# Barkhausen Criteria

Discussion in 'Homework Help' started by Tera-Scale, Jun 7, 2011.

1. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
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Briefly, the two criteria to be met are that the loop gain to be unity and zero phase shift. Is there any of the two that is the most crucial?

2. ### guitarguy12387 Active Member

Apr 10, 2008
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Actually, my understanding is that Barkhausen is necessary but not sufficient.... it doesn't tell the whole story.

3. ### jegues Well-Known Member

Sep 13, 2010
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This is true. There are circuits that satisfy the Barkhausen criterion, yet provide no oscillation whatsoever.

4. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
164
5
Is it because there is no implementation of a non-linear component such as diode or incandescent bulb? My hw question was: State the Barkhausen criteria. Which of the two criteria is necessary for oscillation and explain why? I did a lot of research and managed to write a good and simple description but in the question it is specifying on one of the criteria :s

5. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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The question might be seeking to draw out the "subtle" distinction that where the loop gain exceeds unity and the total phase shift is zero then instability is not a necessary outcome.

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

The criterion itself states there are two conditions which must be present. When the idea was originally formulated, knowledge of non-linear feedback behavior was poorly (or not at all) understood.

6. ### erik.lindberg New Member

Jan 11, 2014
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Linear oscillators must be damped oscillators. You can't balance the poles on the imaginary axis in the complex frequency plane.

Steady state oscillators must be nonlinear circuits which means that it is very difficult to derive analytical conditions concerning oscillation (frequency and amplitude). Barkhausens criterion (observation) is just a starting point.

The kernel in our SPICE simulation programs is the iterative solution of a linear circuit in each integration step (the instant small signal model at the instant bias point). If you investigate your oscillator as a time-varying linear circuit i.e. if you study the linearized Jacobian of the differential equation model for your circuit - the instant small signal model - you may study poles and zeros. If the imaginary part of the complex pole-pair is as constant as possible as function of time during the period you may minimize phase noise and harmonics as Hewlett did in his master-thesis from 1939 when he invented the Wien Bridge Oscillator. The real part of the complex pole-pair moves between the half planes of the complex frequency plane (RHP and LHP) so we have an energy balance determining the amplitude.

Last edited: Jan 11, 2014
7. ### LvW Active Member

Jun 13, 2013
674
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Hi Erik,
a warm welcome to the club!
LvW

8. ### erik.lindberg New Member

Jan 11, 2014
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Concerning:
_______________________
Hi Erik,
a warm welcome to the club!
LvW
__________________________

Hi Lutz,
Thank you so much for your warm welcome.
I am working on Wien Bridge oscillators
as modified multivibrators at the moment.
All the best for the new year 2014 !
ERIK

9. ### LvW Active Member

Jun 13, 2013
674
100
...and I am still investigating some additional requirements to make the Barkhausen criterion a sufficient one.