110402-1411 EDT
matts0:
Steady state there is no DC component in the input current to the primary of a transformer, loaded or unloaded. Even if you put a half-wave rectifier on the secondary with a load, which produces a DC current in the secondary, there will be no primary DC component on a steady state basis. You have an instrumentation error, your zero balance of the scope amplifier and/or transducer, if you see a DC component and you are truly at a steady state condition, and the source is not producing a DC component.
If your source is an isolation transformer and your transformer under test was the only load, then the primary side of the test transformer would have no DC component. Put a pure resistance in series with the primary of your transformer under test. For 120 V nominal source voltage use 1 ohm if currents are in the range of possibly 1 A. Connect a DC voltmeter across the current sensing resistor. if there is a DC current, then you will read a voltage. 1 A at 1 V is 1 W so use a 5 W resistor. You should see a blip on the meter when you first apply power to the transformer. This will be different from one time to the next. And zero after steady state is reached in a few seconds.
Using my 175 VA transformer, 1 ohm, and a Fluke 27 I saw above and below 0.1 V for the peak and decay to 0 within a couple seconds. With my Simpson 270 on the 2.5 range sometimes about 0.3 V. Note can go either + or -. Note that both the Fluke and Simpson perform integration on short pulses like these. Thus, the reading is not a direct measure of the peak that occurs.
You spoke of a 15 MA offset, but did not mention full scale or the peak magnetizing current.
I have no idea of what a PS110 trainer is, or what is the rating of the transformer with which you are experimenting. This is information you should provide.
You will note in my scope photos I referred you to, that the transformer was rated at 175 VA. So under full load with a pure resistance load the input RMS current would be slightly higher than 1.46 A, or a peak of 1.46/0.707 = 2.06 A. Also note that I indicated the peak steady state magnetizing current was about 250 MA, but the scope trace puts it a little less than 200 MA. If you scaled these values to some other size transformer the results would be quite similar. Most transformers are designed with the same kind of steel for the core and criteria for the normal flux density. New higher efficiency transformers might be somewhat different, and toroid transformers will likely have a more square loop core material.
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