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A coil with a capacitive load (oscilloscope probe or a FPGA input) is a resonant circuit, connecting a different load changes the resonance frequency. It's basically possible to design a wideband inductive coupling, but most likely an amplifier with suitable frequency characteristic is required.
You didn't tell about the waveform that's intended with your application.
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A great answer, and a confirmed one. I checked in the lab and what you said is absolutely true.
As a start I want to send a digital clock signal.
Now I have a problem. I am not sure how much capacitance the FPGA has, but if I only connect a coil of 100microH, I have Wo (the resonant frequency) at around 1.6MHz (which gives the maximum voltage to the FPGA input). I want to increase Wo alot, to a magnitude of 100s of MHz.
I know I have two options to play with on the secondary circuit side: Either to make my L (coil inductance) lower, or make my C (capacitance) lower. At this point I have these questions:
1. What is the capacitance at the input of the FPGA (Stratix II GX)? I can connect a capacitor in series to make the capacitance much lower in this case.
2. If I made my L lower, the communication distance between primary and secondary circuits should be reduced as a result. And since I already have the coils almost touching each other, I do not think this is an option. What do you recommend?
3. Is there another better way to operate the circuit on a much higher frequency?