Talk:Barkhausen stability criterion

Barkhausen book

I changed the title to the 1935 edition. There is a 1924 3 volume set OCLC 760205911. Glrx (talk) 16:03, 1 July 2013 (UTC)

Fantastic! All the secondary sources say he discovered it in 1921, so you would think he must have published it within a few years of that date, but I couldn't find any reference to any publication of his around that time. The earliest reference for the Barkhausen criterion I could find was to his 1935 textbook. Maybe he first proposed it in that 1924 work. --Chetvorno^TALK 17:43, 1 July 2013 (UTC)

Contradiction

Why is the criterion stated in the article the same one described as "erroneous" in the next section? My best guess - but I'm not sure enough to make the edit - is that what's written in the article is literally correct (oscillation only when equality holds) but the more useful and modern form of the criterion is that instability, not necessarily oscillation, requires gain greater than or equal to 1. The "Erroneous version" section seems to be attempting to make that distinction, but does so in a confusing way. 188.182.238.181 (talk) 06:58, 8 January 2015 (UTC)

You're right. This part of the article is confusing and erroneous. The issue is that some circuits that meet the Barkhausen stability criterion do not oscillate because of conditional stability. It is explained here and here. The way I understand it, the Barkhausen criterion $\scriptstyle |A\beta (j\omega )|\;=\;1\quad \angle A\beta (j\omega )\;=\;\phi \;=\;2\pi n$ guarantees that the circuit will start to oscillate, but not that the oscillations are stable with frequency. If the phase is increasing with frequency at the oscillation frequency $\scriptstyle d\phi /d\omega \;>\;0$, which can happen in some circuits with zeros above the poles, the circuit will "latch up". For stable oscillation, in addition to the Barkhausen criterion, the slope of the phase curve at the oscillation frequency must be negative $\scriptstyle d\phi /d\omega \;<\;0$. --Chetvorno^TALK 09:14, 8 January 2015 (UTC)

The general criterion for oscillation startup is derived in this paper. It is that the closed loop transfer function $\scriptstyle (A/(A\beta (s)\;-\;1)$ has poles in the right-half plane (or multiple poles on the $\scriptstyle j\omega$ axis). This can be determined by the Routh-Hurwitz criterion. --Chetvorno^TALK 00:18, 9 January 2015 (UTC)

Surely a phase shift of 0 and a phase shift of 2πn are exactly the same thing (given that its only meaningful to describe this way for a repeating signal in the frequency domain - anthing longer which is different from a complete cycle would be described as a time domin offset) 2.216.92.176 (talk) 17:12, 5 June 2023 (UTC)

Different frequencies for which the phase shift is a multiple of $2\pi$ may not result in the same oscillation behavior - some may result in oscillations and some may not. This is because the Barkhausen criterion has two parts. Not only the phase shift must be a multiple of $2\pi$, but the magnitude of the loop gain must be one. The loop gain changes with frequency. Then secondly, as stated above, the stability of the oscillations may depend not only on the phase shift $\angle A\beta (j\omega )\;=\;\phi \;=\;2\pi n$ but the rate of change of phase shift with frequency $d\phi /d\omega$ --Chetvorno^TALK 20:11, 5 June 2023 (UTC)

Possible Improvements

(This is only my second post to wiki talk, apologies for clumsiness) This article could be improved by the addition of some bode plots, (Loop gain and phase vs frequency), and showing the phase margin. And possible re-word a little differently, a non positive phase margin is necessary for oscillation, but may not be sufficient as another poster has mentioned (for a potential lockup condition). This would then lead to a link to phase margin on an op-amp page. The loop gain transfer function may be amplitude dependent, so a circuit may be stable for low amplitudes, but oscillate when provoked, or vice versa, may be oscillate at some really low amplitude (i.e. within some rattle space defined by crossover distortion) but it never grows any larger. Salbayeng (talk) 01:02, 14 February 2016 (UTC)salbayeng

Actually the loop gain must be amplitude dependent (nonlinear) for a practical oscillator. An oscillator with an exactly linear transfer function is unstable with respect to changes in the component values. The slightest increase in loop gain above one causes the amplitude to increase with time without bound. The slightest decrease below one causes the amplitude to decrease to zero. Practical oscillators must have small signal loop gain greater than one to start up, and a nonlinearity in the circuit (usually clipping of the amplifier) which reduces the loop gain back to one as amplitude increases so the oscillations stabilize at some amplitude. See Electronic oscillator#Startup and amplitude of oscillation. --Chetvorno^TALK 04:50, 6 June 2023 (UTC)