Article : Andy Collinson
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Colpitts Oscillator at Resonance
Using a circuit from the RF schematics section, and the formula from the theory section, you can calculate the resonant frequency for the Colpitts oscillator:

fosc = 1
2π √ LC 

where C is total capacitance of C1 and C2 in parallel.
CT = C1 C2
C1 + C2

When C1 = C2 then the capacitance is simply

CT = C1
2

Working out the parallel capacitance as C1=C2 then C = 27/2 = 13.5pF

Assuming that the coil, L has an inductance of 0.2uH then:

fosc = 1 = 96.8 MHz
2π √0.2x10-6 x 13.5x10-12

This result puts the oscillator in the middle of the UK FM Band (87.5 - 108 MHz). If L1 has an adjustable ferrite core then its inductance can be altered and fine tuning acheived. If L1 is an air spaced coil then fine tuning is achieved by physically squeezing or separating the turns.

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