A phase shift oscillator can be built with just one operational amplifier, as shown in the figure. It is normal to assume that the different phase shift sections are independent, so we can write the following equation for the circuit:
The phase shift for the full loop is -180 degrees since the shift for each of the three branches is –60 degrees. This will happen when = 2f = 1,732 / RC because the 60-degree tangent is 1.73. The value of at this point is (1/2) 3, and therefore, the gain of A must be equal to 8 so that the system gain is equal to 1. The oscillation frequency of the circuit in the figure with the values of the components used is 3.76 kHz, slightly different from the calculated frequency which was 2.76 kHz. It should also be considered that the gain to initiate oscillations must be 26, different from the calculated gain of 8. These discrepancies are due in part due to variations in the characteristics of the components, but the factor that most contributes to this is the fact that we assume each section of the RC network does not influence the others. This configuration was very popular when components for elaborating more complex configurations were expensive.
