Sinusoidal oscillators

Discussion in 'General Electronics Chat' started by LvW, Aug 23, 2013.

  1. LvW

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    Jun 13, 2013
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    An active circuit with feedback must fulfill Barkhausen`s oscillation condition for producing self-sustained sinusoidal oscillations.
    However, there are some active circuits that meet this oscillation criterion without being able to oscillate.

    Examples:
    1.) Symmetric modifications of the classical WIEN oscillator if it is seen as a tuned bridge (element exchange within the positive as well as the negative feedback path)
    2.) Equal component double-T oscillator with positive gain of 4.

    My question: Are there other active circuits with feedback which do not oscillate even though the meet the mentioned oscillation condition?
     
  2. LvW

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    Honestly, I didn`t expect many answers to my request.
    Therefore, in addition, I will give the following justification:

    In
    http://web.mit.edu/klund/www/weblatex/node4.html

    the author (Kent H. Lundberg) claims that "there is no shortage of counterexamples" which would proove that the Barkhausen criterion is "simple, intuitive and wrong"!

    A rather provocative claim, for my opinion.
     
  3. t_n_k

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  4. LvW

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  5. t_n_k

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    So do you hope to correct all the gullible believers in Barkhausen?
     
  6. LvW

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    No - it is not my intention to correct anybody.
    I am looking for the truth - that means, to learn WHY some circuits don`t oscillate even though meeting Barkhausen.
    And in this context I am looking for further examples.
     
    Last edited: Aug 25, 2013
  7. t_n_k

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    Sorry for being flippant.

    Not sure if you will get a substantial response on AAC in this matter. There are a few people around with an strong academic perspective who might have done some thinking on the subject.

    I would think most members , including those formally trained in electronics & systems theory would have not have come across the subtleties of the 'challenge ' to the conventional application of Barkhausen to oscillators. No doubt it (Barkhausen) is still routinely taught without any qualification.

    Hope you have some success!
     
  8. gootee

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    There are quite a few on diyaudio.com who might be worth asking.
     
  9. t_n_k

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    I guess one could also create a substantial family of state-space oscillators whose transfer functions exhibit the conditionally stable characteristics of interest.
     
  10. LvW

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    t_n_k, can you give an example, please?
     
  11. THE_RB

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    Because some oscillators need to be "started"?

    A mechanical pendulum oscillates according to set mathematical rules also, but that does NOT mean it's going to start swinging by itself.
     
  12. t_n_k

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    Sure.

    Attached is a state-space implementation of the Kent Lundberg counter-example.

    If you wish I can also create a similar implementation for the counter-example suggested in the paper submission from Fan He, Raymond Ribas , et. al.

    The ideal model could be physically implemented using op-amps configured as integrators, amplifiers and summing junctions.
     
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  13. LvW

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    Thanks RB for replying.
    Sorry, it was a misunderstanding - I do not speak about start of an oscillator. I am aware what is needed for oscillation to start.
    I have given two examples meeting Barkhausen`s criterion - without being able to produce self-sustained oscillations.
    By the way - I know the reason for this behaviour, however, I am looking for other examples. This would help to find a complement to Barkhausens criterion.
     
  14. LvW

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    @t_n_k, thank you very much for providing the model for Lundberg`s example.
    I will analyze it`s properties and inform you about the results.
    This is really the kind of help I was asking. Thanks again.
    LvW
     
  15. t_n_k

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    @LvW,

    Happy to help.

    By the way - do you know of any sources for Barkhausen's original work on this topic - circa early 1900's I believe? As I can't read German an English translation would be definitely of interest.
     
  16. LvW

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    It`s in a book published in 1934 (it is on my desk now).
    However, an english version doesn`t exist.
    But there are some recent articles taking reference to this book (Erik Lindberg).
    I have copies of some of these papers. If you are interested...
     
  17. LvW

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    Hi t_n-K ,

    here are simulation results of Lundbergs "counterexample" (as provided by you as a block diagram).

    1.) Indeed, the system oscillates in a negative feedback loop with additional damping (gain=0.05) - however, only in case of ideal components (ideal integrators and frequency-independent damping).

    2.) For larger loop gains the oscillation amplitudes decrease (!) and vice versa. This is opposite to the normal behaviour that can be observed for all classical oscillators. With other words: To limit the rising of amplitudes the loop gain must be increased (!). Of course, this is counter-productive and is already an indication for an abnormal behaviour. By the way, this confirms your statement of conditional stability.

