Colpitt’s 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.

from the general condition for an Oscillator 

\left | A\beta \right | =1  \Rightarrow h_{ie}(Z_{1}+Z_{2}+Z_{3})+Z_{1}Z_{2}(1+h_{fe})+Z_{1}Z_{3}=0.

h_{ie}(-\frac{j}{\omega C_{1}}-\frac{j}{\omega C_{2}}+j\omega L)+\frac{j^{2}}{\omega ^{2}C_{1}C_{2}}(1+h_{fe})-\frac{j}{\omega C_{1}}.j\omega L=0

find the real and imaginary parts,

-j(\frac{1}{\omega C_{1}}+\frac{1}{\omega C_{2}}-\omega L)h_{ie}-\frac{1}{\omega ^{2}C_{1}C_{2}}(1+h_{fe})+\frac{L}{C_{1}}=0

equating imaginary part to zero  (\frac{1}{\omega C_{1}}+\frac{1}{\omega C_{2}}-\omega L)=0  ,  since h_{ie}\neq 0 .

\frac{\omega C_{1}+\omega C_{2}}{\omega^{2} C_{1}C_{2}}=\omega L.

after simplification 

\omega ^{2}=\sqrt{\frac{1}{L}(\frac{1}{C_{1}}+\frac{1}{C_{2}})}.

by substituting \omega =2\pi f    results f_{o}=\frac{1}{2\pi }\sqrt{\frac{1}{L}(\frac{1}{C_{1}}+\frac{1}{C_{2}})}.

substituting the value of \omega ^{2}  in the real part gives h_{fe}=\frac{C_{2}}{C_{1}}  . this is the condition for sustained oscillations.

 

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Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.