# Two-core transformer with three windings?

I am trying to understand how a transformer composed as pictured would function. Basically, two separate cores. Both cores go through the secondary winding. But only one of the cores goes through the primary, and the last winding (lets call it the "control" winding..you know where I am going with this..) goes around the last core.

So yes, ultimately I am wondering if you could manipulate the amount of net flux the secondary winding experiences by driving the control winding with the right phase and magnitude to achieve your goals. Goals being a reduced voltage at the secondary compared to what it would be with the control winding open.

The key benefit here is that the net flux that the secondary experiences is reduced, without reducing the flux the primary generates, and therefore, without reducing the inductance of the primary, which would allow more primary current to flow, and is what would happen if you tried this with a single-core transformer.

I have seen this sort of thing called a "three port magnetic component" with a brief discussion here: https://www.researchgate.net/post/Can_anyone_advise_me_on_how_to_build_a_multicore_transformer

LTSPICE will reject modelling of this component if the coupling constants between the inductors is not physically realizable Unfortunately I do not know what that means beyond a very general idea that some coupling will always occur. I would like to know where I can learn exactly how to calculate the "inductance matrix" and solve this myself, and why it is so at an intuitive level.

So I'm looking for an intuitive and algebraic way to understand why the reality deviates from the ideal here.

It seems to me "magnetic amplifiers/saturable reactors" are not this thing.

• found some info on spice and inductance matrix here: sourceforge.net/p/ngspice/bugs/335/#de1c/e2e3 which mentions "Criteria and tests for realizability of the inductance matrix," Yilmaz Tokad; Myril B. Reed, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, Year: 1960, Volume: 78, Issue: 6, Pages: 924 - 926, DOI: 10.1109/TCE.1960.6368492 Commented Feb 21, 2020 at 1:17
• I think the math here may be more complex than I am looking for. So I think what I need here is an intuitive explanation...if there is one. Commented Feb 21, 2020 at 1:19
• I'm thinking I might need to re-do this question so it focuses more on why there are only certain physical possibilities when it comes to how this sort of device can be wound..i.e. "the inductance matrix having a positive determinant" and it not being possible apparently to have a PRI/SEC = 1 and SEC/CTRL = 1 and a PRI/CTRL = .0000001 coupling constant device. (or even something close to that) Commented Feb 21, 2020 at 16:13
• As a side question, if this device is realizable, how come it is apparently not what a "magnetic amplifier" is usually described as? Is this sort of thing actually used anywhere? Commented Feb 21, 2020 at 16:14
• not a mag amp because the control winding can't saturate the other core Commented Feb 21, 2020 at 19:03

Consider a three phase transformer as below (just to satisfy the fact that opposing fluxes don't cause a meltdown): -

Picture from here.

This sets the scene: the centre core has the flux cancelling out and this is how a lot of 3 phase transformers work (secondaries not shown). So, throw away one of the windings and rewire it on the common central leg of the core and you have what you want. The net flux in the central core produces the induced emf in the new central winding.

• Common leg having zero flux, that is true only with symmetrical currents.
– Uwe
Commented Feb 21, 2020 at 11:40
• Hi Andy, I will have to first understand the three phase transformer operation before I can make that mental leap to see what you laid out for me. In the actual three phase transformer, do the fluxes really interact that much just with the cores touching in the middle? I have got to think the influence is minimal since there is the giant air gap along where they meet. But this is far afield from the topic. Sorry if I cant grasp your analogy, I am just not there yet. Commented Feb 21, 2020 at 16:08
• The central core is common and the fluxes cancel but, it’s more clear cut in your example, the fluxes cancel into the secondary but don’t mix. I’m also interested in why you couldn’t get this system to simulate. Commented Feb 21, 2020 at 18:29
• Used? 3 phase transformers make use of it but, unless there is an application, then I’m out of ideas if it’s used elsewhere. Call it a differential magnetic amplifier and see if something comes up on google. Commented Feb 21, 2020 at 22:33
• Maybe a better name is a differential flux transformer? Commented Feb 22, 2020 at 10:29

Many old literature can be found. This is a magnetic amplifier, those days, the power amplifiers were made similarly as that. Book

EDIT:

If the magnetic cores are isolated and there is no common magnetic path, then the result is much simpler:

$$u_i\propto\dfrac{d\Phi}{dt}$$ $$u_{sec}\propto\dfrac{d\Phi_{prim}}{dt}+\dfrac{d\Phi_{ctrl}}{dt}$$

Both fluxes (primary and control) are due to the magnetising currents in primary and control winding. The secondary winding "see" their sum, so the secondary voltage is the sum of both primary voltages. Same as you would have two separate transformers with secondaries wired in series.

• Thanks but your diagram shows a device with a single core/magnetic circuit, and the parameter it varies to accomplish amplification is saturation of the core. The device I am asking about would have two magnetic circuits/cores. It would not operate in the saturation region of the core and would instead rely on manipulating net flux through the secondary to accomplish amplification. Commented Feb 21, 2020 at 16:03
• You have a contradiction in you desription: "inductance and so it would not draw more current as the control winding generates an opposite phase flux that cancels the primary inductance. ", and now "The device I am asking about would have two magnetic circuits/cores". So how can a control voltage influence the primary flux if the magnetic paths are isolated? You should edit the question and describe those tinny important details. Commented Feb 21, 2020 at 18:36
• Thank you I have edited the question to correct the contradiction. To be clear I poorly stated that aspect but my intent has not changed. I should not said the control winding cancels the primary inductance. I meant to say it alters the net flux the secondary sees, without changing the primary inductance. Commented Feb 21, 2020 at 21:34