# 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?

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 :) – scanny Jan 16 '16 at 7:48