I posted a message on qrp-l just recently regarding selecting the right operating frequency for colpitts oscillators. In the schematic you'll notice the connection between a pair of series capacitors. I had wondered if possibly this was behaving as a voltage divider. One member of the list, Nick Kennedy, had an interesting explanation for how it works. With his permission, I am repeating his post here:
I think the capacitors are a voltage divider, sort of, but a voltage
adder too. Depends on where you're standing.
Let's say for example that the caps have a reactance of -100 ohms
apiece. The total would be -200 ohms, so the inductor would also have
200 ohms reactance at the resonant frequency. The circuit is driven by
the voltage across source resistor in parallel with the lower
capacitor. Looking at that element (-100 ohm capacitor) in isolation,
it is in parallel with 200 - 100 ohms or 100 ohms inductive, so it is
driving a parallel resonant circuit.
The resulting circulating current of course creates twice the drop
across the 200 ohm inductor as across the single -100 ohm capacitor.
And the voltage across the other capacitor is the same and in phase, so
the two voltages are additive. The voltage at the gate is twice that
across the lower capacitor. So looking at the two capacitors
separately, we have a divider but looking from gate to ground, and adder.
You can do the though experiment with unequal caps too, say 70 ohms and
30 ohms. You still find the source resistor driving a parallel resonant
circuit and a greater voltage from gate to ground than across either of
the two caps.