Talk:Phase-shift oscillator

Missing resistor for op-amp implementation
Shouldn't there be another resistor to ground between R1 and C1 ? If not, it is not clear how the phase shift of 180° is obtained. Phds 13:02, 13 December 2006 (UTC)
 * No - R1 is already "virtually" connected to ground - due to the "virtual short circuit" across the inputs to the op-amp, so the current reaching the negative terminal will be shifted by up to 270 degrees.
 * Consider the case if R2, C2, R3 & C3 were removed, leaving one end of C1 open circuit and an external stimulus were fed into the open end of C1.
 * $$I_{R_1}=\frac{V_{in}}{R_1+\frac{1}{j\omega C_1}}$$ ( due to the virtual short )
 * $$I_{R_{fb}}=I_{R_1}$$
 * so $$V_{out}=-I_{R_1} R_{fb}$$
 * $$V_{out}=-\frac{V_{in}R_{fb}}{R_1+\frac{1}{j\omega C_1}} $$
 * This expression is shifted according to frequency, without needing another resistor --Ozhiker 14:01, 14 December 2006 (UTC)
 * This expression is shifted according to frequency, without needing another resistor --Ozhiker 14:01, 14 December 2006 (UTC)

Amplitude
I noticed that there is no expression for amplitude and suppose that it depends on initial conditions. Does that make this circuit impractical as it stands? Should there be a mention of this? Cheers. Gaussmarkov (talk) 01:35, 10 January 2008 (UTC)


 * In my first year of college (studying electronics) I constructed and experimented with a switched mode PSU - results in the post below. I can't say I remember exactly, but I THINK the peak output voltage was identical to the input voltage (peak-to-peak voltage = input*2).  Also, changing the input voltage did not seem to affect the frequency.  87.248.2.152 (talk) 01:04, 23 March 2009 (UTC)Peter Heiberg, Norway

The amplitude is that at which the nonlinearities of the amplifier reduce the effective gain below the oscillation threshold - clipping at the power supply voltage if nothing else happens first. There's a nice explanation at http://www-personal.engin.umd.umich.edu/~fmeral/ELECTRONICS%20I/311%20Lab%20Experiments/55%20%25a5Harmonic%20Oscillator.pdf "If the circuit used were truly linear there would be no amplitude limiting mechanism other than that associated with the average energy initially stored in the system. In a linear system signal amplitudes can be scaled (multiplied by a constant) without affecting frequency, and will be whatever the available energy will sustain. In a practical oscillator there is a continual infusion of energy from the amplifier and signal amplitude grows until inherent circuit nonlinearities constrain further growth. Often a controlled nonlinearity is introduced deliberately for this purpose, rather than depending on the unpredictable effect of inherent nonlinearities to limit oscillation amplitude."

Phase shift oscillators typically use amplifier nonlinearities, while Wein bridge oscillators, for example, typically use an external limiter, like the variable resistance of an incandescent lamp, or a rectifier/gain control circuit. So for opamps and clean linear transistor amplifiers, the peak-to-peak amplitude is whatever the amp can deliver without distortion - rail to rail minus a couple of volts. With more nonlinear amplifiers (vacuum tubes), it will be somewhat less. 24.17.178.36 (talk) 21:51, 24 December 2012 (UTC)

Setup Example
I tried to put together this one, and in the first test I used the following components; 3 1kOhm resistors, 1 29kOhm (Seried 27k, 1k, 1k) resistor for feedback and 3 1µF capacitors. This gave me a freqency of about 500Hz. 82.147.34.250 (talk) 08:52, 20 May 2008 (UTC) Peter Heiberg, Norway

German link
Would anybody please link to the german version? >> http://de.wikipedia.org/wiki/Phasenschieber#Phasenschiebergenerator —Preceding unsigned comment added by 80.129.207.244 (talk) 16:47, 2 March 2009 (UTC)
 * Seems to be done now.87.248.2.152 (talk) 01:09, 23 March 2009 (UTC)

Questions and comments
I made some fixed to the article to organize is better and for improving it visually. I add a few questions and comments.

1. Who is the inventor of the PSO?

2a. This article seems to imply each RC circuit contributes to a 90° phase shift. Is that correct?

2b. Does the circuit ever use more or less than 3 RC circuits?

3. "a gain of about 8 to 10 will be sufficient to enable oscillation" and "a larger gain (about 27 to 30) is required to keep the circuit in oscillation".

How is the gain of the operational amplifier implementation calculated? Is there an equation or the equation is nasty like the one for the frequency?

4. "Rs is a separating resistor."

What is a "separating resistor" exactly?

5. "The circuit is taken from."

This is not a complete sentence.

6a. My understanding is that the given frequency equation is only applicable to the op-amp configuration. Is that the case?

6b. If the circuit has 1 or 2 RC circuits, what does the equation become? Does having 2 RC circuits turn the square root of 6 into a square root of 4 for instance?

