Oscillation criterion (barkhausen)

Discussion in 'Homework Help' started by favner85, Feb 27, 2013.

  1. favner85

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    Nov 4, 2012
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    How can I apply the Barkhausen criterion in order to tell if the following square wave generator(relaxation multivibrator) do oscillates?

    [​IMG]
     
  2. t_n_k

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    I believe the Barkhausen Criteriion applies to linear circuit operation. Given this circuit operates in a highly non-linear limit cycle mode then I doubt one can apply the criterion in any simple manner.

    Perhaps the circuit condition at the point just before oscillation start-up might fall within the scope of the criterion.
     
  3. favner85

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    Nov 4, 2012
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    Yes, I agree with you in that the Barkhausen criterion would apply only before startup but how? We need to relate the VR1 and Vc (voltage at R1 and the voltage of the capacitor, respectively) but how and in what way and why?
     
  4. t_n_k

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    I guess you need to justify in your own mind why in the first instance you agree with me - which implies some understanding of the circuit and its applicability or otherwise to the Barkhausen Criterion concept.

    As to the analysis of the circuit wrt the Criterion, that's the subject of the homework task as you present it. So you might need to show some thinking / working in that regard. The usual approach is to recast the circuit as an open loop equivalent and then derive the transfer function - after which one applies the criterion.

    An interesting & contrasting comparison can be made with the analysis of the op-amp Wein Bridge oscillator which would possibly assist your understanding.
     
  5. favner85

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    You are impliying a lot of things.

    First, I do understand the circuit as shown in the following mathematical developement, which proves I'm not being lazy and just waiting for someone's answer without "showing some work/thinking" as you state it. Also you are implying you already have the answer to this problem, just that you are reluctant to provide it because I'm not "showing some working/thinking" and you even provide a clue onto how to proceed to the solution, this in part gives me some hope that at least it is posible to apply the Barkhausen criterion to this relaxation oscillator and I agree with that since you are employing part of your time helping for free and because you want to help and you don't want to give it to lazy people whom you think doesn't deserve it.

    So as for the understanding of the circuit:
    [​IMG]

    As you see in the analysis I assume a certain steady-state starting point conditions within a cycle, and from there proceed to develop further taking care the previous assumptions are still valid. From my understanding of the Barkhausen criterion this is another way to state it, that is, by making this initial assumptions (even when I've already assumed a steady state condition)

    As for showing some work/thinking
    [​IMG]
    How to proceed next?

    Thank you for your input/help I do really have put working/thinking into this as you can see. (Sorry for my bad grammar, I'm not a native english speaker).
     
    Last edited: Mar 1, 2013
  6. t_n_k

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    It's interesting that one might consider applying Barkhausen to determine oscillating frequency in a linear oscillator model. As you show in your analysis one must consider the non-linear operating model to find the relaxation frequency for this circuit. So Barkhausen is of no use on that score.

    As I noted in an earlier post a typical method of linear analysis involves finding the open loop transfer function. To do this one might break the negative feedback path at some convenient point - say at the amplifier output. The input for the purposes of finding the open loop TF then becomes the break point terminal so formed.

    Also one would treat the amplifier as a finite gain of value A which you can then subsequently consider as tending to an infinite value if that is useful. The "problem" arises in this case with the fractional frequency independent positive feedback.

    What will all this reveal in the end? Certainly not the oscillation frequency. At best one would find the necessary amplifier gain to ensure the output will switch between its limiting states.
     
  7. favner85

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    Now, I don't understand what you are trying to explain. Are you telling me that for this specific circuit is not posible to apply the Barkhausen criterion, that is, the frequency of oscillation for which the phase is 0 or multiples of 360 degrees?

    I'm really getting to nowhere, I'm stuck on this problem.
     
  8. The Electrician

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  9. t_n_k

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    Since your course teacher has presumably set this task for you I don't want to impose a viewpoint which differs to what you are being taught.
    Has your teacher worked through a similar problem which would indicate a preferred method of solution?
    As I implied at the outset - it might be possible to apply the criterion before large scale output signal excursions put the circuit in a highly non-linear operating region. My view is that attempting to apply Barkhausen Criterion is not of any use.
     
  10. t_n_k

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    Nice paper Electrician - thanks for the link.
     
