What has me confused is the requirement that L1 and L2 and the mutual
inductance should approach infinity.
I don't think we can expect people to understand component-value properties without first stating what the top-level ideal requirements are. For instance, when you list this: -
The coils have very large reactances (L1, L2, M -> ∞)
These are implications from the following top-level requirements: -
- An un-loaded transformer doesn't draw current from a voltage source.
- A 1:1 transformer (for example) with 1 volt on the primary produces exactly 1 volt on the unloaded secondary.
If we have a top-level requirement, do the statements in your question seem unreasonable?
The next one is this: -
The Coupling coefficient is equal to unity (k=1)
This is redundant and covered in the first point where M approaches infinity.
The third is this: -
The Primary and Secondary coils are lossless (R1 = R2 = 0)
This isn't difficult to understand from the point of view that an ideal transformer must transfer power 100% efficiently. It also modifies the 2nd bullet point I made above like this: -
- A 1:1 transformer (for example) with 1 volt on the primary produces exactly 1 volt on the loaded or unloaded secondary.
So, do you see that the "ideal properties" listed in your question are either redundant or, are implications that satisfy the top-level requirements?
If the inductances are infinite, doesn't that mean the impedance is
infinite and the transformer could never conduct current?
You recognize that an infinite inductance draws zero current from a finite voltage source however, that doesn't mean it produces zero magnetic flux; flux is proportional to amps multiplied by turns and, if you have infinite inductance, there will be infinite turns and, a finite flux.
Because there is both flux and a coupling between primary and secondary, there has to be a secondary induced voltage that can source current into a load.
Then, if the secondary produces a voltage that can source a load current, by implication of the power coupling efficiency being 100%, the same power must be drawn into the primary winding.
I'll also add a note about the "infinite inductance" statement. I think it's confusing to talk about "infinite inductance". Wouldn't it be better to say that the primary inductance is large enough so that the unloaded transformer takes negligible current from a voltage source.
However, saying it has "infinite inductance" is a more efficient use of words.