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Test your magnetics IQ

We haven't had any interesting electronics puzzles for a while, so here is one I haven't seen before.

If you *know* the answer as a result of wiring it up and making the measurements, please wait until Wednesday before posting the answers (any or all of them).

If you simulate it, go ahead and tell us what simulator you used, what magnetic model was used, and the results.

If you just think about it, tell us what you think, and why.

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I have a small filament-type transformer rated for 120 VAC @ 60Hz input, 28 volts @ 3 amps output (I measured the turns ratio as 4:1). This transformer has a laminated iron core. I have a 6 ohm resistive load and I have two thermocouple (correctly responding to AC+DC) ammeters to measure primary and secondary current.

I have a variac to reduce the applied primary voltage to no more than about 45 VAC for reasons that will become apparent.

Everybody has seen such a transformer used in a half-wave rectifier circuit by putting a diode in series with the output winding and the resistive load (I won't be using any reservoir capacitor in this puzzle).

Determine the dotted ends of each winding. For those who don't know what this means, let me explain. Apply 120 VAC to the primary of the unloaded transformer, and with an oscilloscope look at the input voltage on one trace (be safe) and the output voltage with another trace. One end of each winding will be connected to a ground clip of the scope probe, the other to the probe tip. If the waveforms appear out of phase on the scope, reverse the connections of the output winding and its probe (if they appear *in* phase, don't reverse the connections). Now the leads connected to the probe tips are the dotted ends of the windings, primary and secondary. In other words, when the voltage is positive going on the dotted end of the primary, it's also positive going on the dotted end of the secondary. Mark them.

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Case 1: Connect the primary to the variac (preset to zero output), but with a rectifier diode of at least 200 volt and 1 amp rating in series with the primary, and with the diode's arrow pointing toward the dotted end of the primary winding. Put a 6 ohm load on the secondary, and turn up the variac until you get half an amp in the primary (true RMS AC+DC).

What will be the voltage waveshape applied to the primary (after the diode)? What will be the primary current wave shape? What will be the secondary waveshapes? What will be the magnitude of the current (true RMS AC+DC) in the 6 ohm resistor?

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Case 2: Leave the variac setting as it was in Case 1. With the same diode left in the primary circuit, now put a diode (3 amp rating) in series with the secondary winding and its 6 ohm load with the arrow of the diode pointing *away* from the dotted end of the secondary. In this topology, it would seem that when the primary diode conducts, the secondary diode also conducts, and there would be a current in the secondary load resistor.

What will be the voltage waveshape applied to the primary (after the diode)? What will be the primary current wave shape? What will be the secondary waveshapes? What will be the magnitude of the current (true RMS AC+DC) in the 6 ohm resistor?

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Case 3; Leave the variac setting as it was in Case 1. With the same diode left in the primary circuit reverse the diode in the secondary ciruit so that the arrow is pointing *toward* the dotted end of the secondary winding. This is the interesting case.

What will be the voltage waveshape applied to the primary (after the diode)? What will be the primary current wave shape? What will be the secondary waveshapes? What will be the magnitude of the current (true RMS AC+DC) in the 6 ohm resistor, if there *is* a current?

Reply to
The Phantom
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I used the LTspice hysteretic core model based on a model first proposed in by John Chan et la. in IEEE Transactions On Computer- Aided Design, Vol. 10. No. 4, April 1991. This model defines the hysteresis loop with only three parameters:

name | parameter | units -----+-------------------------+---------------- Hc | Coercive force | Amp-turns/meter Br | Remnant Flux Density | Tesla Bs | Saturation Flux Density | Tesla

The upper and lower branches of the hysteresis major loop are given by H + Hc Bup(H) = Bs · --------------------- + µ0·H |H+Hc| + Hc·(Bs/Br-1) and H - Hc Bdn(H) = Bs · --------------------- + µ0·H |H-Hc| + Hc·(Bs/Br-1)

The initial magnetization curve is given by

Bmag(H) = .5 · (Bup(H) + Bdn(H))

Minor loops are obtained by various translations of the above equations per the cited reference. The core's absolute and differential permeabilities are a function of H and the history of values of H.

