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:

Hartley Oscillator:

Fig. 5, shows Hartley oscillator when the LC tank is resonant, the circulating current flows through L₁ in series with L₂. Thus, the equivalent inductance is L = L₁ + L₂.

Fig. 5

In the oscillator, the feedback voltage is developed by the inductive voltage divider, L₁ & L₂. Since the output voltage appears across L₁ and the feedback voltage across L₂, the feedback fraction is

β = V / V_out = X_L2 / X_L1 = L₂ / L₁

As usual, the loading effect of the base is ignored. For oscillations to start, the voltage gain must be greater than 1/ β. The frequency of oscillation is given by

Similarly, an opamp based Hartley oscillator circuit is shown in fig. 6.

Fig. 6

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