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The original post by electrofelon presents an interesting problem. I have not read all the posts. Some are of some value, and others illustrate a total lack of understanding of electrical theory.
electrofelon I suggest you probably don't want to use a base frequency transformer (meaning low frequency). I think you want to design some sort of electronic switching power suipply to provide maximum power transfer to the battery. Besoeker is probably the best person for such a duiiscussion.
Some broad background.
Definition of magnetizing current.
http://www.merriam-webster.com/dictionary/magnetizing current
http://encyclopedia2.thefreedictionary.com/magnetizing+current
The McGraw-Hill reference includes losses in the magnetizing current. I think they should be separate, but in the real world the easy measurement includes both losses and stored energy in the magnetic field.
Now to some basics.
Start with a copper coil with the core being air. At DC or very low frequencies the instantaneous current is basically i = v/R. As frequency is increased the current will drop for a constant voltage amplitude. Under transient or steady state conditions the current will never be greater than the DC value. i^2*R loss will never be greater than at DC excluding secondary effects.
Now add a ferromagnetic core to the coil. The above paragraph still applies. The feromagnetic core greatly increases the magnetic flux density for a given input current. In other words less current is required to produce a given flux density. Thus, the inductance of the coil is greater with the ferromagnetic core than with just an air core.
However, the ferromagnetic material does not have a linear characteristic as flux density changes. If you could fully saturate the ferromagnetic core then the coil would approach the characteristics of an air core coil.
If a transformer is made larger (more turns and more core) to prevent major saturation at some low frequency, then the transformer will have imparied performance at higher frequencies and power levels.
In a transformer designed for power transfer the core material, on a steady state basis, will be driven somewhat into core saturation. This causes a peaking in the excitation current at each voltage zero crossing.
Any inductor, real or ideal, under transient conditions will oppose any instantaneous change in the current thru the inductor. Thus, if an inductor has an initial condition of zero current in the inductor's coil and a battery is connected to the coil at t=0, then just after t=0 the current is still zero. If there is no magnetic core material, then the current will change and gradually become the the steady state current. There is no overshoot type of peaking.
If there is a ferromagnetic core, then the initial state of the flux in the core becomes important in combination with the turn on point in the applied AC voltage. If this turn on point causes the flux to further increase, then a large inrush currrent pulse will occur because this forces the core more into saturation. Major rebalancing of the flux occurs in 1/2 cycle, but many cycles are required to reach steady state conditions.
This large inrush current results from the coil looking more like an air core coil, than like a coil with an unsaturated ferromagnetic core.
Switching power supplies take input energy and put this into an inductor and in some fashion control that inductor to output the desired voltage, current, and waveform.
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