Here is the schematic of Michigan Mighty Mite, a popular transmitter circuit design. It seems to be quite close to a regular feedback oscillator, with a few peculiarities.
What puzzles me is the mechanism how the feedback (output from the transistor amplifier) is fed back to the LC circuit. The inductor in the LC circuit has a tap. I've been explained that the tap is made closer to one end of the inductor because that is the "low-impedance point" of the inductor. As the LC circuit is being fed through a lower impedance, more current gets out of the amplifier and therefore there is more oscillating current on the LC circuit and thus a larger signal gets out to the antenna.
I attempted to draw a simplified schematic of the LC circuit and the amplifier in this circuit, omitting everything else, including the crystal:
The battery appears as a short for an AC signal, so one side of the LC is connected to the ground. I omitted details of the amplifier and replaced it with a generic amplifier whose output is being fed back to the LC circuit, and the two inductors represent the tapped inductor. Is this anything close to representing the circuit?
Now, if the tap is made closer to the battery, the amp sees a lower impedance. But how does the current flow from there? It now sees a lower impedance to the ground, is that where the current goes? But then again, the amplifier is an inverting one, so I'm not sure what happens here.
So my question is: How does this idea of having a lower impedance tap in the LC part of this circuit increase the current oscillating in the circuit?