Barkhausen stability criterion: Difference between revisions
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The '''Barkhausen stability criterion''' is a condition to determine when an [[electronic circuit]] will [[oscillate]]. It was put forth in 1921 by [[Germany|German]] physicist [[Heinrich Georg Barkhausen]] (1881-1956). It is widely used in the design of [[electronic oscillator]]s, and also in the design of general [[negative feedback]] circuits such as [[op amp]]s, to prevent them from oscillating. |
The '''Barkhausen stability criterion''' is a condition to determine when an [[electronic circuit]] will [[oscillate]]. It was put forth in 1921 by [[Germany|German]] physicist [[Heinrich Georg Barkhausen]] (1881-1956). It is widely used in the design of [[electronic oscillator]]s, and also in the design of general [[negative feedback]] circuits such as [[op amp]]s, to prevent them from oscillating. |
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It states that if <math>A\,</math> is the [[gain]] of the amplifying element in the circuit and <math>\beta(j\omega)\,</math> is the [[transfer function]] of the feedback path, so <math>\beta A\,</math> is the [[loop gain]] around the feedback loop of the circuit, the circuit will sustain steady-state oscillations only if: |
It states that if <math>A\,</math> is the [[gain]] of the amplifying element in the circuit and <math>\beta(j\omega)\,</math> is the [[transfer function]] of the feedback path, so <math>\beta A\,</math> is the [[loop gain]] around the [[feedback loop]] of the circuit, the circuit will sustain steady-state oscillations only if: |
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#The loop gain is equal to unity, that is, <math>|\beta A| = 1\,</math> |
#The loop gain is equal to unity, that is, <math>|\beta A| = 1\,</math> |
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#The phase shift around the loop is zero or an integer multiple of 2π: <math>\angle \beta A = 2 \pi n, n \in 0, 1, 2...\,</math> |
#The [[phase shift]] around the loop is zero or an integer multiple of 2π: <math>\angle \beta A = 2 \pi n, n \in 0, 1, 2...\,</math> |
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Barkhausen's criterion applies to circuits with a [[feedback loop]], so it cannot be applied to one port [[negative resistance]] active elements like [[tunnel diode]] oscillators. |
Barkhausen's criterion applies to circuits with a [[feedback loop]], so it cannot be applied to one port [[negative resistance]] active elements like [[tunnel diode]] oscillators. |
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Revision as of 07:39, 9 December 2008
The Barkhausen stability criterion is a condition to determine when an electronic circuit will oscillate. It was put forth in 1921 by German physicist Heinrich Georg Barkhausen (1881-1956). It is widely used in the design of electronic oscillators, and also in the design of general negative feedback circuits such as op amps, to prevent them from oscillating.
It states that if is the gain of the amplifying element in the circuit and is the transfer function of the feedback path, so is the loop gain around the feedback loop of the circuit, the circuit will sustain steady-state oscillations only if:
- The loop gain is equal to unity, that is,
- The phase shift around the loop is zero or an integer multiple of 2π:
Barkhausen's criterion applies to circuits with a feedback loop, so it cannot be applied to one port negative resistance active elements like tunnel diode oscillators. Barkhausen's criterion is a necessary condition for oscillation, not sufficient. This means there are some circuits which satisfy the criterion but do not oscillate. These can be distinguished with the Nyquist stability criterion, which is both necessary and sufficient.
Erroneous original version
Barkhausen's original version was slightly erroneous,[1] and this version is still seen in some sources. Barkhausen originally stated that oscillations would occur if the loop gain was greater than or equal to one, not just equal to one: . However, stable oscillations only occur at frequencies for which the equality holds.
See also
External links
References
- ^ Lundberg, Kent (2002-11-14). "Barkhausen Stability Criterion". Kent Lundberg faculty website. MIT. Retrieved 2008-11-16.
{{cite web}}: Cite has empty unknown parameter:|coauthors=(help); External link in|work= - ^ "Lesson 31: Barkhausen Criteria" (PDF). Rai Foundation colleges.
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