# Resonant circuits for calculating inductance

Discussion in 'General Electronics Chat' started by adam555, Sep 11, 2013.

1. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
Hi, I'm trying to calculated the inductance of different coils using this formula with the results from resonant circuits:
$L = \frac{1}{4 \times \pi^{2} \times f^{2}_{r} \times C}$
The problem is: the coils are too small for the experiment proposed here: Inductor-capacitor "tank" circuit, where they propose this circuit; as I can't see the result on my analog oscilloscope.

So, instead I'm using this circuit (substituting the proposed "search coil" with my own coils):

I can see in the oscilloscope how the coil resonates with the 1n capacitor, and I can get the inductance using the values of the resonance frequency and the capacitor. However, when I change the capacitor for another value, and do the calculations again to check if the formula is working, I get a complete different result; which rather suggests that something went wrong... can you see what it is?

Also tried it with a colpitts oscillator, and I also get a completely different set of values.

What would be the easiest circuit to see the resonance of a capacitor and a coil, repeatedly on the oscilloscope, and which I could use to calculate the inductance?

Thanks,

Last edited: Sep 11, 2013
2. ### MaxHeadRoom Expert

Jul 18, 2013
10,234
2,259
In a parallel tuned circuit, Tuned circuit Impedance is greatest when Capacitive reactance = Inductive reactance.
You need a frequency generator to sweep it.
Max.

3. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
Thanks Max,

I was trying it with just the tank and a 1KHz 500mV square wave. It seems to be working; at least I got the same inductance for a coil with 2 different capacitors. But I still have the same problem as at the beginning: I can only see the resonance with the biggest coils, but not with the small ones. Another problem is that the resonance is barely perceptible, with an amplitude of 30mV peak to peak.

I'm not sure what you mean with this. The truth is, I have no idea how capacitive and inductive reactance are affecting my experiment.

4. ### MaxHeadRoom Expert

Jul 18, 2013
10,234
2,259
Starting with a frequency below the tuned point, the Inductor will present a very low inductive reactance across the circuit, virtually equivalent to the DC resistance of the coil, the capacitor very High, as the frequency of the tuned point is approached and reached, both inductance and capacitance present a very high Equal reactance.
As the tuned point is passed, the impedance roles will reverse.
When doing these experiments, often an old instrument easy to make what used to be known as a grid dip meter, now Dip meter due to Tubes or valves replaced by semi's.
You may find some simple circuits via Google.
Max.

5. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
I see what you mean now. I wasn't doing it that way.

I don't have a function generator, so I was using the fixed 1Khz square wave from the oscilloscope (the one used for calibartion) directly into the tank circuit, and then measuring the resonance it produced after each pulse.

I made last week a pulse generator with a 555 that can be adjusted from 70Hz to 70Khz, so I'm going to try the method you are proposing.

I've been looking through them for a week to see if there's anyone I could use; but either I don't have some of the components needed, or are simply too complicated

6. ### Mike33 AAC Fanatic!

Feb 4, 2005
349
25
I once got some decent measurements by creating a tank circuit (pick your own values for C), and running a line from my PC sound card to it. I DL'd a generic sweep generator program, and measured voltage at the top node of the tank at various evenly-spaced frequencies (not sweeping). I plotted them, looked for the 'dip', and found my mystery inductance that way. Takes patience, but it works! Note that L/C in parallel or in series will give a dip or a peak, accordingly...

When you get 'close', you can actually sweep the tank, use a scope or analog meter to 'see' the dip...pretty cool...

7. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
I tried another method with arduino yesterday. It was supposed to send a pulse to a tank, and then measure the time between peaks to calculate the inductance; but it didn't work. I could see the tank resonating in the oscilloscope, but for some reason arduino was not detecting it.

Last edited: Sep 13, 2013
8. ### DickCappels Moderator

Aug 21, 2008
2,570
604
One thing that you should consider is that all three of the capacitors on the collector and emitter affect the frequency of oscillation, not just the capacitor across the inductor.

The most common way of finding the value of an inductor in a tank circuit is illustrated on this web page: http://www.doc-diy.net/electronics/l_meter/

One thing to watch out for with this circuit is accuracy degrades at low frequencies if the inductor has a high resistance.

