# Transformer Inductance

Discussion in 'General Electronics Chat' started by blah2222, Nov 10, 2013.

1. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
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Hi all,

I received an audio transformer for a project from my prof and went ahead and started to characterize it before using it.

CT-side DC resistance: 46R
Non-CT-side DC resistance: 2R
Voltage gain ratio: 1:13

The part is an audio transformer (1.2K primary, 8R secondary) 60-282-0

While doing LC tank measurements to figure out the inductance, I determined the resonant frequencies with different parallel capacitor values (1nF, 1.5nF, and 10nF) and both the primary and secondary windings had roughly the same inductance 10-12 uH.

Maybe I'm just double-guessing myself but shouldn't the ratio of inductance be roughly the turns ratio and not one?

For each measurement, I left the other winding open and unconnected.

Thank you,
JP

2. ### Alec_t AAC Fanatic!

Sep 17, 2013
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IIRC if both windings have the same density (i.e. number of turns per unit length of the core) and occupy the same core length then the inductance ratio is the square of the turns ratio. I'm open to correction.

3. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
581
38
Right, yeah the I meant the square of the turns ratio. Thanks for the correction.

4. ### #12 Expert

Nov 30, 2010
18,076
9,676
I never physically tested this, but logic seems to say that equal inductance is not at all the right answer.

5. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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All things being equal (which they obviously aren't!), the inductance of a solenoid goes up as the SQUARE of the number of turns.

Eric

6. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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http://www.qsl.net/in3otd/indcalc.html

Here's an interesting Wheeler inductor calculator. The wheeler coil yields the HIGHEST inductance for a given total length of wire. It is slightly "under-square" meaning the length of the solenoid is about 95% of the diameter.

Eric

#12 likes this.
7. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Perhaps if the OP described the method of inductance measurement adopted more clearly along with some measured data, it may be possible to explain the anomaly. How do we know the method used was correct in concept &/or execution?

For instance, let's suppose one resonates a 10nF capacitor with a 10uH inductor - indicative of the OP's nominated values. This would equate to a source frequency of about 500kHz which doesn't obviously fall within an audio transformer's expected operating frequency range.

Last edited: Nov 10, 2013
8. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
581
38
The circuit I had setup was a function generator passing a square wave (50% DC) with a frequency of roughly 6 KHz. It was passed through an buffer op-amp feeding into a 15 pF capacitor in series with the tank circuit. I looked for ringing on step-up transitions of the square wave for the tank circuit and measured that frequency.

With a 10 nF cap I measured a ringing resonant frequency of 490 KHz which works out to roughly 10uH in inductance.

9. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
OK. You mentioned that during any particular test any part of the transformer winding not under consideration was left open. Under these circumstances one would expect to see the driven winding's effective magnetizing inductance as the resonating inductance. This would be typically orders of magnitude greater that 10uH - particularly so looking into the high impedance primary winding(s).

Which begs the question - Are you trying to measure the magnetizing inductance or the leakage inductance seen looking into any winding?

10. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
If one takes a look at the linked details (scant as they are) for the transformer it looks like a bottom end of the market example. There's no way such a transformer could operate out to 500kHz. With your test method you will be observing resonance associated with whatever stray inductance is seen looking into the winding under test. I don't think your approach is sound. Pardon the pun.

As a matter of interest what is the op-amp you are using to buffer the function generator drive to the rest of the circuit? Is it in a unity gain configuration?

Last edited: Nov 11, 2013
11. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
581
38
Yes, unit gain buffer.

To be concise, my main goal for this measurement was to be able to have a rough idea of the inductance values (primary and secondary) so that I could load them into LTSpice for simulation. I know the turns ratio but not the "inductances" which is what LTSpice requires.

I don't really know the difference between magnetizing and leakage inductance tbh.

12. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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Have you studied transformers in your coursework?

I'd guess LTSpice probably requires the magnetizing inductance although some transformer models certainly allow for leakage inductance as well. I don't use LTSpice so I can't comment further.

I'm surprised you went to such lengths to try to determine the inductance. If you only require the magnetizing inductance you simply open the secondary winding (i.e. no load condition) and excite the transformer primary with a sinusoidal voltage at a typical audio frequency within the likely transformer bandwidth - say 10V @ 500Hz. You need to measure the primary current so a DMM (if you have one) on low AC current range would probably suffice for that purpose. Strictly speaking one would measure the magnitude and phase of both the applied primary voltage and the resulting primary current. You know the DC resistance of the winding so with a little math you could deduce the primary magnetizing inductance from the suggested measurements.

If the transformer is of low quality the primary magnetizing current may have some distortion which may lead to some discrepancy with physical reality and presumed equivalent model.

13. ### Alec_t AAC Fanatic!

Sep 17, 2013
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LTspice models a transformer as two inductors with a coupling factor k <=1. The inductance ratio is the square of the turns ratio.

14. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
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Yes, but you actually have to state the inductance values of both windings.

15. ### Alec_t AAC Fanatic!

Sep 17, 2013
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....which means you specify two inductance values with a ratio which is the square of the turns ratio of the tranny you want to model.

16. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
581
38
I did try this initially but the distortion was rather high.

17. ### blah2222 Thread Starter Distinguished Member

May 3, 2010
581
38
Yeah, but how do you come up with those inductance values? Pick them out of the air? The functionality changes quite a bit with different values, even if the ratio is kept constant.

18. ### t_n_k AAC Fanatic!

Mar 6, 2009
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As my earlier post would presumably imply, this should come as no surprise. Welcome to the real world of non-ideal electronic components.

19. ### Alec_t AAC Fanatic!

Sep 17, 2013
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Guestimation is one way. Transformer specs/datasheets may give values. For many simulations the actual values aren't too important: ball-park figures may be sufficient.

20. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Besides what I have outlined earlier, another approach would be to apply a low frequency [say 200Hz] square wave to the transformer winding(s) of interest in series with a known resistance of say 100Ω. Forget about trying to obtain resonance with a parallel capacitor. One end of the resistor should be connected to the ground side of the source - as shown in the attachment. Using an oscilloscope measure the circuit time constant. Taking into account the known (as measured) winding resistance and the additional series 100Ω resistance calculate the effective winding inductance giving rise to the measured time constant.

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