# Where should I look for transformer inductance discrepancy?

I'm experimenting with this smallish (~15VA) toroidal line transformer as a "lab" exercise as I'm learning about transformers. Right now it has its original 115V primary winding only; I "unwound" and removed the secondaries it came with and will be adding new ones of various descriptions for experimental purposes.

The primary is about 1500 turns, with a winding resistance of 28 $\Omega$.

The problem I'm having is I'm getting widely different values for the primary inductance, depending on how I measure it. I have a few hypotheses why, but wondering which might be most likely.

• When I measure the primary with my Agilent U1733C LCR meter, I get a reading of 22.7 H @ 100 Hz. There's no 60 Hz option for whatever reason, so I picked the lowest available frequency. On the 120 Hz setting, it reads 20.4 H, so I'm figuring the 60 Hz value is somewhat higher than 22.7 H rather than lower.

On the 100 Hz setting, it reads 7.7 nF for capacitance.

• My second test is for identifying the core characteristics, specifically the saturation curve, but it also indicates inductance. Basically I apply a voltage (4 VDC in this case) and then observe the current curve with the scope over a 1 $\Omega$ resistor. The slope of the linear portion in the first few microseconds after voltage is applied indicate the inductance. By this measurement method I get about 8.8 H.

• The third test I performed was to measure the magnetizing current. Using my DVM, I get 3.1 mA AC RMS through the primary when plugged in to 120 VAC. (today the line is running about 124 VAC).

That gives an impedance of about 40 $k\Omega$ which would correspond to an inductance of 106 H.

So I'm wondering why there would be so wide a variation in the inductance measurement.

I know the LCR meter is measuring at too high a frequency, but it seems like worst case the actual would be no more than, say, 30 $H$.

On the DC voltage test, I suspect there are some core magnetization hysterisis effects going on because I get a very different (way longer) curve when I reverse the polarity, but only the first time at the new polarity.

The magnetizing current test seems like it should be pretty darn accurate though.

Anyway, I'm pretty stumped here about how to explain this and perhaps modify one or more of my test procedures.

Does anyone have any ideas about how this might be explained?

The proper test is applying the 120V AC and if this implies an inductance of 106 H then that is what I'd assume. So why does the meter indicate a lower inductance? One thing that might indicate a "problem" is the measurement of 7.7nF. If you take the inductance reading of 106 H and calculate the resonant frequency with 7.7 nF you get 176 Hz and this is much to close to make sense of any inductance measurements on your LCR bridge.

Another factor is that the eddy current induction into the laminations rise with some factor of frequency (I think it's like skin effect so it rises with $\sqrt{F}$ from memory). Eddy currents are like partially shorted turns and therefore have the effect of lowering the perceived magnetization inductance of the core.

• Thanks Andy, this gave me the confidence in the effective impedance-based value to look more closely at the other two. I'm thinking now the 7.7nF capacitance value read using the LCR meter is unreliable. I get a totally different reading today, -142nF (yes, negative), so I'm thinking measuring winding capacitance is not just as simple as hooking up the LCR meter. On the core magnetization test, I realized I was triggering the MOSFET gate with the same 4V test voltage, so I think I have a pretty high $R_{DS}$ there that would screw things up. I'll fix that up and try again :) Jan 16, 2016 at 7:48
• I think the ramp current test result is worth mentioning here when you determine it. The -142nF means 17.8 henries at 100 Hz in my book. An LCR bridge can get its knickers in a twist and reporting negative capacitance is something I have heard of before! Jan 16, 2016 at 20:22
• Will do Andy. I'm revamping the inductor test setup to drive the MOSFET with full (~10V) gate voltage pulses; will post results when I've got it finished :) Jan 26, 2016 at 21:36

The main problem is that a constant inductance is too simple a model for a toroidal transformer cored with transformer-iron.

The non-linearity of the permeability will make the inductance sensitive to drive level. There are other effects that will alter the terminal properties of the component, hysteresis, and eddy currents and core losses.

These effects will contribute differently depending on whether an LCR meter is looking at the low swing AC inductance, mains is exploring a near full swing AC inductance, or a linear ramp is running up one side of the hysteresis curve and ignoring the other side, until you reverse it and find it's different.

So the question is 'why do you want to know the inductance'. Presumably it's to predict the behaviour of the core under some particular conditions. If so, you either need to measure the effective inductance under precisely those conditions, or use a much more comprehensive model of the core to fully characterise it.

Well scanny your toroidal transformer primaries have high inductance due to no gap and lots of turns and high permeability steel .This means that your inductive curremt is low unless the test frequency was something silly like 5Hz .The iron losses are low too because those doughnuts are made of good steel .But your Q is actually rather low .I bet you it is less than 10 .At low Q not all inductance meters are equal .Prove this for yourself by measuring a 4ft 40W flouro lamp ballast on your different meters and you will get closer answers mainly because the lamp ballast has a gap .

• 40k reactance and 28 ohms dc resistance looks like a Q in excess of 1000 to me. Jan 15, 2016 at 14:01
• The iron losses can be treated as an effective resistance .This resistance is in parallel with the inductor .This is where the low Q comes from Jan 15, 2016 at 23:22