What is the mathematical relationship between primary and secondary windings?

It can be either in the s-domain, or a time domain expression.

This expression must contain all realistic parameters, like core losses, hysteresis losses, winding inductances, mutual inductance between windings, effect of frequency, etc.

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    \$\begingroup\$ Why do you want to do that? \$\endgroup\$ – Leon Heller Nov 14 '11 at 19:24
  • \$\begingroup\$ @LeonHeller I want to simulate a transformer. \$\endgroup\$ – hkBattousai Nov 14 '11 at 20:10
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    \$\begingroup\$ Use a SPICE simulation. \$\endgroup\$ – Leon Heller Nov 14 '11 at 20:14
  • \$\begingroup\$ @hkBattousai - Programming simulators is off-topic here. It sounds like you're more interested in the transfer function anyways, so I'll strip that part from your question. If you need to know how to program a simulator given operational parameters/a transfer function (and still don't want to use SPICE), then search for a duplicate and go to Stack Overflow. \$\endgroup\$ – Kevin Vermeer Nov 14 '11 at 22:11

I have never seen any formula as the non-linear behavior as a function of freq. depends on stray and winding capacitance, ferrite non-linear properties and many other factors.

For 60Hz here's a simple model http://claymore.engineer.gvsu.edu/~johnsodw/egr325mine/paper2/paper2.html

Which are very different to RF tansformers http://www.minicircuits.com/app/AN20-002.pdf

which are very different to pulse SMPS transformers !

which are very different to Flyback transformers ! http://www.wisegeek.com/what-is-a-flyback-transformer.htm


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