    3.) What happens in case of real components (integrators with real opamps)?
    No oscillations can be observed. In contrary - the output latches immediately at one of the power rails.

    4.) This is exactly the same behaviour as I have observed for the two example circuits I have mentioned in my first post.

    5.) Summary: All three circuits with feedback are able to show oscillatory behaviour for ideal conditions only. In case of real parts with frequency dependent gain additional real and positive poles are created in the closed loop driving the output into saturation.

    6.) What about Barkhausen? Is K. Lundberg right or wrong?
    My opinion: He is right regarding the presented example (he calles it "counterexample) because, indeed, the corresponding closed loop cannot oscillate under real-worls conditions.
    However, this circuit cannot serve as a "counterexample" to Barkhausen`s condition. As mentioned in many articles and serious textbooks, Barkhausen`s criterion can be considered as a necessary condition only - and NOT as a sufficient one.
    Thanks again for creating the block diagram.
    LvW
     
  18. t_n_k

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    LvW,

    Thanks for the feedback on your finding.

    Did you actually build a working physical equivalent using op-amps? Well done if you achieved that so quickly.

    I agree that the counter-intuitive examples seem (almost of necessity) to be based on conditionally stable phenomena. I understand it was this "problem" of the occurrence of conditional instability with reducing gain in physical systems that was one of the drivers for Nyquist's seminal 1932 paper. See http://www.yumpu.com/en/document/view/11795223/of-frequency-response-in-automatic-control-methods

    Simple control system heuristic tuning algorithms, such as that proposed by Ziegler_Nichols might potentially will run into difficulties with conditionally stable examples of the type suggested.

    To me the challenge to Barkhausen is largely academic. Informed students of modern control theory should appreciate the subtlety of the argument but remain confident that the tools currently at their disposal will adequately provide the necessary insights for system analysis and synthesis. "Down with Barkhausen" - I think not. He was a man of great intellect in his time.
     
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  19. LvW

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    I am afraid - too quickly.
    That means: I have to correct myself. Initially, I have simulated the system with classical inverting integrators (real opamps) - and because of the inverting properties I have made an error in sign after closing the loop.
    After correcting the error I got other results than mentioned before (see my points 5 and 6 in my former post):
    * The system oscillates - as expected - for a loop gain of unity.
    * Oscillations decline for a loop gain larger than unity
    * Oscillation amplitudes rise for loop gain below unity until they are limited (power rails) - thereby the frequency is reduced!
    But no latching effect!

    This is an unexpected behaviour which deserves further inverstigations.

    Yes - I agree the whole subject may be considered as academic only.
    However, shouldn`t we try to find some new requirements (supplements to Barkhausen`s rule) which can explain why some circuits oscillate and some not (even though all of then meet loop gain of unity)?

    Up to now - my guess was that as an additional requirement the SLOPE of the phase at f=fo must be negative. This is the case for all known oscillatory circuits.
    And the two circuits mentioned in my first post (which do not oscillate) as well as your state-space implementation exhibit a POSITIVE phase slope at f=fo.
    However, as mentioned above: "Your" circuit oscillates nevertheless - even though with some "abnormal" properties.
    All for now.
    LvW
     
    Last edited: Aug 28, 2013
  20. THE_RB

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    Anything will oscillate if the phase shift is roughly right and there is enough energy input at that phase shift to overcome losses, BUT some systems require a third condition; energy to start the process.

    Oscillators can be built in two basic forms (this is a simplified view);
    A. Feedback is based on position.
    B. Feedback is based on movement.

    Oscillators whose feedback is based on position will generally self-start very well. Oscillators whose feedback is based on movement will usually require a specific start condition where initial energy is added to initiate oscillation.

    I've kept that very general to apply to all oscillators; electrical/mechanical etc.

    To visualise "movement" from an electrical perspective, that would be similar to feedback that is capacitor coupled. Feedback only exists while some voltage is "moving" (and feedback amplitude is likely based on AMOUNT or SPEED of the movement).

    Feedback that is DC coupled is based on "position" as the feedback always exists even if oscillation is paused in some position. And the feedback will be the same, regardless of movement speed.

    So if you need to know "why some circuits oscillate and some not" then the answer is one or more of these;
    1. the phase shift is wrong
    2. not enough energy is input to overcome losses
    3. initial start condition was not met (if type B oscillator)
     
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