This depends on how you define "linear". The cores of the two transformers don't start to saturate at low currents.
As you increase the control current the saturation starts to happen near the end of each alternation. The transformer in which the AC and the control adds, saturates first. An AC current flows in the control winding coupling the low impedance of the saturated one over onto the unsaturated one. This is why I suggested a capacitor across the windings.
As you increase the control current, the saturation point moves towards the peak of th ewave form. This means that the control gain is still increasing in the early part of the range.
Once you pass the peak, the gain of the control signal starts to decrease. When you get to the point where the core is saturated with no AC, the circuit is nearly fully one and the gain is very low. As you go above this point, you start to saturate the core that the AC is bucking in. This takes the leakage inductance out of the picture.
The transformers will have the I^2 * R losses due to the current. For this reason, I don't think you could go with a much smaller transformer.
Both transformers can be in the same leg. This would mean you only need to break into one wire.
Yes I agree.
It would be only several times the no load current of the xformer. The core is sized so that it doesn't saturate in the no load case. The current for the full load case doesn't represent an increase in the field in the core.
When they are not saturated, and if they came from a good maker, the match should be more than good enough to keep this current quite small. When you start to saturate, you want a capacitor between the windings to pass the AC that develops because one core saturates when the other doesn't.
It appears to me that the DC bias current can only saturate the core for one half of the input cycle; the half where the magnetic fields add rather than subtract, and that the original series configuration had the fields add for both halves of the power cycle in one transformer or the other, for symnetrical operation. The parallel circuit would appear to deliver a bunch of DC to the load when saturated. Good test of a Spice transformer model perhaps :-).
Oh all ye of little faith. Didn't I point out that the center opening in my 1kVA toroid transformer, the one with 450 primary turns at 230vac, is 1.5 inches? And yes, the multi-kilo-amp stuff is water cooled.
Interesting. I'd have thought the opposite--for normal transformer use, the core needs to avoid saturating on the current peaks, so to fully saturate the core, the dc secondary current will need to be more than the peak value in normal AC use, plus whatever safety factor was designed into the transformer.
And Glen's point about the DC is important--Win's parallel arrangement can be made to conduct heavily on both half cycles, but the series arrangement can't. It's just like a full wave centre tapped rectifier.
I breadboarded it and the control current turns out to be far higher than I expected...... 60x the secondary magnetising current peak at normal sec voltage. Idcmax is practically equal to the normal sec full load AC current.
However there is actually a good case for designing for a controlled Vout that only goes up to about 90% of Vin..... that last 10% requires almost double the control power. See below.
It needed 7.2W of control power for 80VA out (218Vrms into a 590 ohm load, but only 3.2W for 70VA out (203Vrms).
2x 50VA transformers, wired for 120V primaries and 18V secondaries. Total secondary resistance is 0.8R and the max rated secondary current is 2.77Arms.
230Vrms supply and a 590R load.
I ignored Ken's nagging and just put the 5R in first of all, to see what the circulating current was....... it's large and there is a reason for that. So Ken's cap is a neccessity. By using a huge capacitor the AC peak-peak voltage is always lower than Idc*0.8R, so a polarised electrolytic can be used safely.
Those figures in brackets. Up in the 1.8 to 2A dc control region there seems to be a control hysteresis. If you casually fiddle the DC supply up and down to get it spot on then the AC results can be all over the place. The figures not in brackets were taken by creeping the supply upwards only.
You can see from the table that with a 230V supply then the Load should be rated for about 200V max. The control power increases unreasonably above that figure.
Note that the sec windings are rated for 2.77Arms maximum and at 2.8Adc they are carrying the dc, plus whatever the circulating current is that point.
Note for Win..... I put a large low pass filter across Vout and confirmed that there is Zero net DC voltage there. This allowed a signal transformer across Vout to allow for a scope to look at the output waveform.
And why is there a large circulating current between the two secs, that requires Ken's cap?
