Step input to loaded transformer

[Ambforc]

I am trying to calculate the response of a loaded ideal transformer to a step input. For example a step input in voltage from zero on the primary coil with a resistor connected across the secondary coil.

I already understand that with the second coil disconnected (for all practical purposes not existing) and the resistor connected in series with the voltage source over the primary coil a first order response in primary coil current will be observed. Now I am trying to simulate the response when the resistor is placed over the secondary coil. Of course, with no resistor over either the primary coil and the second disconnected you get an unbounded response in current (pure integrator).

The ideal assumption includes no resistance losses in any part except the load on the secondary coil and the ability to pass infinite magnetic flux.

This is as far as I have come:

Assuming the inductance of both coils to be equal with perfect coupling:

$V_{1} = L \left(\frac{di_{1}}{dt} - \frac{di_{2}}{dt} \right)$
$V_{2} = L \left(\frac{di_{2}}{dt} - \frac{di_{1}}{dt} \right)$
$V_{2} = i_{2}R_{2}$

However this set of equations reduce to:

$V_{1} = -i_{2}R_{2}$

and therefore fails to say anything about the transient response of the current in the primary coil $i_{1}$ and appears to reduce to a normal DC circuit.

Any help will be appreciated.

 

[anorlunda]

Your problem statement is unclear. If you want answers for an integer number of whole cycles, use the transformer equivalent circuit.

If you want instantaneous DC values, then you must solve Maxwells Equations. Circuit analysis is inadequate for that case.