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Anonymous Poster #1

RC Phase Shift Oscillator Theory

09/26/2011 11:07 AM

Hello friends when i tried to understand RC phase shift oscillator its principle of starting oscillation is like this "the random variation of base current caused by noise variations in the transister and voltage variations in the power source produce oscillation". Can anyone explain me it just like LC (simple) oscillation.

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Associate

Join Date: Aug 2011
Posts: 40
Good Answers: 4
#1

Re: RC Phase Shift Oscillator Theory

09/26/2011 8:48 PM

Hi One & All,

RC Oscillator

The RC Oscillator

In the Amplifiers tutorial we saw that a single stage amplifier will produce 180o of phase shift between its output and input signals when connected in a class-A type configuration. For an oscillator to sustain oscillations indefinitely, sufficient feedback of the correct phase, ie "Positive Feedback" must be provided with the amplifier being used as one inverting stage to achieve this. In a RC Oscillator the input is shifted 180o through the amplifier stage and 180o again through a second inverting stage giving us "180o + 180o = 360o" of phase shift which is the same as 0o thereby giving us the required positive feedback. In other words, the phase shift of the feedback loop should be "0".

In a Resistance-Capacitance Oscillator or simply an RC Oscillator, we make use of the fact that a phase shift occurs between the input to a RC network and the output from the same network by using RC elements in the feedback branch, for example.

RC Phase-Shift Network


The circuit on the left shows a single resistor-capacitor network and whose output voltage "leads" the input voltage by some angle less than 90o. An ideal RC circuit would produce a phase shift of exactly 90o. The amount of actual phase shift in the circuit depends upon the values of the resistor and the capacitor, and the chosen frequency of oscillations with the phase angle ( Φ ) being given as:

Phase Angle

In our simple example above, the values of R and C have been chosen so that at the required frequency the output voltage leads the input voltage by an angle of about 60o. Then the phase angle between each successive RC section increases by another 60o giving a phase difference between the input and output of 180o (3 x 60o) as shown by the following vector diagram.


Then by connecting together three such RC networks in series we can produce a total phase shift in the circuit of 180o at the chosen frequency and this forms the bases of a "phase shift oscillator" otherwise known as a RC Oscillator circuit.

We know that in an amplifier circuit either using a Bipolar Transistor or an Operational Amplifier, it will produce a phase-shift of 180o between its input and output. If a RC phase-shift network is connected between this input and output of the amplifier, the total phase shift necessary for regenerative feedback will become 360o, ie. the feedback is "in-phase". Then to achieve the required phase shift in an RC oscillator circuit is to use multiple RC phase-shifting networks such as the circuit below.

Basic RC Oscillator Circuit


The RC Oscillator which is also called a Phase Shift Oscillator, produces a sine wave output signal using regenerative feedback from the resistor-capacitor combination. This regenerative feedback from the RC network is due to the ability of the capacitor to store an electric charge, (similar to the LC tank circuit). This resistor-capacitor feedback network can be connected as shown above to produce a leading phase shift (phase advance network) or interchanged to produce a lagging phase shift (phase retard network) the outcome is still the same as the sine wave oscillations only occur at the frequency at which the overall phase-shift is 360o. By varying one or more of the resistors or capacitors in the phase-shift network, the frequency can be varied and generally this is done using a 3-ganged variable capacitor.

If all the resistors, R and the capacitors, C in the phase shift network are equal in value, then the frequency of oscillations produced by the RC oscillator is given as:

  • Where:
  • ƒ is the Output Frequency in Hertz
  • R is the Resistance in Ohms
  • C is the Capacitance in Farads
  • N is the number of RC stages. (in our example N = 3)

Since the resistor-capacitor combination in the RC Oscillator circuit also acts as an attenuator producing an attenuation of -1/29th (Vo/Vi = β) per stage, the gain of the amplifier must be sufficient to overcome the losses and in our three mesh network above the amplifier gain must be greater than 29. The loading effect of the amplifier on the feedback network has an effect on the frequency of oscillations and can cause the oscillator frequency to be up to 25% higher than calculated. Then the feedback network should be driven from a high impedance output source and fed into a low impedance load such as a common emitter transistor amplifier but better still is to use an Operational Amplifier as it satisfies these conditions perfectly.

The Op-amp RC Oscillator

When used as RC oscillators, Operational Amplifier RC Oscillators are more common than their bipolar transistors counterparts. The oscillator circuit consists of a negative-gain operational amplifier and a three section RC network that produces the 180o phase shift. The phase shift network is connected from the op-amps output back to its "non-inverting" input as shown below.

Op-amp RC Oscillator Circuit

As the feedback is connected to the non-inverting input, the operational amplifier is therefore connected in its "inverting amplifier" configuration which produces the required 180o phase shift while the RCnetwork produces the other 180o phase shift at the required frequency (180o + 180o). Although it is possible to cascade together only two RC stages to provide the required 180o of phase shift (90o + 90o), the stability of the oscillator at low frequencies is poor.

One of the most important features of an RC Oscillator is its frequency stability which is its ability too provide a constant frequency output under varying load conditions. By cascading three or even four RCstages together (4 x 45o), the stability of the oscillator can be greatly improved. RC Oscillators with four stages are generally used because commonly available operational amplifiers come in quad IC packages so designing a 4-stage oscillator with 45o of phase shift relative to each other is relatively easy.