9. ### vk6zgo Active Member

Jul 21, 2012
677
85
You should be able to determine the jnductance from the "ringing" you will see after the transitions of the square wave,knowing the value of the capacitance in the parallel resonant circuit.

For quite small inductances,the rise time of the calibration signal may be too long,& you will need another signal with a faster rise time.

Another thing to remember,is that if the frequency response of your Oscilloscope is insufficient,you may not be able to see the ringing.

10. ### w2aew Member

Jan 3, 2012
219
64
Here's a video that I did that shows exactly that - ringing a tank, measuring the frequency of the ringing, and calculating the inductance. The first part of the video shows one way to measure the value of a capacitor as well.

11. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
For now, and until I finish putting together the function generator, that's the only reliable method that I could find to calculate the inductance of coils. All other methods give me different results for the inductors when I change the capacitors in the resonant circuit.

Thank you for posting those videos; I find them really helpful -especially the one about OpAmps-.

12. ### #12 Expert

Nov 30, 2010
16,013
6,528
Do you want to create oscillations or measure the inductance of the coils?

13. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
I was actually doing both. I began testing oscillating circuits but had problems making them work because I was using coils that I found at home with unknown values; that's why I needed to find a way to calculate the inductance.

Found a simple way just using the oscilloscope's calibrating pulse: I put a capacitor in parallel with the coil and then used the ring after each pulse to calculate the inductance using the following formula:
$L = \frac{1}{4 \times \pi^{2} \times f^{2}_{r} \times C}$

I tested it by changing the capacitor and it seems to be working fine; it always gives the same value for a given coil.

Last edited: Sep 30, 2013
14. ### #12 Expert

Nov 30, 2010
16,013
6,528
OK. Never mind.

15. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
There's one thing that would be really helpful: increasing the amount of times the tank circuit rings. For example: when I test tank circuits in simulators, they ring for a long time; but in real life they only oscillate about a couple of times. I tried using a resistor to see if I can slow down the rate at which the energy that bounces back and forth between the coil and the capacitor is lost; but it doesn't work.

Is there any way to make the tank oscillation go on longer, without interfering with the resonant frequency?

Also, I noticed that some coils work best with smaller capacitors, and some with bigger capacitors. Is there any formula to calculate which capacitor size works best with each coil size?

16. ### #12 Expert

Nov 30, 2010
16,013
6,528
This is something I hacked together with parts I had laying around. It measures inductance. It measures inductance repeatedly, as long as you want to leave the signal generator and the 'scope on.

17. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
I had a look at your blog some time ago, but couldn't try that circuit since I didn't even have an oscilloscope at that time. It's on my list though for when I finish putting together a function generator.

18. ### JoeJester AAC Fanatic!

Apr 26, 2005
3,311
1,108
Place a series resistor between a single pulse generator (1 uS or so) and the parallel L and C circuit.

The natural resonance frequency will be dampened, but you can get the time of that frequency.

Convert time to frequency, plug that into your formula, and calculate the L.

See circuit below ... I used both a 1uF and a 4.7 uF capacitor, measured the time, and calculated L. The calculation was 1.02 mH ... roughly 2 percent error.

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19. ### adam555 Thread Starter Active Member

Aug 17, 2013
858
39
That's how I was doing it, but using the 1Khz calibrating pulse from the oscilloscope instead of a generator.

I had tested it before with the series resistor, but I only get a 5% increase in the duration of the ring; barely perceptible.

In my case it works best with capacitors between 100nF and 470nF; though the coils I was testing are quite small -a couple of up to was 345μH, and the a lot of small ones that I can barely test. I just found a couple more of 560μH, and a big one which just measured around 9mH -and which generates a ring with a cycle bigger than the one produced by the 1Khz pulse.

I also noticed that coils with a core produce a lower frequency ring -which would imply a greater inductance- but the rings are quite short -as if the energy was lost faster-. Is this consistent with how coils work?

20. ### w2aew Member

Jan 3, 2012
219
64
Yes, core materials are used to increase the inductance of the coil. The ring dies out due to losses in the circuit - wire resistance, other resistors, core losses, etc.