What is recorded here?
Nyquist’s 1932 analysis relates the decay of a small disturbance in an idealized linear feedback circuit to how its frequency-response curve winds around a critical point. It explains why high feedback gain can be stable and why looking only at a steady-state gain can give the wrong answer. A microphone near a loudspeaker can create a sustained howl: part of the output returns as new input. Feedback can also make amplifiers more useful. Nyquist asks which of these outcomes a small disturbance produces. He studies one trip around the loop across frequencies, turning the resulting complex response into a curve. The curve’s winding about the critical point reveals growing transients that a steady-state calculation can miss. The original includes conditional-stability examples where increasing gain can first destabilize and then stabilize a system.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The exact target is the original linear, constant-gain feedback analysis, not all modern Nyquist generalizations. Its causal network impulse response has the stated bounded-variation and integrability restrictions; the open-loop auxiliary function is analytic in the right half-plane and has the required high-frequency behavior. Original winding is about +1 under its AJ convention, not blindly about modern -1. Net winding and boundary contacts matter; a gain-above-one crossing alone is not sufficient when phase behavior reverses. Stability means a dying small disturbance produces a response that dies out; a sustained oscillator is unstable under this definition. Unlimited-power linearization excludes general nonlinear amplitude stability. Original example 8 explicitly shows that omitting high-frequency decay invalidates the apparent curve conclusion; distributed effects change the curve. The original restricted criterion does not automatically cover unstable open-loop poles, multivariable or nonlinear systems. the account does not independently certify every formula, numerical curve or physical experiment. Later introductory commentary, generalized argument-principle formulations and global engineering adoption are separate.
Read the original work
- H. Nyquist, Regeneration Theory (1932), original article reprinted with permission in publisher-hosted control anthology excerpt
- Wiley, Regeneration Theory: original January 1932 bibliographic record
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
Harry Nyquist
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English catalogue narrative
Nyquist: when feedback stabilizes or makes a circuit sing
Nyquist’s 1932 analysis relates the decay of a small disturbance in an idealized linear feedback circuit to how its frequency-response curve winds around a critical point. It explains why high feedback gain can be stable and why looking only at a steady-state gain can give the wrong answer.
A microphone near a loudspeaker can create a sustained howl: part of the output returns as new input. Feedback can also make amplifiers more useful. Nyquist asks which of these outcomes a small disturbance produces. He studies one trip around the loop across frequencies, turning the resulting complex response into a curve. The curve’s winding about the critical point reveals growing transients that a steady-state calculation can miss. The original includes conditional-stability examples where increasing gain can first destabilize and then stabilize a system.
Scientific scope
The exact target is the original linear, constant-gain feedback analysis, not all modern Nyquist generalizations. Its causal network impulse response has the stated bounded-variation and integrability restrictions; the open-loop auxiliary function is analytic in the right half-plane and has the required high-frequency behavior. Original winding is about +1 under its AJ convention, not blindly about modern -1. Net winding and boundary contacts matter; a gain-above-one crossing alone is not sufficient when phase behavior reverses. Stability means a dying small disturbance produces a response that dies out; a sustained oscillator is unstable under this definition. Unlimited-power linearization excludes general nonlinear amplitude stability. Original example 8 explicitly shows that omitting high-frequency decay invalidates the apparent curve conclusion; distributed effects change the curve. The original restricted criterion does not automatically cover unstable open-loop poles, multivariable or nonlinear systems. the account does not independently certify every formula, numerical curve or physical experiment. Later introductory commentary, generalized argument-principle formulations and global engineering adoption are separate.
People and systems
Harry Nyquist