Precision inductance tester

[Al (astral highway)]

On the path towards my current major project, I'm making various bits of precision test equipment.

One that I needed acutely is a precision inductance tester, reliable to below 10uH.

I note that commercial models of the kind that come with a DMM are usually only calibrated to 0.1mH (although this finding is a little OT, it's the circuit that's of interest).

I had clocked a circuit in an edition of the AARL handbook (not my current edition, maybe 2001-2003?) a while back and since found it on the internet, but I had to rely on my memory to work out the test and calibration procedure. I haven't bookmarked a source that I found in the past on the internet.

Overview:

1) Build a Colpitts oscillator with a source follower, to avoid loading it unduly. I used MPF102's to good effect. The input should be a capacitative divider with two high stability capacitors of nominally 220pF each.

2) Put Ci for your unknown input capacitance.

3) Test the resonant frequency with this only. Record this frequency, f1.

4) Tack a second capacitor of known capacitance right across the input. This is Ck (not Louis CK, the comedian, 'k' for known). It can be any value up to around 150pF. Silver mica is good. Record the new frequency, f2.

5) Now you have two frequencies, f1 and f2

Ci/Ci+Ck=f1^2/f2^2. This is a ratio, R. I initially found R=0.4443.

6) Now you can calculate the input capacitance (which is going to be approx the value of your capacitative divider, but we need to know more.).

I used 150pF.

So I worked Ci=150E-12 * 0.4443/1-0.4443

Or 120pF.

7) Now we're going to get a constant, K.

This is K=[1/(2pi^2)*Ci]^-E6

My initial K was 211.

8) Try a test inductance. The read-out will be in MHz.

L ,inductance in uH, is found by K/f^2

---------

Calibration.

I wasn't initially satisfied that my K was reliable enough

You will note some longish leads projecting from the circuit. These are 1.3mm Litz wire, but all the same, they have some inductance in nH. However, I need/ed them to be long in order to deal with physically huge inductors such as the one pictured. So I had to find a way to neutralise their effect.

So I tested 6 * nominally 4.7uH, 10% inductors, as well as five or six other inductors of a range of inductances up to the low mH. The area of most concern and precision is, however, around the 10uH order of magnitude. I found the mean inductance of the crucial 4.7uH batch to be 4.51uH, versus the manufacturer's nominal figure of 4.7uH. This is credible.

After comparing readings and taking an average figure from the six frequency readings for the 4.7uH inductor, I re-calculated my K to a new figure of 230. I will shortly mark this on the tester with a tape printer to make sure I remember it.

The results are displayed.

The large inductor is an air-cored inductor of great significance to my project. The inductance I calculated manually was 8.9uH and the measured inductance, using my little tester, is 9.09uH, which is pleasing. (I use https://m0ukd.com/calculators/air-co...or-calculator/)

I am happy that I can now add or remove a turn and know that the effect is predictable and trustworthy.

I also have other applications in mind for the unit. If I find the original source text I'll post it.


The readings on the bright red display are in MHz but are hard to read on the screen (easy in real life!) They are 7.032 and 5.037. It takes seconds for me to pop K=230/f^2 (display) into a calculator for a reading in uH.

The readings on the A4 sheet are Mfr (for manufacturer's value) and then my test reading.

[MrBungle]

Thanks for the write up. These things are always rather interesting to me. That's one hell of an inductor there as well!

This is actually similar to what I'm doing although my approach was somewhat less scientific. I'm misusing a G3UUR crystal tester circuit which I was using for measuring crystal motional parameters/matching crystals for IF filters. This is also a simple colpitts oscillator with buffer stage. The front end is versatile enough that you can jumper out the series capacitance and drop an LC circuit in the crystal socket instead, loosely coupled. C is always for me a Cornell Dubilier 100pF silver mica 1% (from bitsbox.co.uk). Fixture capacitance is calculated based on a "standard inductor" i.e. one I wound, glued solid and tested with a sig gen and the 100pF cap in parallel which came up at 1.1uH (horribly time consuming method of working out the inductance!).

Measures to within 3% of the actual value, compared to a commercial HP LCR meter I managed to steal off someone for a couple of days, which is good enough for my needs.

Photo below:

[Al (astral highway)]

Originally Posted by MrBungle

Thanks for the write up. These things are always rather interesting to me. That's one hell of an inductor there as well!

