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How do Sinusoidal output comes out in the Wein-Bridge Oscillator

  1. Jun 29, 2013 #1
    This question was asked to me in a VIVA.

    What examiner asked.

    How do Sinusoidal output comes out in the Wein-Bridge Oscillator.

    ............

    I tried to solve the problem using the control system. That is, by deriving the transfer function of the Wein-Bridge Oscillator, but first i got confused on where to take the input as there is no input and oscillators work due to noise input(this is what written in the books). Then i assumed the input to be the negative Op-Amp terminal, this time the confusion was on what function the input Voltage should be?

    I have studied two Sinusoidal Oscillators, another one is phase-shift oscillators, and I don't know the 'How' of Phase-Shift oscillators also. The book i follow is Sedra-Smith and doesn't say anything about the 'How' behind the generation of Sinosoidal output. I have one more book on Op-Amp Circuits and nothing is written about it this in that book also.
     
  2. jcsd
  3. Jun 29, 2013 #2

    NascentOxygen

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    The input to the passive network is the output of the op-amp. :smile: As far as the transfer function goes, you need the combination to give 2.Pi radians of phase shift at a gain of just over unity, at some frequency, for oscillations to be self-sustaining.

    I suggest that you include a scan of the particular circuit you have in mind, if you have further questions.
     
  4. Jun 29, 2013 #3
    This is the Circuit, the wein-bridge oscillator.

    1.gif

    I know the two conditions that you just told. This is the only two things that we have studied about oscillators. Which comes from Av*β = 1
    1. β is real.
    2. ∠ Av*β = 2n∏

    I derived the Transfer function taking non-inverting input as the input, but the question is how does the Sine wave comes out. Without knowing input i can't predict the output.
     
  5. Jun 30, 2013 #4

    NascentOxygen

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    The potential divider at the - input sets the gain of the amplifier stage (the OP-AMP), at a value that just makes up for the attenuation of the passive Wein bridge, restoring loop gain to 1. Input to the bridge comes from the output of the OP-AMP. Output of the bridge is seen at the - input of the OP-AMP.

    So long as the loop gain is not much over 1 where phase shift is 2 Pi, and this condition is not met at another frequency, the system noise will develop into a self-sustaining sinusoidal oscillation within a short period of time. The more loop gain you allow, the wider the band over which feedback can give sustained oscillation, and the more frequency components you introduce into your signal, meaning it starts to depart from a pure sinusoid. :smile:
     
  6. Jun 30, 2013 #5
    That means the principal of operation is same as that of a square-wave generator and monostable multivibrator. I understood this part.

    Why sinusoid?. I mean when we study the square wave generator(whose working is similar to this), we derive how output comes out to be the square wave.


    Again same question, why. Isn't there a General output Voltage as function of time and Circuit components as in the case of square wave generator?
     
  7. Jun 30, 2013 #6

    NascentOxygen

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    It's a linear amplifier/network, with a loop gain great enough at only one frequency to stop oscillations dying out. A squarewave can't leap out of nowhere in a linear system. Squarewaves originate from abrupt non-linearities, there are none here.
     
  8. Jun 30, 2013 #7
    So you mean there is no proof for the Sinosiodal output. Is is just an observed fact?
     
  9. Jun 30, 2013 #8
    Output signal is a sinewave because only for this one frequency wein-bridge and the amplifier meets the conditions necessary to start oscillations.
     
  10. Jun 30, 2013 #9
    We assume that the output is Sine wave that is wave we put s=jω. Putting s = jω is only true for sinusoidal transfer functions. My question is why do we assume the output to be sinusoid?
     
  11. Jun 30, 2013 #10
    "Wein network" work as a highly selective bandpass filter. So even if you put square wave ta the input the output voltage will be sinusoidal. So the op amp input will see a sine wave at his non-inverting input. And next the amp will amplifier this sine wave 3x times. So the output also will be sinusoidal. Because just for one single frequency F = 1/(2 * pi RC) circuit meets conditions necessary to start oscillations.

