Colpitt Oscillator Calculation

Explain the concept of Colpitt Oscillator Calculation

The Colpitts Oscillator, named after its inventor Edwin Colpitts is another type of LC oscillator design.

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:

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A Colpitts oscillator was invented by Edwin H. Colpitts in 1920. Colpitts oscillator has number of design. It is also called LC oscillator. Edwin H. Colpitts was an American engineer. The Oscillator was named after Edwin H. Colpitts. The Colpitts oscillator is different from the Hartley Oscillator. In the Colpitts circuit, two capacitors and one inductor determine the frequency of oscillation. The feedback required for oscillation is brought from a voltage divider created by the 2 capacitors. The two capacitors, C1 and C2 are put across a common inductor, L so that C1, C2 and L forms the tuned tank circuit. The benefit of such type of tank circuit configuration is that with less self and mutual inductance in the tank circuit, frequency stability is developed along with a more simple design. The needed external phase shift is received in a similar manner to that in the Hartley oscillator circuit with the needed positive feedback got for sustained un-damped oscillations. The Colpitts oscillator produces a more pure sinusoidal waveform due to the low impedance paths of the capacitors at high frequencies. Also due to these capacitive reactance properties the Colpitts oscillator can work at very high frequencies into the microwave region.

Example
A Colpitts Oscillator circuit having two capacitors of 10pF and 100pF respectively are connected in parallel with an inductor of 10mH. Determine the frequency of oscillations of the circuit.