Working principle of Colpits oscillators

Colpitt’s oscillators

The essential component of colpits oscillator is same with that of Hartley oscillator. The only difference between Hartley and colpits oscillators is that in Hartley oscillator, the inductor is centrally taped but in the case of colpits oscillators, two capacitors are centrally tapped.

The circuit diagram Colpitt’s oscillator is shown in figure which consists of CE amplifier with tan circuit. The tank circuit consists of inductor coil in parallel with central tapped two capacitor \(C_1\) and \(C_2\) as in figure. The voltage drop across \(C_2\) is taken as the feedback voltage which is given to base of transistor through coupling capacitor \(C_3\) . Whereas output voltage is taken across \(C_1\) and collector through \(C_4\). The RFC acts as a dc load resistor for output. The dc power supply (\(+V_{CC}\)) is given through universal biasing circuit through resistor \(R_1\) and \(R_2\).

Working principle:

When power supply \(V_{CC}\) is given, the collector current raises to its Q-value. This collector current develops transient current across tank circuit. This produced the natural oscillator in the tank circuit. Due to oscillation small emf is developed across \(C_2\) which is feedback to the input and CE amplifier reverse the phase by \(180^\circ\). The tank circuit also reverses the phase by \(180^\circ\) due to central tapping of capacitor. As a result/ the necessary sustained condition for oscillation (\(60^\circ\) phase shift) is achieved and continuously generates the periodic sin wave.

AC-equivalent circuit:

For ac equivalent circuit the value of resistance of RFC is infinitely large . So its effect is neglected. Also the resistor \(R_1\parallel\) is large in enough in comparison to input resistance \(r_{in}\) of transistor. The capacitor \(C_1\) and \(C_3\) are shorted as the allow of ac-signal hence the ac-equivalent circuit becomes,

Here,

\(z_1\)=impedance of \(C_1\)=\(\frac{1}{j \omega c_1}\)

\(z_2\)=impedance of \(c_2\)=\(\frac{1}{j \omega c_2}\)

\(z_3\)=impedance of L=\(j \omega \)

and \(r_{in}\)=\(\beta r_e’\) is ac input resistance

Now load impedance is given by,

$$Z_L=z_1\parallel [z_3+(z_2\parallel r_{in})]$$

The gain of CE amplifier is given by,

$$A=\frac{-z_L}{r_e’}$$; negative sign due to phase reversal

Now the voltage drop across \(z_1\) acts as output voltage. And that across \(z_2\) act as feedback voltage.

\(\therefore\) feedback ratio(\(beta’\))=\(\frac{v_f}{v_\circ}=\frac{z_2\parallel r_{in}}{z_3+(z_2\parallel r_{in})}\)

Now, for the oscillation, we must have,

$$A\beta’=1$$

$$\biggl(\frac{z_1\parallel[z_3+(z_2\parallel r_{in})}{r_e’}\biggr).\biggl(\frac{z_2\parallel r_{in}}{z_3+z_2\parallel r_{in}}\biggr)=1$$

$$\frac{z_1.(z_3+z_2\parallel r_{in})}{(z_1+[z_3+z_2\parallel])r_e’}.\frac{z_2.\beta r_e’}{(z_2+\beta r_e’)(z_3+z_\parallel r_{in})}=1$$

$$\frac{z_1\beta}{z_1+z_3+\frac{z_2.r_{in}}{z_2+r-{in}}}.\frac{z_2.\beta}{(z_2+\beta r_e’)(z_3+z_2\parallel r_{in}}=-1$$

$$z_1z_2(1+\beta)+z_2z_3+(z_1+z_2+z_3)\beta _e’=1\dotsm(3)$$

Oscillation frequency:

Comparing imaginary part with zero,i.e.

$$Z_1+z_2+z_3=0$$

$$\frac{1}{j \omega c_1}+\frac{1}{j \omega c_2}+j \omega L=0$$

$$\frac{-j}{\omega c_1}-\frac{j}{\omega c_2}+j \omega L=0$$

$$\frac{-j}{\omega}\biggl(\frac{1}{c_1}+\frac{1}{c_2}+\omega^2 L\biggr)=0$$

$$\Rightarrow \frac{1}{c_2}+\frac{1}{c_2}-\omega^2 L=0$$

$$\omega^2 L=\frac{1}{c_1}+\frac{1}{c_2}$$

$$\omega=\sqrt{\frac{1}{L}\biggl(\frac{1}{c_1}+\frac{1}{c_2}\biggr)}$$

$$f=\frac{1}{2\pi \sqrt{LC}}$$,Where,$$\frac{1}{c}=\frac{1}{c_1}+\frac{1}{c_2}$$

Oscillation criteria

Comparing real part with zero,

$$z_1z_2(1+\beta)+z_2z_3=0$$

$$1+\beta=\frac{-z_2z_3}{z_1z_2}=\frac{-z_3}{z_1}$$We have,

$$z_1+z_2+z_3=0$$

$$1+\beta=\frac{z_1+z_2}{z_1}$$

$$1+\beta=1+\frac{z_2}{z_1}$$

$$\beta=\frac{-z_2}{z_1}$$Where,$$z_2=\frac{1}{j\omega c_2}$$ $$\beta=\frac{c_1}{c_2}$$Which is required condition for sustained oscillation.

Advantages:

• It has simple construction.
• It is possible to obtain oscillation at very high frequencie
• Good wave purity
• Good stability at high frequency
• Wide operation range 1 to 60 MHz

Disadvantages:

• It is difficult to adjust the feedback as it demands change in capacitor values.
• Poor frequency stability
• It is hard to designed.

Application of colpits oscillators:

• It is used for generation of sinusoidal output signals with very high frequencies.
• The Colpits oscillator using SAW device can be used as the different types of sensors such as temperature sensor.As the device used in this circuit is highly sensitive to perturbation, it senses directly from its surface.
• Ir is frequently used for the applications in which very wide range of frequencies are involved
• Used for applications in which undamped and continues oscillations are desired for the functioning.
• This oscillator is preferred in situations where it is intended to withstand high and low temperatures frequently

References:

(1)Theraja, B.L. Basic Electronics. N.p.: S.Chand, n.d. Print.

(2)C.L.Arora. Refresher Course in Physics. Vol. II and III. N.p.: S.Chand, 2006. Print.

(3)Malvino. Electronic Principles. N.p.: Tata McGraw-Hill, n.d. Print.

(4)N.Nelkon and P.Parker. Advanced Level Physics. 5th ed. N.p.: Arnold Heinemann, n.d. Print.

(5)Priti Bhakta Adhikari,Diya Nidhi Chaatkuli, Ishowr Prasad Koirala. A Textbook of Physics (2nd Year). N.p.: Sukunda Pustak Bhawan, 2070. Prin