# What if secondary winding is magnetically insulated from primarty core in 1:1 transformer?

We know that secondary winding receives it's voltage kick due to the fact that changing magnetic flux creates a rotational electric field that does not care about the ferromagnetic core.

This creates current in the secondary coil which creates a rotational magnetic field which further energizes the primary core.

This creates more current in the primary coil and the cycle is excited till it is stabilized by power requirement of secondary circut, power supply of primary circut or the core is saturated.

What happens when the secondary coil cannot pass back its field to the primary?

My assumption is that the secondary coil is only able to produce a stable current up to the (more or less) the same as the one in primary, forming a current stabilized power source. Please comment on that.

I also curious what happens if it has triple the amount of windings as the primary. I assume that the convervation of energy still functions but I would like to confirm that it will be one third of the current in the primary. Please comment on that too.

PS. Of course in perfect transformer.

• I don't understand. If the magnetic flux of the secondary does not thread the primary, how does the magnetic flux of the primary thread the secondary? May 20, 2020 at 20:56

What happens when the secondary coil cannot pass back its field to the primary?

This is not possible. The flux that links the primary to the secondary is exactly the same as the flux that links the secondary to the primary. That is why it is called mutual inductance. It is a mutual relationship.

The mutual inductance of a pair of coils is given by $$M=k\sqrt{L_1 L_2}$$ where $$L_i$$ is the self inductance of each individual coil and $$k$$ is a coupling constant which is close to 1 for a good transformer. The voltage in one coil is given by $$v_1=L_1 \frac{d}{dt}i_1 - M \frac{d}{dt}i_2$$ and the voltage in the other is $$v_2=L_2 \frac{d}{dt}i_2 - M \frac{d}{dt}i_1$$ so the mutual inductance is the same either way. See http://web.mit.edu/viz/EM/visualizations/notes/modules/guide11.pdf equation 11.1.8 and the associated derivation for a detailed explanation about why the mutual inductance is the same.

For an ideal 1:1 transformer $$L_1=L_2=M$$. For a basic circuit with a primary loop and a simple resistive load on the secondary loop and with a source voltage $$v_1(t)= v_1 \cos(\omega t)$$ we get that the secondary voltage is $$v_2=\frac{M}{L_1}v_1$$. Combining the above gives $$v_2=v_1$$ for a 1:1 transformer.

Please comment on that. I also curious what happens if it has triple the amount of windings as the primary.

If the secondary has triple the turns of the primary then it will no longer be a 1:1 transformer. You will have $$L_2=3 L_1$$. It will now be a step-up transformer. The voltage in the secondary will be 3x as large and the current will be 1/3x as large as the primary.

• But it is not the magnetic flux that creates current but the electric field around it it does not matter what kind of ferromagnetic you will put outside of it. And no, it is not only the usage of the energy that in the electric part of the field that acts in this process. The current produced also create a magnetic flux which normally contributes to the field in core and strengthens the reaction. May 21, 2020 at 12:43
• The ferromagnetic material is not relevant to my response. Regardless of the presence or absence of any ferromagnetic material and regardless of the coil geometry $M_{12}=M_{21}=M$ always. See web.mit.edu/viz/EM/visualizations/notes/modules/guide11.pdf equation 11.1.8. It is simply not physically possible that "the secondary coil cannot pass back its field to the primary" if the primary can "pass its field" to the secondary. It always goes both ways.
– Dale
May 21, 2020 at 14:58
• The purpose of the ferromagnetic material is only to make k close to 1.
– Dale
May 21, 2020 at 19:57
• @doker, note that the symmetry of the coupled inductor matrix is due the reciprocity theorem which is, well, a theorem. What you seem to be proposing would run afoul of this. Even without the theorem, I think it's pretty straightforward to see that what you propose would violate the conservation of energy principle. May 22, 2020 at 18:17
• Hi @AlfredCentauri I've run the test and long story short, the result is that the secondary winding is not delayed in phase in accordance to voltage (when unloaded and loaded) to the primary coil. How I did it: I have a core, and primary winding (100x), a first secondary winding (100x) on other part of the core and a third secondary winding on another part of the core. This one is wound on a piece of paper on which there are sections of steal rods (fi 2mm) parallel to the core, arround it, and then a insulated coil wrapped arround it all as usuall. The voldatege is almost in sync. May 31, 2020 at 22:39

So I did the test and:

the outcome is that the voltage (even when loaded) on the secondary coil is almost not delayed in regards to the primary coil. I hope that helps someone. So if you put the transformer in to resonance then both coils will work in resonance with only slight delay (a couple of degrees).

Just remember to put rods of ferromagnetic material parallel to the main core in a way that they do not form a closed perpendicular circuit because you do not want to have eddy current in the outer core.

• @Dale would you like to reproduce? May 31, 2020 at 22:56
• @Alfred Centauri would you like to reproduce? May 31, 2020 at 22:56
• I'll be content to read your patent. May 31, 2020 at 22:59
• @AlfredCentauri I can't find any good use for this so no chances for patent. Jun 1, 2020 at 17:30