### RC Phase shift oscillator.

RC phase shift oscillator or simply RC oscillator is a type of oscillator where a simple RC network (resistor-capacitor) network is used for giving the required phase shift to the feedback signal. In LC oscillators like Hartley oscillator and Colpitts oscillator an LC network (inductor- capacitor network) is used for providing the necessary positive feedback. The main feature of an RC phase shift oscillator is the excellent frequency stability. The RC oscillator can output a pure sine wave on a wide range of loads.

##### RC phase shift network.

RC phase shift network is a simple resistor capacitor network that can be used to give a desired phase shift to a signal. The circuit diagram of a simple single stage RC network is shown in the figure below.

Theoretically in a simple RC circuit , the output voltage will lead the input voltage by a phase angle Â Î¦ =90Â°. Anyway in Â practical case Â the phase angle will be something below 90Â° just because it is impossible to get a purely ideal capacitor. Phase shift of Â a practical RC network depends on the value of the capacitor, resistor and the operating frequency.

*Let F be the operating frequency, R be the resistance and C be the capacitance. Then the capacitive reactance Xc to the frequency F can be given by the equation Â Xc = 1 / (2Ï€FC)*

*The effective impedance of the circuit can be given by the equation Z =Â âˆš( RÂ² + XcÂ²)*

*The phase angle of the RC network can be derived as Â Î¦ = tan^{-1Â }(Xc/R)*

Just by making an RC network with phase shift equal to 60Â° and cascading three of them together the desired phase shift of 180Â° can be attained. This 180Â° phase shift by the RC network plus the 180Â° phase shift made by the transistor gives a total phase shift of Â 360Â° between the input and output which is the necessary condition for maintaining sustained oscillations. The circuit diagram of a three stage RC network producing a phase shift of 180Â° is shown in the figure below.

Connecting such a three stage RC phase shift network between the input and output of a common emitter transistor amplifier will result in a transistor based RC phase shift oscillator. The circuit diagram is shown below.

In the circuit diagram resistor R1 and the resistor R (close to the base of Q1 in the diagram) gives a voltage divider bias to the transistor Q1. Resistor Rc limits the collector current while Re is meant for thermal stability. Ce is the emitter by-pass capacitor and Cout is the output DC decoupling capacitor. By using more than three RC phase shift stages (like 4 x 45Â°)Â the frequency stability of the oscillator can be further improved. Â The frequency of the transistor RC phase shift oscillator oscillator can be expressed by the equation:

Where F is the frequency, R is the resistance, C is the capacitance and N is the number of RC phase shift stages. The RC pahse shift oscillator can be made variable by making the Â resistors or capacitors variable. The common approach is to leave the resistors untouched the three capacitors are replaced by a Â triple gang variable capacitor.

#### RC phase shift oscillator using opamp.

The circuit diagram of an RC phase shift oscillator is shown above. Feedback resistor Rf and resistor R (close to the inverting pin of the opamp in the circuit) is used to set the gain of the oscillator. Three stage phase shift network comprising of R and C produces 180Â° phase shift and the opamp itself wired in inverting mode produces another 180Â° phase shift. Thus the required phase shift of 360Â° is obtained between input and output.

## Comments