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## AIM

To construct a Colpitts oscillator and to measure its output frequency.

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## APPARATUS

Transistors, resistors, capacitors, inductance coil, dc power supply, C.R.O.

## THEORY

A Colpitts oscillator, invented in 1920 by American engineer Edwin H. Colpitts, is a device that generates oscillatory output (sinusoidal). It consists of an amplifier linked to an oscillatory circuit, also called LC circuit or tank circuit. One of the advantages of this circuit is its simplicity; it needs only a single inductor and widely used in commercial signal generators upto 100 MHz.

## Tank circuit

An LC circuit can store electrical energy oscillating at its resonant frequency. A capacitor stores energy in the electric field between its plates, depending on the voltage across it, and an inductor stores energy in its magnetic field, depending on the current through it.

If a charged capacitor is connected across an inductor, charge will start to flow through the inductor, building up a magnetic field around it, and reducing the voltage on the capacitor.

Eventually all the charge on the capacitor will be gone and the voltage across it will reach zero. However, the current will continue, because inductors resist changes in current, and energy to

keep it flowing is extracted from the magnetic field, which will begin to decline. The current will begin to charge the capacitor with a voltage of opposite polarity to its original charge. When themagnetic field is completely dissipated the current will stop and the charge will again be stored in the capacitor, with the opposite polarity as before. Then the cycle will begin again, with the current flowing in the opposite direction through the inductor.

The charge flows back and forth between the plates of the capacitor, through the inductor. The energy oscillates back and forth between the capacitor and the inductor until (if not replenished by power from an external circuit) internal resistance makes the oscillations die out. Its action, known mathematically as a harmonic oscillator, is similar to a pendulum swinging back and forth, or water sloshing back and forth in a tank. For this reason the circuit is also called a tank circuit. The oscillation frequency is determined by the capacitance and inductance values used. In typical tuned circuits in electronic equipment the oscillations are very fast, thousands to millions of times per second

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**About LC Oscillatory net work **

A Colpitts oscillator is the electrical dual of a Hartley oscillator. Fig. 4 shows the basic Colpitts circuit, where two capacitors and one inductor determine the frequency of oscillation. The feedback needed for oscillation is taken from a voltage divider made of two capacitors, whereas in the Hartley oscillator the feedback is taken from a voltage divider made of two inductors (or a single, tapped inductor).

LC oscillators are designed to operate in the radio-frequency range, above 1 M Hz. However they can also be designed to produce oscillations in the low audio-frequency range. But for the low-frequency operation, the inductors used become very large in value and hence in physical size. Since Colpitt’s oscillator is a high frequency oscillator, its inductors will be in micro henries and capacitor in pF.

The circuit oscillates when the components are suitably selected to satisfy the Barkhausen criteria.

i.e.βA=+1(feedback factor must be unity).

Where A is the gain of the amplifying element and β is the transfer function of the feedback path, so βA is loop gain around the feedback loop of the circuit. Also there must be a positive feedback. i.e., the phase shift around the loop is zero or an integer multiple of 2π:

The frequency of oscillation is given by

Where C_{eq} is the effective capacitance of the capacitor C_{1} and C_{2}, given by

Colpitts Oscillator basically consists of a single stage inverting amplifier and an L-C phase shift network, as shown in the circuit diagram (Fig 4). The two series capacitors C_{1} and C_{2} form the potential divider used for providing the feedback voltage – the voltage developed across capacitor C_{2} provides the regenerative feedback required for sustained oscillations. Parallel combination of R_{E} and C_{E} along with resistors R_{1} and R_{2} provides the stabilized self bias. The collector supply voltage V_{cc} is applied to the collector through a resistance R_{C} which permits the flow of maximum current through the transistor. The presence of coupling capacitor C_{c} in the output circuit does not permit the dc currents to go to the tank circuit (the flow of dc current in a tank circuit reduces its Q). The output of the phase-shift L-C network is coupled from the junction of L and C_{2} to the amplifier input at base through coupling capacitor C_{C}, which blocks dc but provides path to ac. Transistor itself produces a phase shift of 180° and another phase shift of 180″ is provided by the capacitive feedback. Thus a total phase shift of 360° is obtained which is an essential condition for developing oscillations. The frequency is determined by the Tank circuit and is varied by gang-tuning the two capacitors C_{1 }and C_{2}. It is to be noted that capacitors C_{1} and C_{2} are ganged. As the tuning is varied, values of both capacitors vary simultaneously, the ratio of the two capacitances remaining the same

The oscillations across capacitor C_{2} are applied to the base-emitter junction and appear in the amplified form in the collector circuit. Of course, the amplified output in the collector circuit is of the same frequency as that of the oscillatory circuit. This amplified output in the collector circuit is supplied to the tank circuit In order to meet the losses. Thus the tank circuit is getting continuously energy from the circuit to make up for the losses occurring in it and, therefore, ensures undamped oscillations. The energy supplied to the tank circuit is of correct phase, as already explained and if Aβ exceeds unity, oscillations are sustained in the circuit.