In colpitts oscillator CE amplifier is used as amplifying element and LC circuit has a feedback element.

Since CE amplifier provides phase shift of 180 degree between input and output, therefore feedback tank circuit has to provide additional 180 degree phase shift to full-fill Barkhausen's criteria.

Barkhausen's criteria of AB = 1 can be fulfilled by selecting resistor Rc as potentiometer because gain of the CE amplifier is given as $Av = \frac{-Rc}{r_c}$

Frequency of oscillation is given as

$f_o = \frac{1}{21 \ T \ \sqrt{G.L}}$

where $C_T = \frac{c_1 c_2}{c_1 + c_2}$

Applications.

1] Microwave engineering.

2] Broadband communication.

3] Spectrum spreading.

4] Signal masking.

5] A surface acoustical wave resonator.