It's obvious when you look at the scope and see that the circulating current is mainly peaks and at 100Hz.
The DC signal drives the two cores in opposite directions, so one core handles +AC peaks and the other -AC peaks. So the AC voltages across each are mirror images, and that's where the circulating current comes from when the secs are connected together.
I admit that it is going on 40 years since I did this same sort of experiment myself but it looks like the laws of physics haven't changed too much in that time. It may be worth measuring the primary side resistance so you can back that out of your figures and see how much the controlled impedance is changing.
Also:
0.4R * 2 * (120/18)^2 = 35.5555 Ohms
When only one transformer is saturated, this will appear in the primary side circuit.
230 * 590 /(590 + 36) = 217V
This combined with the primary resistance may explain some of the knees in the curve.
When one core saturates, the other doesn't. One transformer still functions as a transformer. Its secondary current is shorted out by the one that is saturated. This is a disadvantage to this method vs a real mag-amp.
I assume you are in a 50Hz mains place. Here in the US, there would be a lot of 120Hz on the secondaries. The difference int eh secondaries only appears in that part of the cycle where the core is saturated. This is late in the alternation.
From what you say there it would be better to run the two primaries in parallel so that the non-saturating primary can directly pick up the voltage change that is happening on the saturating primary. So I tried it, as below.
Primaries were relinked for 240Vrms (45 Ohms each) and wired in parallel.
With the promaries in series any inexactness in the matching of the transformers has far less impact on the results. The two primaries can settle on two different voltages as determined by there turns ratios.
I mismatch in the open load inductance will cause an AC current in the secondary that will force this into balance.
If somehow there is a difference in phase angle, this should also drop out because the primaries can have slight differences in their phase as well.
I had not though a great deal about nor actually tried the parallel case because of the above thoughts. I now go on with interest to see what happened.
One very nice thing about the circuit is that you can get the transformers from sites like Digikey or from the electronice surplus shop. I suspect that for a given power, this will be a lower cost system than one that uses a purpose made part. Normal transformers are made in huge quantities.
Another nice thing is the fact that you are abusing a part in a clever way. It adds to the mystery and magic of your designs. You always want another engineer to feel "I would have never thought of that" when he gets a look at your design.
Great job in finding a viable solution to replace the hard to find 3 winding sat. reactor. Looking at your schematic of the primaries in parallel and trying to reduce DC control power loss, is there any reason for not using lower secondary voltage transformers with their lower DC resistance? Also dose the 11R serve any purpose other than match to 28VDC? Looks like removing the 11R and using a 0 to 2.0V DC supply would save power and maybe reduce the 10mF cap. Thanks, Harry
Playing with the breadboard has given an opinion which may be interesting Ken.
If the primaries are wired in series, then it is highly desirable to allow an AC circulating current to flow in the series'd control winding. Indeed, that balancing AC current is a neccessity. It does mean though that the control winding has to be able to carry both the DC control and AC circulating currents.
There has to be a large capacitor across the control winding, which the DC control circuit must be able to drive.
However, if the primaries are in parallel then it is not really desirable to have an AC circulating current flowing in the series'd control winding. Any AC circulating current is due to transformer mismatch, does not aid in the saturable reactor operation, and causes a small (and unneccessary) power loss in the transformers.
If possible the DC control driver should have a high output impedance and able to run with the peak-peak ripple voltage due to transformer mismatch. A capacitor may be used to reduce the ripple voltage but only as large as neccessary.
Having played with it I prefer the paralleled primaries, (mainly because I can better imagine what is happening), but also because of a dislike of additional circulating currents flowing in the control windings.
I haven't thought about optimising the control power Harry but get the feeling that Ampere-Turns is Ampere- Turns.... reduce the Turns and the Amps have to go up.
See the other post replying to Ken. The paralleled primaries probably requires a high impedance drive.
However, with the series'd primaries you could possibly make that required 10000uF the output capacitor of a low voltage variable DC supply.
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