Electronic – Even vs Uneven Magnetic Field Cancellation in Toroidal Transformers

What you may be getting confused about is the "ideal transformer" in the equivalent circuit. You should not regard it as having any magnetic qualities at all. Try and see it like this: -

Whatever voltage you have on the input to the ideal transformer, \$V_P\$ is converted to \$V_S\$ on the output of this "theoretical" and perfect device. It converts power in to power out without loss or degradation such that: -

\$V_P\cdot I_P = V_S\cdot I_S\$

The ratio of \$V_P\$ to \$V_S\$ happens to be also called the turns ratio and almost quite literally it is on an unloaded transformer because there will be no volt-drop across R3 and L3 and only the tiniest of volt-drops on R1 and L1.

This means you now have a relatively easy way of constructing scenarios of load effects and recognizing the volt drops across the leakage components that are present.

The equivalent circuit of the transformer is really quite good once you accept that the ideal power converter is "untouchable" and should just be regarded as a black box. For instance you can measure both R1 and R3 and, by shorting the secondary you can get a pretty good idea what L3 and L1 are. With open circuit secondary you can measure the current into the primary and get a pretty good idea what \$L_M\$ is too.

Consider this circuit of a smps circuit:

You can clearly see three windings. Right one is secondary which is producing the output. Top left is primary and bottom left is auxiliary.

Auxiliary is nothing but an additional secondary. Usually in a switching circuit, we need some low voltage power source for the working circuit. You can't power them using 220V or 110V line directly. So you are left with two options -

1) Somehow use the low voltage output which is being generated which will be a very bad idea because the sole purpose of using such a schematic is to provide galvanic isolation to the secondary side and by connecting output side to switching IC, you have defeated the purpose.

2) Make a separate low power winding just to provide enough power for the chip to run which is what we do by making an auxiliary winding. When you cut open a transformer, you will find that secondary winding will be usually made using thicker wire because it has to handle a larger current whereas auxiliary will be made using thin wire because it has to carry just small amount of current to keep the chip functioning.

Both secondary and auxiliary windings get their energy from primary winding. You can add more windings to the transformer and call them aux2, aux3, sec2, sec3 etc in case you need such an arrangement.