  11. favner85

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    Nov 4, 2012
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    My teacher has set this task indeed. Any viewpoint is acceptable as long it is correct, relies and is backed up mathematically.
    My teacher has not taught me any similar example to this, we jumped straight to this problem by starting the chapter on oscillators.

    If it helps, this is the complete problem statement:

    For the circuit in the figure (the relaxation oscillator shown in both figures above):

    a) Determine the conditions for oscillation and the corresponding analysis
    b) Modify the circuit so that you can vary the frequency in at least three intervals with coarse and fine adjustment
    c) Modify the circuit so that you can have control over the duty cycle of the generated signal
    d) With the results obtained in a) Design a circuit for a triangle waveform generator

    As you can see this is such an ugly and hairy question, yet I've manged to solve b) and c).

    For a) and d) I'm in the assumption that by "conditions of oscillation" means apply Barkhausen, that is find the frequency of oscillation for which the phase is zero or multiples of 360 degrees.

    Normally, with any other teacher I would ask for clarification about the question but not with this teacher in particular, believe it or not, in that specific classroom for that 1.5 hrs of lecture duration, it becomes the soviet union, so asking for calrification is a no-no, chances are if I do it he will hand me a "special" test which is twice as difficult as a "normal" test.

    What satisfactory/acceptable/correct answer I can provide for the questions in a) and d) ?
    I'm interested mainly about a) as for c) it is just a matter to make R1 = 0.86R2 so that the logarithm becomes 1 and you get a linear relationship (triangular wave) but for this I don't know what and how it will affect what must be obtained from a)


    (For those who may benefit from it: for b) put two potentiometers in series on the negative feedback, as this resistor is the one that varies linearly the frequency of oscillation, as you can see in the analysis above. For c) you need to add two diodes, one pointing in the direction form output to the capacitor, the other one on the oppsite direction, bot diodes are in parallel to each other and are connected to the capacitor and the output, post a message if you require the schematic)
     
    Last edited: Mar 2, 2013
  12. The Electrician

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    AHA!!

    It appears that the instructor did not tell you to apply Barkhausen; the problem says "...determine the conditions for oscillation...".

    You made the assumption that Barkhausen should apply. Perhaps your difficulty in showing the truth of that assumption should now lead you to reconsider.

    In other words, look for other conditions for oscillation.

    Do you know what a neon relaxation oscillator is? See:

    http://en.wikipedia.org/wiki/Relaxation_oscillator

    There's no feedback at all there (at least not in the ordinary sense), yet it oscillates. How could the Barkhausen criterion apply to it?

    You might do some Google searches on stability in network theory, and negative resistance:

    http://en.wikipedia.org/wiki/Pearson–Anson_effect
     
    Last edited: Mar 2, 2013
  13. favner85

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    Nov 4, 2012
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    Yes but my instructor did not tell me NOT to apply Barkhausen either :)

    What does it means conditions for oscillation then?
    For me, it means the frequency at which the system starts to oscillate, that is when the system is in a steady-state, as shown in the analysis above. Is there any other conditions of oscillation, apart from frequency of oscillation?

    Then if you agree, I've already found that other ways for oscillating conditions, see the analysis in one of my previous posts where I include figures, please.

    Well, now that leads to the question:

    Why I couldn't apply Barkhausen for this SPECIFIC circuit? Is it because (to put it simple) there is no lag/lead circuit, that is, RC circuit, in the positive feedback as in a wien bridge oscillator?
     
    Last edited: Mar 2, 2013
  14. The Electrician

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    I already gave you my answer to that: "Perhaps your difficulty in showing the truth of that assumption should now lead you to reconsider."

    Did you read the link to the Pearson-Anson effect? Did you see where it says " As the neon lamp exhibits negative differential resistance in the A–B part of its I–V curve (see the figure on the right), if it is driven by a voltage source (the charged capacitor here), it behaves as a switching element with hysteresis (a sort of Schmitt trigger)." That seems like a condition for oscillation.

    See this reference: http://en.wikipedia.org/wiki/Electronic_oscillator

    The Barkhausen criterion applies to linear oscillators. A relaxation oscillator is very non-linear, so I don't think Barkhausen is relevant.
     
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