Colpitts oscillator

Colpitt’s Oscillator is an excellent circuit and is widely used in commercial signal generators upto 100MHz.

It consists of a single-stage inverting amplifier and an LC phase shift Network.

The two capacitors $C_{1}$ and $C_{2}$ provides potential divider used for providing $V_{f}$ . $C_{1}$ is the feedback element and which provides positive feedback required for sustained Oscillations.

The amplifier circuit is a self-Bias Circuit with $R_{1}$ , $R_{2}$ and parallel combination of $R_{E}$ with $C_{E}$ .

$V_{CC}$ is applied through a resistor $R_{C}$ (or) RFC choke some times. This RFC choke offers very high impedance to high frequency currents.

$R_{C}$ value has chosen in such a way that it offers high impedance. Two coupling Capacitors $C_{C1}$ and $C_{C2}$ are used to block d.c currents, that means they do not permit d.c currents into tank circuit.

These capacitors $C_{C1}$ and $C_{C2}$ provides a path from Collector to Base through LC Network.

when $V_{CC}$ is switched on , a transient current is produced in the tank circuit an consequently damped oscillations are setup in the circuit.

The oscillatory current in the tank circuit produces a.c voltages across $C_{1}$ and $C_{2}$ . If terminal 1 is more positive w.r. to 2 , then voltages across $C_{1}$ and $C_{2}$ are opposite thus providing a phase shift of $180^{o}$ between 1 and 2.

as the transistor is operating in CE mode , it provides a phase shift of $180^{o}$ .

Therefore the over all phase shift provided by the circuit results $360^{o}$ which is an essential condition for developing oscillations.

If the feedback is adjusted so that the loop gain $A\beta =1$ then then the circuit acts as an Oscillator.

The frequency of oscillation depends on the tank circuit and is varied by gang (or) group tuning of $C_{1}$ and $C_{2}$ means $C_{1}=C_{2}$ .

working:-

The capacitors $C_{1}$ and $C_{2}$ are charged by $V_{CC}$ and are discharged through the coil $L$ setting up of oscillations with frequency

$f_{o}=\frac{1}{2\pi }\sqrt{\frac{1}{L}(\frac{1}{C_{1}}+\frac{1}{C_{2}})}$ .

these oscillations across $C_{1}$ are applied to the Base-Emitter junction and the amplified version of output is collected across Collector (the frequency of amplifier output is same as that of input of the amplifier) .

This amplified energy is given back to tank circuit to compensate losses.

therefore un damped oscillations results in the circuit.

Derivation for frequency of oscillations:-

chose $\left | A\beta \right |\geq 1$ for sustained oscillations.

Analysis(Qualitative):-

if $Z_{1}$ , $Z_{2}$ and $Z_{3}$ are pure reactive elements such that $Z_{1}=\frac{1}{j\omega C_{1}} =\frac{-j}{\omega C_{1}}$ , $Z_{2}=\frac{1}{j\omega C_{2}} =\frac{-j}{\omega C_{2}}$ and $Z_{3}=j\omega L$ .