Using a single coil, the microcontroller program is pretty complicated. It needs to pulse the coil very briefly on a regular basis and measure the resonant fre

Using a single coil, the microcontroller program is pretty complicated. It needs to pulse the coil very briefly on a regular basis and measure the resonant frequency. If you do the capacitor-less design, you might want to have a steel core with sawtooth top, and then use software to measure the position of the ball relative to each tooth and turn the coil on while the ball is heading towards a tooth and off when the ball is heading away. That allows the energy to be extracted from the battery slower. You might also choose to have your coil driven by an h-bridge. That means you can put the energy from the magnetic field that builds up in the steel core back into the battery between each 'tooth'. That should dramatically increase energy efficiency, allowing you to use a smaller (cheaper, lighter, more eco friendly) cell or have the battery last longer. To do that, you'll need current sensing too.