The RC Phase Shift Oscillator:

At the low frequencies (around 100 KHz or less), resistors are employed usually to determine the frequency oscillation. Various circuits are used in the feedback circuit including ladder network.

Figure 1

A block diagram of a ladder type RC phase shift oscillation is shown in the figure 1. It consists of 3 resistor R and C capacitors. If phase shift through the amplifier is 180º, then the oscillation may occur at frequency where the R_C network produces an additional 180 phase shift.

To find frequency of the oscillation, let us neglect the loading of phase shift network. The KV equations are as follows,

For the phase shift equal to 180 in between V_x  and V_O, imaginary term of V_x  / V_O  should be zero. Therefore,  

This is frequency of the oscillation. Substituting this frequency in the V_x / V_O expression.

In order to ensure oscillation, initially |Aβ| >1 and under study state Aβ =1. This means that the gain of amplifier should be initially greater than 29 (such that Aβ >1) and under steady stat conditions it decreases to 29.

This oscillator can be realized by using FET amplifier as shown in the figure 2. The feedback circuit is same as above.

                               Figure 2                                                                                  Figure 3

The input impedance of FET is quite high so that there is no loading of feedback circuit. In this circuit, the feedback is voltage series feedback.

V_x =V_GS +V_S            or            V_GS = V_x - V

The same circuit can be realized using OPAMP. The circuit is shown in the figure 6. The input impedance  is  high  and  there  is  no  overloading  of  feedback  circuit.  The OPAMP is connected in the inverting configuration and drives 3 cascaded R_C sections. The inverting amplifier causes a 180° phase shift in signal passing through it. RC network is used in feedback to provide additional 180° phase shift. Therefore, total phase shift in the signal, of a particular frequency, around loop will be equal to 360° and oscillation will occur at that particular frequency. The gain necessary to overcome the loss in RC network and bring the loop gain up to 1 is supplied by amplifier. The gain can be given as follows

Note that input resistor to the inverting amplifier is also the last resistor of R_C feedback network.

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