Thanks, Andy! And is quite a hefty old inductor!

And nice to know where to get 1% tolerance caps - I haven't used Bitsbox before - although it isn't crucial for the test I've described.

Measures to within 3% of the actual value...

Nice work! 1.1uH!! Measuring close to the nH level is exacting, but must be worth the effort. The application you mention is useful - I'll make a note to come back to it!

[Al (astral highway)]

I hope people aren’t put off but the calibration and testing method.

Once you’ve got K, it’s easy to check it back against the mean of some precision indicators.

Then it’s just:

L (uH) = k/readout in MHz^2

As I say, incredibly accurate and useful! I’ve teeaked my K to 233 for even greater accuracy and precision (noting that precision without accuracy is pretty pointless)

So I hope a few folks are tempted to try it.

[G0HZU_JMR]

It might be a good idea to show a schematic if you want to create some more practical interest

I think there a few DIY inductance meters out there that are oscillator based and the name of the most popular one escapes me for now... but it was quite accurate.

However, one minor niggle with your large 9uH solenoid is that it will have a lot of capacitance and this will begin to affect the oscillation frequency if your oscillator tank resonates up around 5MHz. At a guess there could be 6 or 7pF in that big inductor. This is based on a guesstimate of a scaled down version of your inductor. i.e. something scaled to have dimensions 10 times smaller would have about 900nH inductance and maybe 0.7pF capacitance. So your coil could have maybe 10 times this capacitance?

This capacitance is the parallel capacitance in the classic (but flawed) inductor model seen in lots of text books. However, it should be OK as a model in your case as you are still some way away from resonance. I think the /10 scaled inductor will be self resonant at just over 200MHz so I'd expect your big inductor to be self resonant just over 20MHz?

So by 5MHz I think you will be just starting to see the effect of the capacitance on the measured (9uH) inductance of your large inductor. On something like a VNA I'd expect the indicated inductance to be maybe 6% higher at 5MHz than it would be at 1MHz because of this. Not a huge difference but maybe worth a mention...

[Terry_VK5TM]

Originally Posted by G0HZU_JMR

I think there a few DIY inductance meters out there that are oscillator based and the name of the most popular one escapes me for now... but it was quite accurate.

AADE? There are a few versions similar to it by different people around.

Only tested inductors etc with a low test frequency (low 100kHz range from memory), so possibly not useful for what Al is doing.

[MrBungle]

AADE one was oscillator based. It used an LM311 as the oscillator. There are other variants that use the built in comparator inside a PIC to do the same job.

I think they are all loosely derived from this article in QST: http://www.qsl.net/wm5z/cq199301b.pdf

The AADE added self-calibration and a built in PIC to do the counting and processing rather than relying on an external counter and data entry.

I've been after an original AADE for a bit but they're unobtainable now pretty much after the owner of the company Neil Hecht went SK in 2015.

[jimmc101]

These ones?
Original with LM311 and PIC16F84
Mk2 with 16F628

Jim

[Al (astral highway)]

Originally Posted by G0HZU_JMR

It might be a good idea to show a schematic if you want to create some more practical interest

Hi Jeremy, yes! Always a good plan. My attention has been devoted to some other big and challenging life things this week and until now, I've been too busy to do that. I actually built mine I jotted down from a hand-drawing I sketched in my 'lab-book' ages ago, and memorised the source follower, but I've finally found the source on the internet again. At the time of posting my results, I'd written down just the principle and worked from that!

The author is Rob AK4AA. I think his description is well intentioned but if followed literally won't result in a correct reading.http://www.robkalmeijer.nl/techniek/...e47/index.html - hence my reworking of the key formula.

..,one minor niggle with your large 9uH solenoid is that it will have a lot of capacitance and this will begin to affect the oscillation frequency if your oscillator tank resonates up around 5MHz. At a guess there could be 6 or 7pF in that big inductor.

Thank you, Jeremy, it's a really good point. Indeed, I spend a lot of thought in trying to envisage and map out lumped elements. In this case, those few Pifs are not so much of an issue, as the inductor will be in series resonance at around 180KHz. But yes, supposing it was a tank coil in a VHF transmitter, for example, then it would be highly relevant.

I don't know if others have worked out a method of back-calibrating such as the one I describe. Take a whole batch of manufacturer's values, (here, I used six), use them against the initial calibration and then find the mean.

