# RC Phase Shift Oscillators

#### Mazaag

Joined Oct 23, 2004
255
Hey guys,
I wanted to know a bit more on RC Phase Shift Oscillators when I came across this website.. :

http://www.aikenamps.com/PhaseShiftOscillators.html

Under the " How do they work? " section , there is a sentence that reads as follows :

"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). "

I don't quite see why we need a gain higher than unity and a total phase shift of 360 degrees... could someone elaborate and explain that sentence ? ( probably an explanation on positive feedback and how it results in oscillations)

Thanks Guys..

#### hgmjr

Joined Jan 28, 2005
9,027
.....I don't quite see why we need a gain higher than unity and a total phase shift of 360 degrees... could someone elaborate and explain that sentence ? ( probably an explanation on positive feedback and how it results in oscillations)....
The gain must be greater than unity to overcome the signal losses that will occur as it passes through the feedback network. The 360 degrees of phase shift is needed to satisfy the positive feedback requirement of the oscillator.

In a properly designed oscillator, these two conditions will usually be met at a specific frequency. This frequency is the one at which the oscillator will operate.

hgmjr

#### Mazaag

Joined Oct 23, 2004
255
What I don't understand is , how is the 360 degree phase shift related to positive feedback..? and why is it a requirement for oscillation.

#### hgmjr

Joined Jan 28, 2005
9,027
The term "positive feedback" simply means that the feedback signal is in phase with the input signal. Hence the signal must undergo a delay that is equivalent to one complete cycle at the frequency of the oscillator.

The amplifier inverts the signal which accounts for 180 degrees of the phase shift and the feedback network accounts for the remaining 180 degrees.

In the case of the example circuit you cited, the three RC integrators (if composed of identical components) each contributes 60 degrees to the overall phase shift at the frequency of oscillation. The result is the required 360 degrees needed to produce the oscillation.

You might think of the process as similar to manually keeping a pendulum swinging. You instinctively know that you must wait until the pendulum is at its peak before giving it a sustaining push. You will also know that you must replace the energy lost since the last time you gave it a push in order to keep it swinging through the same arc.

hgmjr

#### Mazaag

Joined Oct 23, 2004
255
Could you please explain to me how each stage contributes 60 degrees phase ? does the shift in phase depend on the frequency..? i'm confused...:S

#### hgmjr

Joined Jan 28, 2005
9,027
Not to worry. Confusion frequently accompanies the learning of a new concept.

does the shift in phase depend on the frequency..?
Yes. The shift in phase does depend on frequency.

Could you please explain to me how each stage contributes 60 degrees phase ?
Using the oscillator in the link you supplied as the circuit under dicussion, I should make clear that each RC stage contributes its portion toward the overall phase shift. This phase shift contribution by each RC stage is 60 degrees only if the feedback network is made up of three identical RC stages.

I call your attention to the plot that is included in the write-up at the link you provided. You will see that the y-axis is marked off in degrees of phase shift and the x-axis is a logarithmic plot of frequency. Set aside the blue and yellow traces for the moment as they relate to the phase-lead configuration. You will see that one of the phase-lag plots (the red trace) starts at zero frequency with a phase-shift of zero degrees and as the frequency increases the phase shift which is negative indicating delay increases to a value of -90 degrees. It never quite reaches -90 degrees, it just approaches -90 degress. The green trace is a different RC phase-lag stage. It goes through the same change but does so at a different rate due to the fact that is it made up of a different values of R and C. This limitation of the phase-lag RC circuit to -90 degrees is the reason that it takes more than two RC stages to accomplish the total -180 degrees.

By performing this plot for each of the three RC stages in the oscillator design, it is possible to predict the frequency of oscillation by summing the phase shift of all three RC stages at each frqeuency and noting at which frequency the three sum to 180 degress or in the phase lag case -180 degrees.

I think you would benefit by studying more material on RC circuits such at the material that is available on the AllAboutCircuits tutorial website. This would give you a stronger foundation for you to use in your study of oscillators.

hgmjr

#### Audioguru

Joined Dec 20, 2007
11,248
The RC networks load each other. That affects the loss of each one and the frequency of each one. If each RC network has a buffer stage between them then they won't load each other, the frequency will be easy to calculate and the gain of the opamp must be only a little more than 3.

Spice does not start an oscillation without some kind of kick.

#### JoeJester

Joined Apr 26, 2005
4,390
Spice will start oscillations if you tell it to start with zero initial values ... or you can set the initial conditions.

Starting with zero initial values is like throwing on the power switch.

#### The Electrician

Joined Oct 9, 2007
2,952
The RC networks load each other. That affects the loss of each one and the frequency of each one. If each RC network has a buffer stage between them then they won't load each other, the frequency will be easy to calculate and the gain of the opamp must be only a little more than 3.
In this case, the gain needs to be 8.

#### Audioguru

Joined Dec 20, 2007
11,248
In this case, the gain needs to be 8.
You are correct. I was wrong because I was thinking about a Wien Bridge oscillator.

Texas Instruments has a pretty good article about sine-wave oscillators.

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#### The Electrician

Joined Oct 9, 2007
2,952
I've seen that article and it's pretty good. But in connection with the phase shift oscillator, he says on page 16 "...the usual assumption is that the phase shift sections are independent of each other." I don't think that "usual" at all. How many times have you seen phase shift oscillators where the design has independent buffers for each section? If you search on the web, you'll find that most don't. I think his bias (Mancini works for TI, and they make quad op amps) is showing.

#### Audioguru

Joined Dec 20, 2007
11,248
The phase-shift oscillator made by Texas Instruments has its third RC stage loaded down the the input impedance of the inverting opamp. Therefore its gain is a little higher than 8 and its frequency is a little off.

I made a phase-shift oscillator with buffers between the stages and an extra buffer for the third RC stage and it works better.

#### The Electrician

Joined Oct 9, 2007
2,952
The phase-shift oscillator made by Texas Instruments has its third RC stage loaded down the the input impedance of the inverting opamp. Therefore its gain is a little higher than 8 and its frequency is a little off.

I made a phase-shift oscillator with buffers between the stages and an extra buffer for the third RC stage and it works better.
In what sense does it work better? More stable output frequency? Lower distortion?

#### digitalenigma

Joined Apr 11, 2008
11
Thanx for the excellent TI article. That was extremely helpful

~D