Phase margin

Phase margin

In electronic amplifiers, phase margin is the difference, measured in degrees, between the phase of the amplifier's output signal and -360°. In feedback amplifiers, the phase margin is measured at the frequency at which the open loop voltage gain of the amplifier and the closed loop voltage gain of the amplifier are equal.cite book
author=Paul Horowitz & Hill W
title=The art of electronics
year= 1989
page=§ 4.33 pp. 242-249
edition=Second Edition
publisher=Cambridge University Press
location=Cambridge MA

Phase margin and its important companion concept, gain margin, are measures of stability in closed loop dynamic [control] systems. Phase margin indicates relative stability, the tendency to oscillate during its damped response to an input change such as a step function. Gain margin indicates absolute stability and the degree to which the system will oscillate without limit given any disturbance.

The output signals of all amplifiers exhibit a time delay when compared to their input signals. For the most part, the delay is caused by internal resistances, current limits and capacitances within the amplifier. This delay causes a phase difference between the amplifier's input and output signals. If there are enough stages in the amplifier, at some frequency, the output signal will lag behind the input signal by one wavelength. In this situation, the amplifier's output signal will be in phase with its input signal though lagging behind it by 360°, i.e., the output will have a phase angle of –360°. This lag is of great consequence in amplifiers that use feedback. The reason: the amplifier will oscillate if the fed-back output signal is in phase with the input signal at the frequency at which its open loop voltage gain equals its closed loop voltage gain and the open loop voltage gain is one or greater. The oscillation will occur because the fed-back output signal will then reinforce the input signal at that frequency. ["Ibid", p. 245.] In conventional operational amplifiers, the critical output phase angle is –180° because the output is fed back to the input through an inverting input which adds an additional –180°.

In practice, feedback amplifiers must be designed with phase margins substantially in excess of 0°, even though amplifiers with phase margins of, say, 1° are theoretically stable. The reason is that many practical factors can reduce the phase margin below the theoretical minimum. A prime example is when the amplifier's output is connected to a capacitive load. Therefore, operational amplifiers are usually compensated to achieve a minimum phase margin of 45° or so. This means that at the frequency at which the open and closed loop gains meet, the phase angle is -135°. The calculation is: -135° - (-180°) = 45°. See Warwickcite book
author=K Warwick
title=An introduction to control systems
year= 1996
edition=Second Edition
page=Chapter 5, pp. 137-196
publisher=World Scientific
isbn= 9810225970 (pb), or 9810215630 (hc)
] or Stoutcite book
author=David F Stout & Kaufman M
title=Handbook of operational amplifier circuit design
year= 1976
page=Sec. 3-4
isbn= 007061797X
] for a detailed analysis of the techniques and results of compensation to insure adequate phase margins. See also the article on pole splitting. Often amplifiers are designed to achieve a typical phase margin of 60 degrees. If the typical phase margin is around 60 degrees then the minimum phase margin will typically be greater than 45 degrees. A phase margin of 60 degrees is also a magic number because it allows for the fastest settling time when attempting to follow a voltage step input (a Butterworth design). An amplifier with lower phase margin will ring [Ringing is the displaying of a decaying oscillation for a portion of the output signal's cycle.] for longer and an amplifier with more phase margin will take a longer time to rise to the voltage step's final level.

A related measure is gain margin. While phase margin comes from the phase where the loop gain equals one, the gain margin is based upon the gain where the phase equals -180 degrees.


ee also

* BIBO stability
*Nyquist stability criterion
*Routh-Hurwitz stability criterion
*Root locus method
*Bode plots & phase margin
*Step response & phase margin

Wikimedia Foundation. 2010.

Нужен реферат?

Look at other dictionaries:

  • phase margin — fazės atsarga statusas T sritis automatika atitikmenys: angl. phase margin vok. Phasenrand, m; Phasenvorrat, m rus. запас по фазе, m pranc. marge de phase, f …   Automatikos terminų žodynas

  • Phase (waves) — Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.[1] Contents 1 Formula 2 Phase shift 3 Phase difference …   Wikipedia

  • Phase compensation — is the correction of phase error (i.e., the difference between the actually needed phase and the obtained phase). A phase compensation is required to obtain stability in an opamp. A capacitor/RC network is usually used in the phase compensation… …   Wikipedia

  • Phase-locked loop — PLL redirects here. For other uses, see PLL (disambiguation). A phase locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input reference signal. It is an electronic… …   Wikipedia

  • Phase Change Random Access Memory — Phase change RAM (Abk.: PCRAM oder PRAM, in einer speziellen Ausführung auch Ovonics Unified Memory / OUM oder chalcogenide RAM / C RAM) ist ein neuartiger nicht flüchtiger Speicher in der Elektronik. Das Wirkprinzip des Speichers ist die… …   Deutsch Wikipedia

  • Phase-change random access memory — (Abk.: PCRAM oder PRAM, in einer speziellen Ausführung auch „Ovonics Unified Memory“, OUM, oder „chalcogenide RAM“, C RAM) ist ein neuartiger nicht flüchtiger Speicher in der Elektronik (Stand 2009). Das Wirkprinzip des Speichers ist die Änderung …   Deutsch Wikipedia

  • Phase-change memory — Computer memory types Volatile RAM DRAM (e.g., DDR SDRAM) SRAM In development T RAM Z RAM TTRAM Historical Delay line memory Selectron tube Williams tube Non volatile …   Wikipedia

  • Phase response curve — A phase response curve (PRC) illustrates the transient change in the cycle period of an oscillation induced by a perturbation as a function of the phase at which it is received. PRCs are used in various fields; examples of biological oscillations …   Wikipedia

  • marge de phase — fazės atsarga statusas T sritis automatika atitikmenys: angl. phase margin vok. Phasenrand, m; Phasenvorrat, m rus. запас по фазе, m pranc. marge de phase, f …   Automatikos terminų žodynas

  • Four-phase logic — is a type of, and design methodology for, dynamic logic; it enabled non specialist engineers to design quite complex ICs, using either PMOS or NMOS processes.HistoryIn 1968 Lee Boysel [ Phase Systems AL1] ,… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”