RC Oscillators

RC OSCILLATORS

All the oscillators using tuned LC circuits operates well at high frequencies. At low frequencies, as the inductors and capacitors required for the time circuit would be very bulky. RC oscillators are found to be more suitable. Two important RC oscillators are (i) RC phase shift oscillator and (ii) Wien Bridge Oscillator.

RC PHASE SHIFT OSCILLATOR

In this oscillator the required phase shift of 180° in the feedback loop from output to input is obtained by using R and C components instead of tank circuit.

The Fig.4.15 shows the circuit of RC phase shift oscillator using cascade connection of high pass filter.

Here a common emitter amplifier is followed by three sections of RC phase shift network, the output of the last section being returned to the input. In order to make the three RC sections identical, R₃ is choosen as R₃ = R - R_i.

Where R_i - input impedance of the circuit. The phase shift, φ given by each RC section is  If R is made zero then φ will become 90°. But making R = 0 is impracticable because if R is zero, then the voltage across it will become zero. Therefore, in practice the value of R is adjusted such that becomes 60°.

If the values of R and C are chosen that for the given frequency f_o, the phase shift of each RC section is 60°. Thus such a RC ladder network produces a total phase shift of 180° between its input and output voltages for the given frequency. Therefore, at the specific frequency f_o, the total phase shift from the base of the transistor around the circuit and back to the base will be exactly 360° or 0°, thereby satisfying Barkhausen condition for oscillation. The frequency of oscillation is given by

At this frequency, it is found that the feedback factor of the network is |β| = 1/29. In order that |Aβ| shall not be less than unity, it is required that the amplifier gain |A| must be more than 29 for oscillator operation.

The RC phase shift oscillator is suitable for audio frequencies only. Its main drawbacks are that the three capacitors or resistors should be changed simultaneously to change the frequency of oscillation and it is difficult to control the amplitude of oscillation without affecting the frequency of oscillation.

Analysis

From 4.15 (b), we can write the following three equations

Solving the above simultaneous equations, we get

For determining the frequency of oscillation the phase shift, ie., the imaginary part must be equal to zero.

Hence

The condition for maintanence of oscillation is obtained by substituting α = √6 into β thus, we get

Hence a transistor with gain < 29 cannot be made to oscillate in a circuit and the frequency of oscillation may be varied by changing any of the impedance element in the phase shifting network.

WIEN BRIDGE OSCILLATOR

The Fig. 4.16 shows the circuit of Wien-bridge oscillator. The circuit consists of a two-stage RC coupled amplifier which provides a phase shift of 360° (or) 0°. A balanced bridge is used as the feedback network which has no need to provide any additional phase shift.

The feedback network consists of a lead-lag network provides a positive feedback to the input of the first stage and the voltage divider provides a negative feedback to the emitter of Q₁.

If the bridge is balanced, 

Where X_C1 and X_C2 are the reactance of the capacitors.

Simplifying the above equation and equating the real and imaginary parts on both sides, we get the frequency of oscillation as,

The ratio of R₃ to R₄ being greater than 2 will provide a sufficient gain for the circuit to oscillate at the desired frequency. This oscillator is used in commercial audio signal generators.