A Phase shift Resistor-Capacitor (RC) network can be formed using just only one resistor and one capacitor formation. This is the same as a basic passive High pass filter circuit. A typical RC phase shift oscillator can be produced by a capacitor in series along with a resistor in parallel. The circuit left is a single pole phase shift network. Theoretically if an in phase signal is applied across this RC network the output phase will be shifted by exactly 90 degrees. In reality if the phase shift is checked then a shift of 60 degree to less than 90 degrees is achieved. This depends on the frequency, and the components tolerances, which create adverse effect in reality. Nothing is perfect so there should always be some difference between actual and expected values. Temperature and other outer dependencies create difficulties to achieve exact 90 degree phase shift. Cascading such circuits can achieve the desired phase shift. If the phase shift is 60 degree three filters in series are required to give 189 degrees phase shift and four filters if the phase shift is 45 degree.

The relationship between the phase lag and the resistance and capacitance can be seen in the phasor diagram , right. The lag increases as the resistance decreases/ capacitance increases and decreases as the resistnace increases/capacitance decreases. It also explains why a RC circuit can't achieve 90o phase shift as the resistance is never zero.

The phase shift that results from one RC combination and a multiple combination can be seen in the figure left. By connecting together three RC networks in series a total phase shift of 180o can be produced at the chosen frequency. This forms the bases of a "phase shift oscillator" otherwise known as a RC Oscillator circuit. An amplifier circuit either using a Bipolar Transistor or an Operational Amplifier will produce a phase-shift of 180o between its input and output. If a three-stage RC phase-shift network is connected between this input and output of the amplifier, the total phase shift necessary for regenerative feedback will become 3 x 60o+ 180o = 360o as shown.

The three RC stages are cascaded together to get the required slope for a stable oscillation frequency. The feedback loop phase shift is -180o when the phase shift of each stage is -60o. This occurs when ω = 2πƒ = 1.732 / RC (tan 60o = 1.732). Then to achieve the required phase shift in an RC oscillator circuit is to use multiple RC phase-shifting networks such as the circuit right.. The basic RC Oscillator, also known as a Phase-shift Oscillator, produces a sine wave output signal using regenerative feedback obtained from the resistor-capacitor combination. This regenerative feedback from the RC network is due to the ability of the capacitor to store an electric charge, (similar to the LC tank circuit).

This resistor-capacitor feedback network can be connected as shown above to produce a leading phase shift (phase advance network) or interchanged to produce a lagging phase shift (phase retard network) the outcome is still the same as the sine wave oscillations only occur at the frequency at which the overall phase-shift is 360^o.

By varying one or more of the resistors or capacitors in the phase-shift network, the frequency can be varied and generally this is done by keeping the resistors the same and using a 3-ganged variable capacitor.
If all the resistors, R and the capacitors, C in the phase shift network are equal in value, then the frequency of oscillations produced by the RC oscillator is given as:

f_T =

1 / 2πRC √2N

• f_T is the Output Frequency in Hertz
• R is the Resistance in Ohms
• C is the Capacitance in Farads
• N is the number of RC stages. (N = 3)

Since the resistor-capacitor combination in the RC Oscillator circuit also acts as an attenuator producing a total attenuation of -1 / 29 th ( Vo / Vi = β ) across the three stages, the voltage gain of the amplifier must be sufficiently high enough to overcome these RC losses. Therefore, in our three stage RC network above, the amplifier gain must be equal too, or greater than, 29. The loading effect of the amplifier on the feedback network has an effect on the frequency of oscillations and can cause the oscillator frequency to be up to 25% higher than calculated. Then the feedback network should be driven from a high impedance output source and fed into a low impedance load such as a common emitter transistor amplifier but better still is to use an Operational Amplifier as it satisfies these conditions perfectly.

As the feedback is connected to the inverting input, the operational amplifier is therefore connected in its "inverting amplifier" configuration that produces the required 180o phase shift while the RC network produces the other 180o phase shift at the required frequency (180^o + 180^o). Although it is possible to cascade together only two single-pole RC stages to provide the required 180o of phase shift (90^o + 90^o), the stability of the oscillator at low frequencies is generally poor.

One of the most important features of an RC Oscillator is its frequency stability, which is its ability to provide a constant frequency sine wave output under varying load conditions. By cascading three or even four RC stages together (4 x 45^o), the stability of the oscillator can be greatly improved.
RC Oscillators with four stages are generally used because commonly available operational amplifiers come in quad IC packages so designing a 4-stage oscillator with 45^o of phase shift relative to each other is relatively easy.