With the build I've shown - designed for large air-cored inductors - I can measure down to around 3uH. The limiting factor is the Litz wire leads. If I put croc-clips right on the board, I can measure a little lower reliably. But the neat thing is, I now know that my coil is adequately modelled by the applet I posted, and I can hence work out exactly the effect of adding or removing a turn or half a turn in two ways. It's just a feature of my nature that I need more than one source of reliable evidence to make a conclusion that I'm happy with.

[G0HZU_JMR]

Thank you, Jeremy, it's a really good point. Indeed, I spend a lot of thought in trying to envisage and map out lumped elements. In this case, those few Pifs are not so much of an issue, as the inductor will be in series resonance at around 180KHz. But yes, supposing it was a tank coil in a VHF transmitter, for example, then it would be highly relevant.

I think the 7pF self capacitance will also affect your meter result a bit as well. I think the change in reading could be about 6%.

I just tried simulating your oscillator in SPICE and I got a K of 219.9 for a perfect 9uH inductor. The Fosc was 4.944MHz. But when I added the 7pF across the 9uH inductor the frequency of oscillation fell to 4.811MHz and this then equates to an inductance of 9.5uH using the same K equation.

So in other words, on an LC meter that measures at 180kHz I'd expect a large 9uH coil like this (large as in maybe 6 inches diameter) to measure 9uH at 180kHz but at about 5MHz it will measure 9.5uH due to the 7pF of self capacitance of a coil this physically big.

[MrBungle]

Originally Posted by jimmc101

These ones?
Original with LM311 and PIC16F84
Mk2 with 16F628

Jim

Didn't even know that existed! Have just ordered all the bits to make one! Thank you.

[Al (astral highway)]

Originally Posted by G0HZU_JMR

So in other words, on an LC meter that measures at 180kHz I'd expect a large 9uH coil like this (large as in maybe 6 inches diameter) to measure 9uH at 180kHz but at about 5MHz it will measure 9.5uH due to the 7pF of self capacitance of a coil this physically big.

Hi Jeremy, that's a useful bit of deduction, I'll bear that in mind. The result is still one that I couldn't obtain using a typical inductance tester on a DMM and as long as I'm aware of the tolerance, it's very helpful.

The coil is indeed pretty large - 7 ins in diameter. The author of the report illustrates its use with some rather more typical inductors and I'm delighted with its performance meausuring the 33uH commercial inductors and the others depicted in my 'infomatic'

Fortunately or otherwise, there are numerous other variables that will be playing fast and loose with the self-resonant frequencies of two coils, loosely coupled, in my major project (this is just one of them). Hence the need for quite an agile feedback mechanism!

[ms660]

Does anyone know if inductance varies with frequency?

Lawrence.

[Al (astral highway)]

Does anyone know if inductance varies with frequency?

No, it doesn't...

But inductive reactance obviously does: it's proportionate to the frequency and inductance.

This is a limitation with some commercial meters. And as Jeremy points out, with lumped (self) capacitance, although the actual inductance hasn't changed, the measured result can be off by some margin.

If we're measuring big old inductors of hundreds of mH, probably no big deal. But when they're in the nH to uH range, the parasitic capacitance gets trickier to factor in.

[ms660]

A home brew Hays would probably do but calibration might be a pain.

Lawrence.

[G0HZU_JMR]

In the case of a real inductor like the big air cored solenoid Al is using, the inductance will appear to vary with frequency because of the self capacitance. I'd expect a plot of inductance vs frequency for that inductor to look something like the plot below. This is based on a simple model of Al's inductor. You can see that the measured inductance of this inductor slowly climbs as resonance is approached.

[G0HZU_JMR]

It's just a feature of my nature that I need more than one source of reliable evidence to make a conclusion that I'm happy with.

If you want to do some cross checking at a lower frequency, another classic method would be to use a sine wave source at maybe 100kHz and a series sense resistor. This is known as the three voltage method and the equations are available in various places online.

For example:
http://www.kennethkuhn.com/electroni...easurement.pdf

Obviously, the sense resistor resistance needs to be known quite accurately and it should have minimal inductance in its package for obvious reasons.

