Colpits Oscillator

COLPITS OSCILLATOR

The Colpitts oscillator shown in Fig. 4.14.

Z₁ and Z₂ are capacitors and Z₃ is an inductor. The resistors R₁, R₂ and R_E provide the necessary dc bias to the transistor CE is a bypass capacitor. C_C1 and C_C2 are coupling capacitors. The feedback network consisting of capacitors C₁ and C₂ and an inductor L determines the frequency of oscillation.

When the supply voltage + V_CC is switched ON, a transient current is produced in the tank circuit and consequently, damped harmonic oscillations are setup in the circuit. The oscillatory current in the tank circuit produces ac voltage across C₁ and C₂. As terminal 3 is earthed, it will be at zero potential. If terminal 1 is at a positive potential with respect to 3 at any instant, terminal 2 will be at a negative potential with respect to 3 at the same instant. Thus the phase difference between terminals, 1 and 2 is always 180°. In the CE mode, the transistor provides the phase difference of 180° between the input and output. Therefore the total phase shift is 360°. Thus at the frequency determined for the tank circuit, the necessary condition for sustained oscillations is satisfied. If the feedback is adjusted so that the loop gain Aβ = 1, the circuit acts as an oscillator. The frequency of oscilation is

It is widely used in commercial signal generators for frequencies between 1 MHz and 500 MHz. It is also used as a local oscillator in super heterodyne radio receiver.

Analysis

For this oscillator

Substituting these values in oscillator equation, and simplifying, we get

The frequency of oscillation, f_o = ω_o/2π, is found by equating the imaginary part of above equation to zero. Thus we get

Substituting this value and simplifying, we get