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I was reading an Article of LC-Tuned Oscillators in Microelectronics Circuits (By Sedra Smith).

I came across the the Colprit Oscillator. I did the simulation of the circut given in exerciseto understand it. Colprit Oscilator

I dont understand How Colprit Oscilator Satisfy Barkhausen criterion?

The book says "Detailed analysis of amplitude control, which makes use of nonlinear-circuit techniques, is beyond the scope of this book". Does their is any reference to understand it in simple way.

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  • \$\begingroup\$ The Barkhausen criterion is only applicable to linear circuits, if I recall correctly. \$\endgroup\$
    – Fizz
    Nov 14, 2016 at 7:02
  • \$\begingroup\$ See electronics.stackexchange.com/q/110651/54580 for another, simpler example of non-linear oscillator. \$\endgroup\$
    – Fizz
    Nov 14, 2016 at 7:12
  • \$\begingroup\$ I'd suggest to stop using the Barkhsusen criterion. See here: web.mit.edu/klund/www/weblatex/node4.html \$\endgroup\$
    – user110971
    Nov 14, 2016 at 7:50
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    \$\begingroup\$ It is really bad that the contribution - as given with the above link - is still available in the internet. Its message is that Barkhausens criterion would be "simple but wrong". This statement is simply WRONG!. As it seems, the author of that article did not understand the meaning and the contents of this criterion. He presents an example, which does fulfill the criterion but does not oscillate. Hence, he did not recognize that the criterion is only a NECESSARY one. He should read Barkhausens book!. I urgently recommend not to continue to reference this (unqualified) article. \$\endgroup\$
    – LvW
    Nov 14, 2016 at 9:47
  • \$\begingroup\$ @LvW +1 for pointing that out! \$\endgroup\$
    – Mario
    Dec 14, 2016 at 11:48

1 Answer 1

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The Oscillation Criterion (Barkhausen) requires that the magnitude of the loop gain (turn-around gain within the complete feedback loop) is somewhat larger than "1" (0 dB) with a phase shift of exactly 0 deg (-360 deg) at one single frequency only. In the shown circuit this is accomplished by the amplifier (common emitter stage with 180deg phase shift) and the L-C combination in the collector path (additional 180 deg at resonance). Feedback to the base is accomplished by the capacitor C3.

However, each oscillator with a loop gain >1 will generate a sinusoidal signal with rising amplitudes with hard-limiting caused by the fixed supply voltage. As a consequence, the signal will have much distortions (bad THD). For this reason, it is wise to incorporate an amplitude-sensitive part or circuitry which causes "soft-limiting" of amplitudes. This will automatically reduce the loop gain to the theoretical (ideal) value of "1". For this purpose, you can use diodes, thermistors, FET`s (as resistors) or other non-linear (amplitude-sensitive) devices.

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  • \$\begingroup\$ -1 Firstly, gain must be 1, not greater than 1. Secondly, it is a necessary not sufficient condition for oscillation. See \$H(s) = 10(s+1)^2/s^3\$. Therefore, it is not true that each oscillator with loop gain >1 will generate a sinusoidal signal with rising amplitude. See page 28 here: qucosa.de/fileadmin/data/qucosa/documents/3913/… \$\endgroup\$
    – user110971
    Nov 14, 2016 at 8:07
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    \$\begingroup\$ user110971, correct - loop gain (theoretically!) must be unity, however, can you dsign such a circuit? No! More than that, it MUST be >1 for a safe start of oscillation. That is the reason for amplitude control for rising amplitudes. And - yes - Barkhausen`s criterion is a necessary one only. If you read my answer carefully, you will notice the wording "...oscillation criterion requires...". That is a necessary condition, right? I did not start with " A circuit oscillates when....". This would imply a sufficient criterion. By the way - do you know a sufficient oscillation criterion? \$\endgroup\$
    – LvW
    Nov 14, 2016 at 9:18
  • \$\begingroup\$ user110971, perhaps you can decide to correct your down-voting? I do not need points, however, it may confuse the questioner when a correct answer is voted down (with erroneous arguments). Thank you. \$\endgroup\$
    – LvW
    Nov 14, 2016 at 9:22
  • \$\begingroup\$ How can i incorporate an amplitude-sensitive part or circuitry which causes "soft-limiting" of amplitudes? \$\endgroup\$ Nov 23, 2016 at 20:35

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