Designing Phase Shift Oscillators

What is a phase shift oscillator?

"Phase shift oscillator" is the term given to a particular oscillator circuit topology that uses an RC network in the feedback loop of a tube, transistor, or opamp to generate the required phase shift at a particular frequency to sustain oscillations.  They are moderately stable in frequency and amplitude, and very easy to design and construct.
Where are they used?
Phase shift oscillators are most commonly used in tremolo circuits in guitar amplifiers. They are used as the low-frequency oscillator (LFO) that generates the sinusoidal waveform which amplitude modulates the guitar signal to produce the characteristic tremolo amplitude variations.
How do they work?
In order to create and sustain an oscillation at a particular frequency, a circuit must have a gain higher than unity, and a total phase shift around the loop of 360 degrees (which is equivalent to 0 degrees, or positive feedback).  When used with a single-stage inverting amplification element, such as a tube, transistor, or inverting opamp configuration, the amplifier itself provides 180 degrees of phase shift (a gain of -A, where A is the gain of the amplification stage). The remaining 180 degrees of phase shift necessary to provide a total of 360 degrees is provided by an external network of resistors and capacitors.

Following is a schematic diagram of a typical phase shift oscillator:


Phase Shift Oscillator

The triode is configured as an inverting amplifier to provide the necessary gain, and the feedback network is connected from the plate to the grid.

The phase shift elements are C1/R1, C2/R2, and C3/R3.  Three of these phase lead1 networks contribute a total of 180 degrees of phase shift at the oscillation frequency.  Note that a phase shift oscillator could also be built using four or more phase shift elements, with each element contributing less overall phase shift at the oscillation frequency.  Normally, there is no need to do this, as it takes extra components.  A minimum of three phase shift networks is required, however, because the maximum theoretical phase shift available from any one RC network is 90 degrees, and the actual phase shift approaches this value asymptotically.

A phase shift oscillator can also be made using three phase lag networks, which are obtained by swapping the positions of the R and C value components in the above schematic.  The lag network would require one additional coupling cap to block the DC on the plate voltage from the grid, and one additional resistor to provide the grid bias ground reference for V1A, so it is not normally used.

Following is an example of both a phase lead and a phase lag network, designed for a 45 degree phase shift at the -3dB point of f = 1/(2*Pi*R*C) = 1/(2*Pi*1Meg*.01uF) = 15.9Hz:


Phase Lead Network                                  Phase Lag Network





Following is a plot of the phase shift and attenuation characteristics of the phase lead and phase lag networks:
 
 

(click on image for larger view)

As can be seen from the plot, the phase lead network starts at near +90 degrees at 0.1Hz, and shifts through +45 degrees at the -3dB point of 15.9Hz, continuing on toward 0 degrees above 1kHz. The phase lag network, on the other hand, starts at 0 degrees, shifts through -45 degrees at the -3dB point, and continues on towards -90 degrees above 1kHz.  Either one will provide an effective 0 degrees phase shift when three of them are combined with the 180 degree phase shift of the amplifier as shown in the phase shift oscillator schematic.

It can be shown2 that the attenuation of the phase shift elements in the feedback loop is 1/29, so the oscillator will oscillate if the amplifier gain is greater than 29 (which  will bring the overall loop gain above unity gain, and satisfy the gain criterion for oscillation).  The oscillations will occur at a frequency given by the following equation:

fo = 1/(2*Pi*Sqrt(6)*R*C)

In order to obtain the lowest distortion for the best sine wave, the amplifier should be operated with a gain of exactly 29, which is just the bare minimum necessary to sustain oscillation.  This will produce the purest sine wave, however, it is impractical if tubes of varying gains may be substituted (this usually requires an adjustment control to trim the gain), or if the frequency of oscillation must be adjusted in such a manner as to change the gain of the network.  For these reasons, the gain is usually made higher, and post-filtering of the waveform is done to remove unwanted harmonic distortion.

If four phase lead networks are used, the phase shift per section at the oscillation frequency is lower, therefore, the attenuation of the network is also lower, around 1/18.  This allows use of lower gain tubes if necessary, since the gain of the amplifier only has to be at least 18.


The design procedure


Design modifications for a tremolo oscillator

Design considerations for using a single pot to control frequency Design considerations: footswitch and startup issues for tremolo circuits
Revised 09/08/00