Harmonic Oscillators

According to Barkhausen criterion, a feedback type oscillator, having Aβ as loop gain, works if Aβ is made slightly greater than unity. As discussed in previous lectures, all practical oscillations involve:

• An active device to supply loop gain or negative resistance.
• A frequency selective network to determine the frequency of oscillation.
• Some type of non-linearity to limit amplitude of oscillations.

Harmonic Oscillator:

One feedback type harmonic oscillator circuit is shown in fig. 1.

Fig. 1	Fig. 2

The dc equivalent circuit is shown in fig. 2. The dc operating point is set by selecting V_CC, R_B and R_E. The ac equivalent circuit is also shown in fig. 3.

Fig. 3

The transformer provides 180° phase shift to ensure positive feedback so that at the desired frequency of oscillation, the total phase shift from v_in to v_x is made equal to 0° and magnitudes are made equal by properly selecting the turns ratio. R_E also controls and stabilizes the gain through negative feedback. C₂ and the transformers equivalent inductance make up a resonant circuit that determines the frequency of oscillation.

C₁ is used to block dc (Otherwise the base would be directly tied to V_CC) through the low dc resistance of transformer primary. C₁ has negligible reactance at the frequency of oscillation, therefore it is not apart of the frequency-determining network, the same applies to C₂.

In this circuit, there is an active device suitably biased to provide necessary gain. Since the active device produces loop phase shift 180º (from base to collector), a transformer in the feedback loop provides an additional 180º to yield to a loop phase shift of 0º. The feedback factor is equivalent to the transformer's turns ratio. There is also a turned circuit, to determine the frequency of oscillation.

The load is in parallel with C₂ and the transformer. If the load is resistive, which is usually the case, the Q of the tuned circuit and the loop gain are both affected, this must be taken into account when determining the minimum gain required for oscillation. If the load has a capacitive component, then the value of C₂ should be reduced accordingly.