Wireless Power Transfer for a toothbrush
My initial question was how the RFCs affect the circuit and why. Thanks to Russel McMahon did i gain a better understanding and realising it was in fact a Royer oscillator led med to the paper linked above that has a similar circuit:



The paper also presents a mathematical model of how the RFCs affect the frequency:



In this case, the term under the root will quickly approach 1 as the value of the RFC increases. This is something that can be clearly seen in my simulations and measurements.
By changing to a centre-tapped coil the idle current fell by a factor 3 and I could eliminate one RFC.

The circuit is not ideal. The frequency will change when the circuit is loaded, but the receiver coil is not tuned and all it has to do is to charge an AA NiMH cell in a resonable time. The prototype will have a small timer that starts when the brush is inserted and run for 2-3 hours which is the time it takes to recharge after use.

Thanks again Russel!

Edit:
Some additional insight can be had from the Wikipedia article:


  A drawback of the voltage mode operation is that the stress on switch
  transistors is high during the cross over time, when both the voltage
  and current are high. This drawback is alleviated by using current
  mode operation. This is achieved by inserting an inductor in the
  transformer center tap supply. This inductor drops the center tap
  voltage down when the dI/dt would be very high in voltage mode.


And strictly speaking, if I do not drive the inductor to saturation then it is probably a Baxandall oscillator :)