In addition to the core property parameters Hc, Br, and Bs, mechanical dimensions of the core are required:

name | parameter | units -----+----------------------------+----------- Lm | Magnetic Length(excl. gap) | meter Lg | Length of gap | meter A | cross sectional area | meter**2 N | number of turns | --

Note that if specifying a non-zero gap the magnetic field, H, is not proportional to the current in the windings. LTspice solves for the magnetic fields in the core and gap under the assumption of uniform cross sectional area and thin or uniformly distributed gap.

For the primary of the simulated transformer I used these parameters:

Hc=.2 Bs=1.8 Br=.4 Lm=50m Lg=50u A=.5m N=600 Rs=1.6 Rp=10k Cp=1n

The turns ratio was 4:1 with 100 percent coupling. Rs=.1 on the secondary side. Without loading the primary just starts going into hard saturation at about 144 Vac (at 60 Hz).

The primary winding voltage is a slightly distorted *sinewave* of 12 Vrms. The primary current exhibits a half wave saturation peak of about 1.8 amps with an rms value of 590 ma. The secondary voltage is also nearly a sinewave, but of about 1/4 the amplitude (2.9 Vrms) and the load current is about 480 ma rms.

The primary winding voltage is a less distorted sinewave of 12.7 Vrms. The primary current does *not* saturate and is only 21 ma rms. The secondary voltage is 3.1 Vrms and the resistor load current is half wave rectified to about 360 ma rms (230 ma average dc value).

Surprisingly, this seems to work in flyback mode with primary waveforms almost like Case 1 (560 ma rms) and secondary waveforms almost like Case 2 (330 ma rms and 220 ma average, but of opposite polarity, of course).

Great problem, Mr. T Phantom. :) -- analog

Reply to
analog

Sorry, I reported the primary *magnetizing* current. Primary total current is 621 ma rms 357 ma average.

Again, I reported only the primary magnetizing current. Primary total current is 99 ma rms 70 ma average. Notice how these currents now are at least 4x greater than those on the load side, properly reflecting the transformer turns ratio (saturation masks the other two cases).

That was magnetizing current. Primary total current actually is 566 ma rms 291 ma average.

Reply to
analog

"The Phantom"

** Trick question.

The magnetics of the transformer need to be known to predict the waveforms you ask for.

Stuff like I mag at various AC voltages, L leakage, the saturation characteristic of the core and the resistances of each winding. Is the tranny an E- core, C-core, R-core, toroidal or other ?

Are the primary and secondaries wound over each other or on separate halves of a bobbin ?

........ Phil

Reply to
Phil Allison

Indeed! Isn't it fun?

I'm not looking for a lot of precision here. If one assumes this is a typical filament transformer, the results would be pretty close. I'm more interested in explanation about what's happening in case 2 and 3 than exact numbers.

Like I said, standard Radio Shack filament-type transformer.

It's an E-core, EI-100HS laminations:

formatting link
The laminations are .0185" (26 gauge), with a .9 inch stack; this is about

1.46 pounds of iron. With 120 VAC applied to the primary and the secondary open (the current was .16 amps), the core loss as measured by my small wattmeter was about 2.9 watts; the current waveform was fairly peaky. The published curves from Tempel would indicate that this is M-19 material with a peak flux density of about 16000 Gauss with 120 VAC applied.

The two windings are concentrically wound. The primary DC resistance is 12.25 ohms; the secondary DCR is .9 ohms. With 15 VAC applied to the primary and the secondary open, the current was 5.65 mA, giving a primary inductance of 7 Henries. With the secondary shorted, the leakage inductance measured at the primary is 4.4 mH. The turns ratio is

4:1.

Reply to
The Phantom

Follow the directions-------------------------------^^^^^^^^^^^

You were supposed to adjust the primary voltage until you got .5 amps (true RMS AC+DC)

Reply to
The Phantom

"The Phantom" "Phil Allison"

** Wanker.

** No such thing as "typical".

** Funny how you ask for wave shape diagrams and current values then.

Consistency is not your forte - is it ?

** Blatant lies.

You never mentioned the word "standard" or Radio Shack.

28 volts is not a filament voltage and a 90 VA tranny is not small.

** Now you tell us.

Yawn......

............ Phil

Reply to
Phil Allison

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