RC Phase Shift Oscillator Design for Sine Wave Generation

Key Takeaways

• An RC phase shift oscillator is one of many AC oscillator circuits that is adaptable to a wide range of loads.

• This circuit outputs a clean sine wave with scalable frequency by applying feedback through successive RC networks.

• These circuits are highly stable, and the phase noise in the output will depend on the level of jitter in the amplifier circuit.

RC phase shift oscillator waveform.

Oscillators are everywhere, including in your AC PCB designs. They hum quietly in the background and can provide stable reference waveforms for use in mixers, receivers, transmitters, and other circuits. Among the range of oscillators available for low-frequency AC designs, and even for RF circuits, one option is a phase shift oscillator. The most common of these is the RC phase shift oscillator, but there are other phase shift oscillator circuits you can use.

So when is an RC phase shift oscillator the best choice, and when should you opt for something like an LC resonant phase shift oscillator? It all depends on the components that are available in your circuit. An RC phase shift oscillator is a great starting point for generating high kHz sine waves with simple circuits. Once you need to get into the MHz regime, you’ll need to use a different type of oscillator. Here’s how the RC phase shift oscillator works and when it becomes limited in terms of frequency output.

RC Phase Shift Oscillator Design

An RC phase shift oscillator, just as its name suggests, takes advantage of the phase shift that occurs in an RC circuit during discharge. These circuits typically rely on an op-amp wired up with feedback, similar to a comparator. Thermal noise in the circuit kicks off the initial rise in the output voltage thanks to feedback in the circuit. As the circuit output rises, successive RC stages in the circuit will charge and discharge and there will be a phase shift in their output voltages. This produces an oscillation due to charging/discharging in successive RC networks.

The circuit diagram below shows two typical configurations for RC phase shift oscillator circuits with 3 RC networks and an op-amp. Note that an RC phase shift oscillator could have any number of RC networks in the feedback loop. These circuits are typically set up so that all the resistors and capacitors have equal values, which simplifies an analysis of this type of circuit.

Two types of RC phase shift oscillator circuits built around an op-amp.

The RC networks in an RC phase shift oscillator are constructed such that the sum of phase shifts across these networks equals 180°, giving a total phase shift of 360° between the differential input and op-amp output (180° for the RC networks plus 180° for the inverted output). This is the critical condition that allows the circuit to output a clean sine wave. The phase difference between the charging/discharging current in the RC networks and the output voltage/current will determine the output frequency. Finally, a feedback resistor is normally added to set the gain of the op-amp to the desired value.

Output Frequency

In the above equation, N refers to the number of RC legs in the circuit (N = 3 above), so the output can be scaled by carefully adding or removing RC legs in the feedback loop. 

Phase Shift

Each RC network in the feedback loop induces a phase shift on the voltage/current in the feedback loop. Just using the standard definition of phase shift for lumped RC networks, the phase shift per RC network is also a function of the output frequency. The reason we often set the values of passives equal in all legs is that it is very easy to set the phase shift to a specific value. For N = 3, the phase shift in each leg must be equal to odd integer multiples of 60°. Simply select a resistor and calculate the required capacitor, or vice versa.

Limits of an RC Phase Shift Oscillator

An RC phase shift oscillator has a number of advantages over other oscillators:

• Self-starting: These circuits use feedback to kick off the oscillation and eventually reach a dynamic equilibrium.

• Low noise: If laid out correctly, the system will have noise that is limited by the noise power spectral density of the op-amp.

• Adjustable gain: Like any other op-amp circuit, the output gain can be selected by setting the feedback resistor to the appropriate value.

There are, however, some disadvantages of an RC phase shift oscillator:

• Frequency limited: The output frequency is limited by component values, so it is difficult to get frequencies higher than a few MHz without a large number of RC stages in a phase-lag oscillator. Self-resonance in the capacitors also limits the output frequency.

• Bandwidth limited: The bandwidth of the op-amp limits the available gain at high frequencies. Beyond the unity-gain bandwidth, the gain will drop below 0 dB. The amplifier’s output impedance will also be reactive near the bandwidth edge, so the amplifier will contribute its own phase shift.

• Gain limited: The op-amp section needs to have relatively high gain (usually ~30), which also limits the output frequency due to the op-amp’s bandwidth (see above).

An alternative version of this circuit uses a transistor, which provides physically smaller dimensions and lower parasitics. However, it still suffers from the same problems. Therefore, if higher frequencies are required, the oscillation frequency needs to be stepped up with a PLL, or a different RF oscillator circuit should be used. The image below shows a typical RC phase shift oscillator circuit with a BJT:

RC phase shift oscillator with a transistor.

If you look at the above equations for phase shift and output frequency, it should be obvious that there is a complex nonlinear relationship between these two values. In a practical design, the circuit designer would simply select a frequency and practical resistor value, then they would calculate the R value required in 3 or 4 RC networks on the feedback line.