By measuring the 3 voltages around the sense resistor with a decent DVM (one with true rms bandwidth >100kHz on ACV) it should be possible to predict the inductance and the ESR at 100kHz. However, the ESR at 100kHz is obviously going to be vanishingly small in that huge 6" diameter solenoid. General purpose axial inductors for PCB use will generally have an ESR much higher. Typically several ohms? But this method should predict the inductance quite accurately as long as the resistance of the sense resistor is known accurately and it is a pure resistance (not wirewound). It does mean entering the above info in an excel spreadsheet or a dedicated computer program. I mainly use this method to measure capacitors for ESR and capacitance but it will also work with inductors.

See below for an example video showing a 9uH inductance in series with 1 ohm being measured using this technique. This is tested at 100kHz with a 10R sense resistor.


https://www.youtube.com/watch?v=nfn5...ature=youtu.be

The results will depend on how carefully you make the measurements and also on the quality of the meter and the accuracy of the sense resistor. The source should ideally be a pure sine wave with very low harmonic content.

You can also use a dual channel scope and measure two voltages and the relative phase and get similar results but it won't be as accurate. But you could go to much higher test frequencies with a scope.

[Argus25]

Originally Posted by astral highway

... there are numerous other variables that will be playing fast and loose with the self-resonant frequencies of two coils, loosely coupled, in my major project (this is just one of them). Hence the need for quite an agile feedback mechanism!

Al,

I have wondered about these myself. I might have mentioned this on another thread. I have never built a Tesla coil (its on the to do list) But a while back for another project I needed to understand how coupling into a resonant circuit affected that circuit, its damping and its resonant frequency. It is interesting that the coupling coil effectively couples in negative inductance, raising the resonant frequency of the resonant circuit and its effects are very dependent on the resistance in the primary circuit and the mutual inductance. The only satisfactory explanation I could find for these effects was in Terman's book. I have attached a pdf, one page with a diagram (Terman's) and an explanation from one of the articles I wrote on the topic. Could be of interest for your Tesla coil.

Hugo.

[Al (astral highway)]

Originally Posted by G0HZU_JMR

If you want to do some cross checking at a lower frequency, another classic method would be to use a sine wave source at maybe 100kHz and a series sense resistor. This is known as the three voltage method and the equations are available in various places online.

For example:
http://www.kennethkuhn.com/electroni...easurement.pdf

Obviously, the sense resistor resistance needs to be known quite accurately and it should have minimal inductance in its package for obvious reasons.

....

See below for an example video showing a 9uH inductance in series with 1 ohm being measured using this technique. This is tested at 100kHz with a 10R sense resistor.


https://www.youtube.com/watch?v=nfn5...ature=youtu.be

That's great, Jeremy, really helpful. I'll investigate and have a go. I have in my test equipment a 'home-built' a precision 1R resistor from 5x 1 per cent precision 0.2R metal oxide resistors in parallel.

Originally Posted by G0HZU_JMR

The results will depend on how carefully you make the measurements and also on the quality of the meter and the accuracy of the sense resistor. The source should ideally be a pure sine wave with very low harmonic content.

You can also use a dual channel scope and measure two voltages and the relative phase and get similar results but it won't be as accurate. But you could go to much higher test frequencies with a scope.

I might try the 'scope method anyway, just for comparison. But I'll pay more attention to the first method.

Thanks again!

[Al (astral highway)]

Originally Posted by Argus25

I have wondered about these myself. ...It is interesting that the coupling coil effectively couples in negative inductance, raising the resonant frequency of the resonant circuit and its effects are very dependent on the resistance in the primary circuit and the mutual inductance. The only satisfactory explanation I could find for these effects was in Terman's book.

Thank you, Hugo. That looks relevant and interesting and I'll take a good look at it.

One of the additional complexities, beyond those that you mention, is that the plasma at the antinode has properties that are not obvious and are complex to model. But the first that comes to mind is that the plasma is constantly changing in length and volume at a variably variable rate and has self-capacitance, so that the secondary coil's resonant frequency is constantly changing. Obviously there is reflection back to the primary, but overall, the system is multivariate in ways that are not particularly well theorised, although more so for conventional spark-gap coils.

In my project, the control signal feedback and overcurrent will each be sampled with suitable agility by current transformers in the primary circuit. Some people put these in the secondary coil ground circuit, but the results are less convincing. I have put more care and planning into the magnetics for the project than any other component so far.

This emphasis will change when I come to the power electronics, but they are only as good as their control signals.

Cheers!