RC Oscillators are stable and provide a well-shaped sine wave output with the frequency being proportional to 1/RC and therefore, a wider frequency range is possible when using a variable capacitor. However, RC Oscillators are restricted to frequency applications because of their bandwidth limitations to produce the desired phase shift at high frequencies.

Example No1

Determine the frequency of oscillations of a RC Oscillator circuit having 3-stages each with a resistor and capacitor of equal values. R = 10kΩ and C = 500pF

The frequency of oscillations for a RC Oscillator is given as:

The circuit is a 3-stage oscillator which consists of three 10kΩ resistors and three 500pF capacitors therefore the frequency of oscillation is given as:


In the next tutorial about Oscillators, we will look at another type of RC Oscillator called a Wien Bridge Oscillators which uses resistors and capacitors as its tank circuit to produce a low frequency sinusoidal waveform.

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BEN

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Guru

Join Date: May 2007
Location: Geelong, Australia
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Good Answers: 54
#2

Re: RC Phase Shift Oscillator Theory

09/26/2011 10:34 PM

If there is enough gain in the circuit the noise, which contains the frequency of interest, in the circuit will be sufficient to kick start the oscillator.

If it doesn't start reliably increase the (positive feedback) gain.

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Guru

Join Date: Jan 2008
Posts: 1756
Good Answers: 59
#3

Re: RC Phase Shift Oscillator Theory

09/27/2011 12:43 AM

There is no "simple oscillator", except in theory. That is why - even today - there is plenty of literature, and product development there.

But the bare bones basics are the same in all. You need frequency determining element, and amplifier. Together, they provide 360deg. phase shift and amplification larger than 1 at the oscillation frequency. It does not matter, how you get there.

Obviously, the normal starting point is with thermal noise in any existing current. Averaging, any and all frequency present in frequency domain. Viewing the same in time domain, impulse noise is present to excite the frequency establishing element(s). Amplification and feedback, then magnifies the components selected by the frequency selective components. With external excitation, impulse excitation is quite frequent.

You may have noticed by now, that I did not present a separate theory for this or that oscillator, because there is none. But the descriptive language varies by discipline. An aerodynamic oscillation, a mechanical pendulum, a bridge's swinging or a chemical oscillation should not be described in the abstract alone, to make it understandable in the particular discipline.

Yo will not find a "single" explanation for oscillators in the details, and I do not see why you should, either.

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Anonymous Poster #1
#4

Re: RC Phase Shift Oscillator Theory

09/27/2011 9:06 AM

Thanks for the lecture but i was expecting the reason for the initial cause of oscillation.There should be some storing and discharging followed by switching and feedback.

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Guru

Join Date: Jan 2008
Posts: 1756
Good Answers: 59
#5
In reply to #4

Re: RC Phase Shift Oscillator Theory

09/27/2011 9:56 AM

Yes, and you are perfectly capable doing it. Go for it!

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Power-User

Join Date: Jan 2009
Posts: 225
Good Answers: 7
#6

Re: RC Phase Shift Oscillator Theory

09/27/2011 12:29 PM

Hi AnPos1,

as pointed out by ben1son1, the circuit will sustain an existing oscillation, i. e., have hen, will have eggs etc.

The noise (not "noise variations"; "noise" is a random variation, usually with a small amplitude, but it's always there) is like a very small egg, which will be amplified (your ckt must have gain>1). Little hen, a little bigger eggs, and so on.

brgds

Snel

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Active Contributor

Join Date: Jun 2011
Posts: 17
Good Answers: 2
#7

Re: RC Phase Shift Oscillator Theory

09/27/2011 5:18 PM

AP1, everything written above is OK, but I think you wanted to know this:

In order to sustain oscillations the active components (amplifiers) must be employed in order to provide for the energy lost in the passive components, so that the system's poles (the inverse of the characteristic time constants) are placed exactly on the imaginary axis of the complex plane. Think of the complex plane as the imaginary axis being associated with reactive components (L,C), the negative real axis with resistance (energy dissipating components) and the positive real axis associated with "negative resistance", i.e., generators (amplifiers). If the losses within the circuit are compensated the oscillator will run at a constant amplitude. In a system where the losses prevail, the oscillator will exhibit damped oscillations after power switch on; if the added energy prevails, the amplitude will increase exponentially up to the supply rails.

What an oscillator does at startup is to increase the loop gain slightly above unity, so that any signal at the amplifier's input (thermal noise, or a power-on transient) gets amplified and the larger signal is returned at the input suitably phase shifted so that it is amplified again, and again, and so on. The amplitude increases exponentially, until the amplitude stabilization circuit kicks in and reduces the loop gain to unity or slightly below, so that the output amplitude stabilizes. Well designed oscillators will settle to a constant amplitude within a few periods; not so good ones can modulate the amplitude up and down at a frequency much lower than that of the circuit is oscillating at and set after seconds, or even exhibit low frequency amplitude modulation permanently.

A well designed amplitude regulation circuitry is actually a critically damped oscillator itself, an oscillator within an oscillator, but with losses tuned so that the amplitude settles to a constant peak level as quickly as possible.

Hope this helps.

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