The Colpitts Oscillator:

Wein bridge oscillator is not suited to the high frequencies (above 1MHz). The basic problem is the phase shift through amplifier.

The alternative is an LC oscillator, a circuit which can be used for frequencies in between 1MHz and 500MHz.  The frequency range is beyond  the  frequency  limit  of  most of the  OPAMPs.  With the amplifier and LC tank circuit, we can feedback a signal with right amplitude and phase is feedback to sustain oscillations. The figure 1, shows circuit of the colpitts oscillator.

                                            Figure 1                                                                       Figure 2

The voltage divider bias sets up the quiescent operating point. The circuit then has a low frequency voltage gain of r_c / r'_e where r_c is the AC resistance seen by selector. Because of base and collector lag networks, high frequency voltage gain is less then r_c / r'_e.

The Figure 4, shows the simplified AC equivalent circuit. The circulating or loop current in tank flows through C₁  in the series with C₂. The voltage output equals the voltage across C₁. The feedback voltage vf appears across C₂. This feedback voltage drives the base and sustains the oscillations developed across tank circuit provided there is sufficient voltage gain at the oscillation frequency. Since the emitter is at AC ground the circuit is a CE connection.

Most LC oscillators use tank circuit with the Q greater than 10. The Q of the feedback circuit can be given by

Because of this, the approximate resonant frequency can be given as follows

This is accurate and better than 1per cent when Q is greater than 1%. The capacitance C is the equivalent capacitance the circulation current passes through. In Colpitts tank the circulating current flows through C₁ in the series with C₂.

Therefore                  C = C₁ C₂ / (C₁ +C₂)

The desired starting condition for any oscillator is A β > 1 at the resonant frequency or A > 1/ β. The voltage gain A in the expression is gain at the oscillation frequency. The feedback gain β can be given by

β = v_f / v_out≈ XC₁ / XC₂

As the same current flow through C₁ and C₂, therefore

β = C₁/ C₂;         A > 1/ v;           A> C₁ / C₂

This is a crude approximation as it ignores the impedance looking into base. An exact analysis would take base impedance into the account because it is in parallel with the C₂.

With small β, the value of A is only a bit larger than 1/β. and the operation is roughly close A. When power is switched on, the oscillations build up, and signal swings over more and more of AC load line. With this increased signal swing, the operation changes from small signal to large signal. As this occur, the voltage gain decreases slightly. With the light feedback value of Aβ can decreases to 1 without the excessive clapping.

With heavy feedback, the large feedback signal drives the base into saturation and cut off. This charges capacitor C₃ producing negative dc clamping at the base and changing the operation from class A to class C. The negative damping adjusts automatically the value of Aβ to 1.

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