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In other words, when looking at the small-signal circuit analysis you will see the one cap at the input of the amp and the other at the output with the inductor as the feedback. Being a CE amplifier, the one cap is 180 degrees out of phase with the other which can create a push-pull effect. Satisfying Barkhuizens criteria.
It is called a neutralized amp. The output resonant tank is AC ground tapped in between the two ends. This means the AC swing on the far end of the coil (at resonance) is 180 degs output of phase with the AC swing on the collector. The bottom of coil output is fed back to base on transistor to cancel output the coupling internal to the transistors (Ccb).
The capacitance ratio (or tapped coil turns ratio) of output tank determines the amplitude of the far end compared to the collector end. Lets say the far end is 1/3 the voltage swing on the collector end, then the proper feedback cap from far end to base of transistor would be 3 times the Ccb of the transistor to neutralize the amplifier.
Ccb is a function of DC bias on transistor, particularly the DC voltage from base to collector, so you have to keep this voltage relatively constant to avoid Ccb from changing with change in average DC bias.
The main limitation of a neutralized amp is narrow bandwidth, being only that of the operating Q of the output tank circuit.