# RC phase shift oscillator : how to give positive feedback?

why is negative feedback given in a rc shift oscillator although a oscillator requires a positive feedback? as shown in this figure. And as shown here positive feedback is given by connecting the positive input terminal to output terminal,which is contradicting to the earlier figure. Please explain this disparity. Thank You.

Your premise is incorrect: "a oscillator requires a positive feedback".

There are two requirements for an amplifier circuit to oscillate:

1. The overall ("loop") feedback must be 0 degrees ( or a multiple thereof, e.g. 360, 720 degrees).

2. There must be enough overall gain to start & sustain oscillation. (This is sometimes states as "The loop gain must be greater than 1.")

The prior commentor suggested: "the signal will have been inverted once more by the RCs". Not true. RC networks cannot "invert" a signal. They can only delay or phase shift it. For practical purposes phase shifting a signal by 180 degrees is nearly equivalent to "inverting" the signal because true inversion ( as thru an inverting amplifier) also results in a virtual phase shift of 180 degrees - but only for symetrical waveforms like sine waves, triangle wave and square waves, but not for complex waves like musical notes and voice signals. Be mindful of this distinction when analyzing oscillators and amplifiers.

One RC network can phase shift a sine wave by 0 to 90 degrees. In the act of phase shiting the signal it also reduces the amplitude of the signal. Since 90 degrees phase shift is at the outer limits of an RC's phase shifting ability, we can't use just two RCs. So, we stack three RC networks in series and allow each to contribute 60 degrees of phase shift, for a total phase shift of 180 degrees ( but at only one specific frequency!). These three series-connected RC networks will also attentuate the signal signifcantly at the specific frequency. That attentuation has to be made up in the gain of the amplifier in order to meet the oscillation requirement #2 of having a loop gain greater than 1.

It's also possible to make oscillators using 4,5,6 or more series connected RC's. But there's usually no good reason to take this design approach.

The inversion of the amplifier provides the other 180 degrees of "phase shift". So we have a total loop feedback of 360 degrees or 0 degrees, depending on how you look at it. Either case will meet oscillation requirement #1.

By the way, these RC oscialltors are not very good at making pure sinusoidal outputs. To get the most-sinusoidal-like output you must keep the gain of the amplifier itself low enough so it just exceeds that necessary to maintain oscillation (i.e. 1.000) . Make it too high and the output will be a clipped sine wave, often approaching a square wave in appearance. Experiment with the gain to get both a near sinusoidal output and ensure the oscillator will start reliably. The lower the amplifier's gain, the slower and less reliably the oscillator will properly start up. Power the oscillator on and off a number of times to ensure it will reliably start every time power is applied. It's also a good idea to observe the envelope of the oscillation on an oscilloscope as you apply power to the circuit. You should see a nice exponential increase of the envelope starting immediately at power application, with no drop-outs or squiggles.

• I think, your premise is correct: "a oscillator requires a positive feedback". A loop gain of "+1" is possible with oberall positive feedback only. – LvW May 5 '14 at 6:37

The feedback signal passes through all the RC networks: - By the time it reaches the inverting input, the signal will have been inverted once more by the RCs. Each RC (on average) adds 60 degrees phase shift at one particular frequency so, at only one particular frequency, will the system oscillate.

• This circuit looks a bit uncommon - however, it works. Explanation: In a "classical" C-R phase shift oscillator the last R is NOT connected to ground but at the invereting opamp input - thus enabling normal inv. amplifier operation. In contrast, in the present circuit this resistor between the inv. input and ground can be OMITTED (remember the principle of virtual ground). In this case, the opamp does NOT work as an inverting amplifier (with a gain of -29) but as an inv. differentiator (phase shift -90 deg). That means, the total phase shift of the remaining two C-R sections is only +90 deg. – LvW May 5 '14 at 6:52
• @lvw I totally agree dude that's why I said average phase shift is 60 degrees because I considered that a slightly dumbed down answer is more useful to the op. AFAIK, I've never seen this modified version of this oscillator either and yes, the final resistor is redundant. – Andy aka May 5 '14 at 9:42
• Yes - this modification is seldom used - however, it is not bad at all. As another example, the known RC lowpass phase shift oscillator can be modified if the last RC section - together with the inverting amplifier - is replaced by an inverting integrator. Similarly, here the last CR highpass section (together with the inverter) can be replaced by a differentiating circuit. – LvW May 5 '14 at 12:44

@user41340: To answer your question: "Positive feedback" does not necessarily mean that the non-inv. opamp input terminal is connected to the feedback path. For example, there are opamp based circuits with negative feedback and phase inversion WITHIN the feedback path.

In the present case, we have such a phase shift within the feedback path - and because we need POSITIVE feedback we have a connection to the inverting input node.

The last circuit as shown is a modification of the classical phase shift oscillator (which needs an inverting gain of -29). Here we have replaced the last C-R highpass section by an inverting DIFFERENTIATOR (the R between neg. input and ground can be omitted, it has no influence). This part of the circuit contributes -90 deg to the overall phase shift.

As a consequence, the remaining two C-R sections must contribute in total +90 deg. Thus, there is one single frequency for which we have positive feedback with a total phase shift of zero deg within the loop. This is the osillation frequency. Does this answer your question?