at the time that an inductive load could switch to capacitive. Granted this was not due to interwinding capacitance but the effect was the same.

 

[Landru]

I see, it's finally sinking in now. Thanks a lot for providing that picture, berkeman.

 

[berkeman]

Quiz Question -- Which one of the HP 4194 Equivalent Circuits would probably be the best match for measuring the parasitic capacitance and DCR of an inductor?

 

[Landru]

Quiz Question -- Which one of the HP 4194 Equivalent Circuits would probably be the best match for measuring the parasitic capacitance and DCR of an inductor?

B

 

[berkeman]

B

Yep!