The Colpitts Oscillator

The Colpitts Oscillator:

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

The alternative is an LC oscillator, a circuit that can be used for frequencies between 1MHz and 500MHz. The frequency range is beyond the frequency limit of most OPAMPs. With an amplifier and LC tank circuit, we can feedback a signal with the right amplitude and phase is feedback to sustain oscillations. Fig. 3, shows the circuit of colpitts oscillator.

Fig. 3	Fig. 4

The voltage divider bias sets up a 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 the selector. Because of the base and collector lag networks, the high frequency voltage gain is less then r_c / r'_e.

Fig. 4, shows a simplified ac equivalent circuit. The circulating or loop current in the tank flows through C₁ in series with C₂. The voltage output equals the voltage across C₁. The feedback voltage v_fappears across C₂. This feedback voltage drives the base and sustains the oscillations developed across the tank circuit provided there is enough 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 a Q greater than 10. The Q of the feedback circuit is given by

Because of this, the approximate resonant frequency is

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

Therefore                  C = C₁ C₂ / (C₁ +C₂)

The required 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 the gain at the oscillation frequency. The feedback gain β is given by

β = v_f / v_out≈ X_C1 / X_C2

Because same current flow through C₁ and C₂, therefore

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

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

With small β, the value of A is only slightly larger than 1/β. and the operation is approximately close A. When the power is switched on, the oscillations build up, and the 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 happen, the voltage gain decreases slightly. With light feedback the value of Aβ can decreases to 1 without 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 automatically adjusts the value of Aβ to 1.

Example - 1

Design a Colpitts oscillator that will oscillate at 100 kHz.

Solution:

Let us choose R₁ = R_f = 5 kΩ and C = 0.001 µF. From the frequency expression,

The quality factor (Q) of the LC circuit is given by: