Hello Berti,in your reply No. 6 (Jan. 30th) you have mentioned Barkhausen with reference to a document from K. Lundberg.
For Lundbergs publication see my contribution below.
Hello Vivek !
At first, I agree with you that the discussion has somewhat deviated from the starting point as the “secret” of the two-integrator oscillator seems to be revealed. But as there are some misunderstandings and misinterpretations connected with the term “stability” (perhaps also on my side ?) I consider this discussion nevertheless still as helpful.
Quote (Vivek):
If you would actually read the comments from Lundberg (I just did), he does not quote Barkhausen as proposing a criteria for stability……… other people having misinterpreted this as a means of deciding whether a system is stable or not….Sorry, but I cannot agree because Lundberg himself contributes to the confusion as the title of his paper is “Barkhausen
Stability Criterion” ! (
http://web.mit.edu/klund/www/weblatex/node4.html).
And his last sentence reads as : “…….knowing the value of the loop transfer function at one frequency gives us no information about
stability. Down with Barkhausen!”
Quote (Vivek):
Instead, Lundberg mentions that Barkhausen developed his criteria as a tool to determine the frequency of oscillation of a linear oscillator. Agreed, this formulation is correct, and thatīs exactly the reason I refuse a statement like “Barkhausen is wrong”.
Vivek, I have a question: you mentioned “Lundberg's example of a system which has a constant gain at all frequencies”. Can you please give me the corresponding reference ? I only know one single “counter-example” contained in the Lundberg paper referenced above.
Finally, of course I totally agree with you that Barkhausen must not applied “blindly to a system which is only conditionally stable”. This exactly is the reason for my former remark that the Barkhausen formula is nothing more than a
necessary (!!!) condition for a system designed to function as an oscillator.
Generally spoken, in any case an electronic engineer must not apply a rule or a formula “blindly” because – to my knowledge - there is no formula in the world of analog electronics which is “correct up to 100%” under all conditions. (Perhaps a more philosophical remark: is such a formula “wrong” ?). Instead, one must carefully prove all presumptions and decide if the error resulting from this simplified view is acceptable for the specific application.
Thanks to all contributers to this discussion.
Lutz