Question

I'm looking for an expression to calculate the inductance of a transformer as a function practical parameters, like the diameter of the wire, the lenght, etc.

Answer 1

Can we assume ideal or are we accounting for leakage?

Answer 2

No, I'm dealing with real transformers

Answer 3

We can find the ideal magnetic flux density as \[B = {\mu_o I \over 4 \pi} \int\limits{dl \times \hat r \over r^2}\]and relate this to the EMF on either winding as \[E_{rms} = {2 \pi f N a B_{peak} \over \sqrt{2}}\]

It is hard to directly relate the actual EMF to the magnetic flux directly without knowing a little about the leakage.

I'm sure there are accurate models out there. Here is one paper on such a model: https://docs.google.com/viewer?a=v&q=cache:DIWhcDkjsaQJ:fmtt.com/Transformer%2520SPICE%2520Model%25202-14-08.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESil11QcIo8DDkzaqFjkibK1JNHJQV3gjO6uiOPLBf7eim_knb9SrNWYCeH-OTZZJkRJoqtMXWU3bipTpVbhbpLlpndb_gAuIwdaoUgwQ4dYy2ZIhWO5N5vjcejZrxVxQ9cbpF1o&sig=AHIEtbSehu98WV8p3eF6UyUcKzH_ZCxeUQ