Explain the Colpitts oscillator circuit and how to calculate oscillation frequency.

The Colpitts oscillator uses an LC tank circuit with two capacitors (C1, C2) in series and an inductor (L) in parallel for frequency determination. The transistor provides gain and the capacitive divider provides feedback. Oscillation frequency is f = 1/(2*pi*sqrt(L*Ceq)) where Ceq = C1*C2/(C1+C2). The feedback factor beta = C1/C2, so C2 > C1 for proper feedback. Start-up requires loop gain > 1, typically achieved with gm*R > C1/C2.