Why is a capacitor connected across the collector-emitter of the transistor? How does this capacitor prevent decay of LC oscillations?
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Some of us are clairvoyant.
With the base effectively grounded at RF, the transistor is obviously acting as a common-base amplifier, which is non-inverting. Therefore the collector-emitter capacitor provides positive feedback.
OK I cheated. You asked another question about the same circuit yesterday.
EDIT : The circuit is rather clever; it uses the same transistor for three separate purposes: