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Wien Bridge Oscillator analysis

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CataM

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I am trying to re-draw this Wien Bridge Oscillator to find out the open loop gain and the feedback "β" but I do not see how. I am unable to see which is the open loop gain "A" and the feedback network.

How would it be drawn regarding the general feedback scheme:


The circuit is this one:
 

A Wien bridge oscillator usually uses capacitors, not inductors.
Open loop gain is not used for any of the calculations because at low frequencies the gain of an opamp is almost infinity, the closed loop gain is slightly more than 3.
An AGC circuit is used to keep the output from saturating.
 

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I am trying to re-draw this Wien Bridge Oscillator to find out the open loop gain and the feedback "β" but I do not see how. I am unable to see which is the open loop gain "A" and the feedback network.

How would it be drawn regarding the general feedback scheme:


The circuit is this one:

The ideal Op Amp has infinite open loop gain, and practical gains are 1e6
The feedback gain has two loops. Stable sinusoidal oscillation ONLY occurs the positive feedback matches the negative feedback givning a linear output and a near zero differential input. For both loops this feedback ratio is 1/3 . The difference between the positve input gain and the negative input gain is 1+Av -Av =1 or unity gain. In practise this gain is critical so nonlinear gain or soft limiters or AGC (ref Audioguru's comment) is used to prevent clipping or under unity decay of oscillation.

In practise it works but with limitations on stability, amplitude control or distortion, so improved designs exist.
 
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I am trying to re-draw this Wien Bridge Oscillator to find out the open loop gain and the feedback "β" but I do not see how. I am unable to see which is the open loop gain "A" and the feedback network.
How would it be drawn regarding the general feedback scheme:

1.) At first, replace L with C in order to realize an RC bandpass
2.) With respect to your "general feedback scheme":
A=3 (in practice: slighly above 3) and β=1/3.
3.) An oscillator does not need an input signal (in your model: Set signal source Vs=0)
 
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I forgot to mention that my last post (β=1/3) applies to the oscillation frequency only.
In general, the feedback factor is frequency-dependent (RC-bandpass function).
 
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A Wien bridge oscillator usually uses capacitors, not inductors.
Open loop gain is not used for any of the calculations because at low frequencies the gain of an opamp is almost infinity, the closed loop gain is slightly more than 3.
I forgot to mention that my last post (β=1/3) applies to the oscillation frequency only.
In general, the feedback factor is frequency-dependent (RC-bandpass function).

Ok then, using Wien bridge oscillator of Audioguru, A=3 and β=1/3 when oscillating. How did you know with what loop to calculate that "A=3" (you used 1+20/10 I assume which is the loop feed back to the negative input) ?

How do I find the A(jω) and β(jω) expressions ? I mean, having 2 loops that feed back(one goes to the - input and other one to + input of the OP amp), which one is the β network and which one is used for the gain calculation ? (the one with RC or the one with only resistors?)

In other words, what are my Vf and Vi in the following picture?

That picture comes from https://en.wikipedia.org/wiki/Barkhausen_stability_criterion and is the simple Barkhausen criterion.
 

It is quite simple:
The WIEN RC-network with equal componenets (R1=R2 and C1=C2) is a bandpass with a miaximum gain of 1/3 at the mid frequency w=1/RC.
Hence, according to the oscillation criterion you need a gain stage with a closed-loop gain of Acl=1+R2/R1=3
For a safe start-up at t=0 the gain should slightly larger (app. 3.1....3.2).
 
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Of course ß and ß*Aol can be calculated for the original RL circuit as well, using elementary AC network theory.
 

The gain of the Wien bridge oscillator must be slightly more than 3 because the two RC filters have a phase shift that causes a signal loss of 3 times.
Here is a simulation of the simple bandpass filter showing the signal loss of 3 times:
 

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Of course ß and ß*Aol can be calculated for the original RL circuit as well, using elementary AC network theory.
"ol" refers to open loop?

So β(jω)=V+/Vout and A=Vout/V-. Is there any oscillator that has the gain "A" as a function of jω too ?
 

No. As previously mentioned by others, feedback factor is a difference of two terms in this circuit.

ß = V+/Vout - V-/Vout = jωL*R/(-ω²L² + 3*jωL*R + R²) - R1/(R1+R2)

Aol is the OP open loop gain, Aol = Vout/(V+ - V-)
 
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Using a Wien Bridge Oscillator, it is possible to set a oscillating frequency more than 300 kHz ? Or in what range of oscillating frequencies could be used a Wien Bridge ?

To get big oscillating frequencies should I use another type of capacitors (MICA for example ? ) or it just works with simple ceramic cap's ?
 

Using a Wien Bridge Oscillator, it is possible to set a oscillating frequency more than 300 kHz ? Or in what range of oscillating frequencies could be used a Wien Bridge ?
To get big oscillating frequencies should I use another type of capacitors (MICA for example ? ) or it just works with simple ceramic cap's ?

Of course, each deviation of actual parts values from nominal values as well as each parasitic property of the parts will cause a deviation from the desired oscillation frequency.
This also applies to deviations from the ideal gain value of the active unit.
For an oscillation frequency of 300kHz the used opamp should have a transit frequency (gain-bandwidth product GBW, frequency where the open-loop gain Aol is 0 dB) which is at least larger by a factor of 20.
(That is: GBW=6...10 MHz). Otherwise, the parasitic phase shift of the opamp creates frequency errors.
 
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