# A couple Q's about parasitic capacitance in an inductor

1. Nov 18, 2015

### 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?

2. Nov 18, 2015

### 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 cant 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.

3. Nov 18, 2015

### Staff: Mentor

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...

4. Nov 18, 2015

### Landru

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?

5. Nov 18, 2015

### Staff: Mentor

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...

6. Nov 18, 2015

### The Electrician

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).

7. Nov 18, 2015

### 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.

8. Nov 19, 2015

### Landru

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

9. Nov 19, 2015

### 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 [Broken]

Last edited by a moderator: May 7, 2017
10. Nov 19, 2015

### Landru

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?

Last edited by a moderator: May 7, 2017
11. Nov 19, 2015

### The Electrician

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.

12. Nov 24, 2015

### sophiecentaur

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

13. Apr 14, 2016

### 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?

14. Apr 15, 2016

### 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. Lets look at Capacative and Inducive Impedance (just a slightly more complex flavor of resistance).

ZL = jwL
ZC = -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. Lets assume that our frequency, inductance ans capacitance are all fixed numbers, and lets replace them with constants tomake it easier to look at.

KL for all of our inductive junk ( KL = wL) and
KC for all of our capacitive junk ( KC = 1/wC )

Our equations then become

ZL = j*KL
ZC = -j*KC

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 lets say your ZL and ZC 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.

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)

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.

ZL = ZC

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.

15. Apr 15, 2016

### Staff: Mentor

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.

16. Apr 15, 2016

### 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.

17. Apr 15, 2016

### Landru

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.

18. Apr 15, 2016

### 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?

19. Apr 15, 2016

### Landru

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.

20. Apr 15, 2016

### 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?