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Design >> Analog Design >> oscillation frequency and Bode plot
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Message started by ywguo on Feb 5^th, 2007, 2:36am

Title: oscillation frequency and Bode plot
Post by ywguo on Feb 5^th, 2007, 2:36am

Hi, Guys,

Can I deduce the oscillation frequency from Bode plot? For eg., an amplifier or something else.

Define
A(jw)
A_cl(jw)=-------------------
1 + A(jw)F(jw) ,
where A(jw) is the open-loop transfer function, F(jw) is the feedback, and A_cl(jw) is the closed-loop transfer function.

I am sure that the closed-loop system oscillates at the frequency w1 if |A(jw1)F(jw1)| = 1 when phase[A(jw1)F(jw1)]=pi radian. Furthermore, the closed loop system oscillates and the oscillation will grow in magnitude if |A(jw1)F(jw1)| > 1 when phase[A(jw1)F(jw1)]=pi radian. But at which frequency?

Thanks
Yawei

Title: Re: oscillation frequency and Bode plot
Post by mg777 on Feb 5^th, 2007, 6:46am

Instability is one thing, oscillation another. Then there are different types of oscillators - for example, a monostable multivibrator is a different beast compared to a harmonic oscillator. A harmonic oscillation a fine balance between stability and instability, where the phase space trajectory closes on itself. OTOH an unstable system exhibits a phase space signature that spirals out.

Assuming you are interested in harmonic oscillations, poles on the jω axis are only a (rough) necessary condition for oscillation. A harmonic oscillator is an inherently non-linear circuit i.e; even though the circuit elements appear linear, the amplitude of the oscillation is determined by a saturation of the negative resistance characteristic. That is, the oscillations grow in amplitude until any further growth leads to a drop in negative resistance and damps out the oscillations. Further, due to pulling, the oscillation amplitude ends up shifting the frequency as well.

We electrical engineers get too caught up in linear analysis because it's easy, but there is plenty to life beyond jω. An excellent tutorial on oscillators can be found at:

http://www.uni-potsdam.de/u/phys_gprakt/html/projekte/emwellen/EM-Schwingungen_1.pdf

M.G.Rajan
www.eecalc.com

Title: Re: oscillation frequency and Bode plot
Post by Croaker on Feb 5^th, 2007, 8:27am

MG, so in short, is the answer no? ;)

Title: Re: oscillation frequency and Bode plot
Post by mg777 on Feb 5^th, 2007, 10:14am

It's what I call the AWGN approach - say a lot and you can be sure something will match :-)