    On the other hand in multivibrator we have a all pass filter network so for all frequancy circuit meets the conditions necessary to start oscillations. And this is why we have a square wave output.
     
    Last edited: Jun 30, 2013
  12. Jun 30, 2013 #11

    sophiecentaur

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    For some reason you keep ignoring the explanation you are being given. The feedback is only 'right' at one frequency so no other frequencies will be sustained - that makes the output a single frequency with no harmonics (i.e. a sine wave).
    PS In general, it's pretty fruitless to question why the (well established) analysis of a common system happens to be done in a particular way. Science and Maths is full of apparently arbitrary approaches to solving problems - which just happen to work. Very annoying until you know the particular crafty dodge. Why do you divide both sides of an equation by the coefficient of x (etc. etc.)? Because you know it will work. Why do you try a sinusoidal solution to this sort of problem? Because you know it works. :smile:
     
  13. Jun 30, 2013 #12

    NascentOxygen

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    It's a second order linear system, and the natural response of every second order system is a sinusoid, just as you see in a child's swing. Give it a jolt and it adopts SHM; give this filter/amplifier system a voltage jolt at switch-on, and it responds with SHM. The sinusoid doesn't decay away because of accurately setting the loop gain to just sustain the response.
     
  14. Jun 30, 2013 #13

    NascentOxygen

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    The principal of operation of a square-wave generator, and of a sinusoidal oscillator, are totally different. Granted, superficially their schematics may sometimes bear a resemblance, but one is highly non-linear, and the other very linear. The two are horses of a different colour!
     
  15. Jul 1, 2013 #14
    A second order linear system. If you could tell me where did you get this from.
     
  16. Jul 1, 2013 #15
    I am not ignoring that explanation. Okay the feedback is right at only one frequency-agree. Then you say feedback is right at only one function(sine wave). How do match these two things-frequency and function. I mean the output could have been a different function with the same frequency!
     
  17. Jul 1, 2013 #16

    sophiecentaur

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    Yes, but the phase and amplitude characteristic of the feedback in this oscillator is such that only one component of your hypothetical waveform would satisfy the requirement for oscillation. There is only one function that has one frequency component and that is a sinewave. The amplifying device in this sinewave oscillator needs to be linear so you can use superposition and treat signals of all possible frequencies independently. When you have a non-linear amplifying device, other waveforms may result - but the same thing could happen if you followed the nicely sinusoidal Wien Bridge with a non linear amplifier.
    In practice, of course, there will be a certain amount of harmonic content, even in the Wien Bridge output.
     
  18. Jul 1, 2013 #17

    NascentOxygen

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    It's from mathematics. Differential equations, etc., it's all a part of physics. The current through a capacitor is determined by the derivative of the voltage across it, and so on.
     
  19. Jul 1, 2013 #18
    I am pretty okay at maths and physics. The EE curriculum at my university is quite mathematical. For me understanding circuits with mathematical equation is the easiest method. I mean this is way we are taught circuits at our University. So if you could tell me those Differential equations describing wein-bridge oscillator, i would be very keen to solve those myself.
     
  20. Jul 1, 2013 #19

    sophiecentaur

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    I googled "wein bridge oscillator analysis". Did you try that? You get loads of hits with treatments at various levels of difficulty. I suggest you look at them. It's a far more efficient way of learning than just asking questions and getting off - the - cuff answers, many of which will come straight off the net as people refresh their memories of stuff they knew quite well in the past.
     
  21. Jul 1, 2013 #20
    Why are the phase and amplitude characteristics satisfying only sine function? If you could go into some mathematical proof, that would be easier for me to understand.


    And finally we assume it to be linear. I don't understand why this are assumptions is made. Not many Op-Amp circuits are linear, including the square generator, comparator, monostable multivibrator. I will definitely agree that this circuit is linear just because you and others saying this. I just want to know how do we came to conclusion that this is linear.
     
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