i have to design a two winding coupled circuit for contact less power transfer and its control scheme. i need the derivation of above problem.
On the practical side, two windings will couple less hard if there is simply air in the centre. You can send a high frequency current into the lower one, and measure an RF current in the upper one.
If you need to transfer considerable amounts of energy, you need to place ferrite material in the centre. For example a cup shaped ferrite will assure a hard coupling. Even with a few millimeter gap between the upper and lower parts.
The third thing to do is to initiate a resonance in both windings, by adding a suitable capacitor. The optimal resonance frequency will depend on the ferrite material and the size of the loops.
Make sure that your primary and secondary side resonance frequencies are matched, and that the current or voltage you are putting into that primary side is at that resonance frequency. Like Henrik said, you can change resonance frequency by adding a capacitor. You want to add the capacitor in parallel to your primary coil and in series to your secondary coil for best results. A resonance frequency in the MHz range or higher is necessary and will give you decent power transfer even across a significant air gap. The rule of thumb is that your maximum air gap is equal to the radius of the coils you are using. You will definitely still get attenuation though.
As for the control scheme, the easiest way to do it is to just add a zener diode after your rectifier and filtering capacitor on the secondary side, to ensure that the voltage doesn't get too high and break whatever circuit you are powering. I can't really speak to more complicated control circuits, but there is plenty published on this for you to browse through. Good luck!
Have a look at the Qi standard documents - including datasheets, application notes etc.
https://en.wikipedia.org/wiki/Qi_(standard) may be a good point to start.
Qi is current technology, having covered and documented a lot of the "ground work" to implement wireless power transfer.
Regards
The approach will depend on the power requirements:
1) How much power do you want to transfer?
2) What is the separation distance, d, between the TX and RX coils?
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