ICE77 (talk) 00:40, 12 August 2015 (UTC)


 * 2. The phase shift of each RC section increases smoothly with frequency from 0° at DC to 90° at infinite frequency. The inverting amplifier provides 180° phase shift, so to satisfy the Barkhausen criterion, at the oscillation frequency the RC network must provide the other 180°.  Two cascaded RC sections approach 180° phase shift at very large (infinite) frequency, but to achieve 180° at a finite frequency requires at least three sections.  So phase shift oscillators can be built with 3 or more RC sections.  With 3 sections each section provides (an average of) 60° phase shift.  I read somewhere that 4-section circuits were also used, and they provide better frequency stability. I will try to find that reference.  I would think that each additional RC section increases the attenuation of the feedback loop, requiring more gain in the amplifier to compensate. The 3 section oscillator already requires a large gain of 29, so that may be why circuits with more than 3 sections are rarely heard of.
 * 3. I don't understand that sentence; it doesn't appear to make sense. The 3 RC section feedback network has an attenuation (gain) of 1/29, it reduces the sine wave amplitude by that factor, so the amplifier has to have a gain of 29 to increase the signal back up to its original level to give a loop gain of unity.  It will need at least that much gain to start up.  Feedback oscillators are normally designed with excess gain, to ensure they will start up quickly even if the component values drift.  So I would think the circuit would need substantially more than a gain of 29 to start up.
 * 6a. That frequency equation assumes (a) the source resistance, that is the output resistance of the amplifier, is very small, negligible compared to the impedance of the input resistor and capacitor, C3 and R3, and (b) the load resistance, that is the input resistance of the amplifier, is similarly very large compared to the value of C1 and R2, so it can be neglected. These are good assumptions for the op amp, assuming R1>>R3.  For a transistor amplifier they might not be, as the output resistance of a transistor can be several kilohms.  The assumption of low source and high load resistance should probably be mentioned with the equation in the article.
 * 6b. See 2. above

Chetvorno, thank you again for the useful information (you didn't sign yourself but I can tell it's you). :)

2b. Based on your comment it sounds as if the only practical implementation of the oscillator has 3 RC sections.

3. What I am asking is whether -Rfb/R1 is the equation for the gain in this case so that Rfb can be 29kΩ and R1 can be 1kΩ. I am also questioning why use two different ranges to make sure the oscillator works if a minimum of gain of 29 is necessary.

Here's another question with a circuit and some waveforms.

7. I have been trying to simulate this circuit without any success:

https://en.wikipedia.org/wiki/Phase-shift_oscillator#/media/File:RC_phase_shift_oscillator.svg

I then tried with this circuit and I was able to get some waveforms that I a trying to interpret:

http://www.play-hookey.com/oscillators/audio/images/phase_shift_oscillator.gif

Clearly, the first circuit has 2 grounded resistors and it looks like an RC high-pass filter chain whereas the second has 3 grounded capacitors and it looks like an RC high-pass filter chain.

What is the difference between the two circuits? I think they look dual of each other with R1 being at virtual ground replaced by a C that goes to ground and C3 being replaced by an R that goes to the same point, the output of the op-amp.

ICE77 (talk) 03:09, 14 August 2015 (UTC)

3. and 7. I re-simulated the circuit shown here: https://en.wikipedia.org/wiki/Phase-shift_oscillator#/media/File:RC_phase_shift_oscillator.svg. I must agree with Chetvorno that the gain must be more than just 29. In fact, in PSpice A/D I can only get oscillation with a gain of no less than 46. This is with C=1nF, R=1kΩ and Rfb=46kΩ. Since the equation for Rfb is not sourced I think it should be removed. Simulation proves the gain cannot be just 29 and the calculated frequency would have to be 41.666kHz (according to the oscillation frequency equation) but the simulation shows 64.964kHz. Also, it would be nice if the image for the op-amp implementation had actual values and they were proven in simulation.

ICE77 (talk) 05:21, 21 September 2020 (UTC)

3. and 7. I finally found a good example: https://www.electronics-tutorials.ws/oscillator/rc_oscillator.html. It has some numeric values but I tried some of my own. I can force oscillation with a gain of 28 with Rfb=280kΩ and R=10kΩ so it's not true that a gain of at least 29 is required. I used C=1nF and the frequency is about 6kHz. I also found the missing source for the frequency equation and that square root of 6 is actually a square root of 2 * N where N is the number of RC stages. This answers my 6b question from 2015.

ICE77 (talk) 06:53, 24 September 2020 (UTC)

Reference 3 Link
Op Amps for everyone link does not work. Correct Link: https://focus.ti.com/lit/an/slod006b/slod006b.pdf — Preceding unsigned comment added by 103.225.103.68 (talk) 17:30, 26 March 2017 (UTC)


 * fixed. Glrx (talk) 17:47, 26 March 2017 (UTC)