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Image:Simple harmonic motion.svg The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion The same concept applies to sine wave motion, viewed either at a point in space over an interval of time or across an interval of space at a moment in time. Simple harmonic motion is a displacement that varies cyclically, as depicted to the right. It is described by the formula: :$x(t)\; A\backslash cdot\; \backslash sin(\; 2\; \backslash pi\; f\; t\; +\; \backslash theta\; ),\backslash ,$ where A is the amplitude of oscillation, f is the frequency t is the elapsed time, and $\backslash theta$ is the phase of the oscillation. The phase determines or is determined by the initial displacement at time t 0. A motion with frequency fhas Wave period $T\backslash frac1\}f\}.$   Two potential ambiguities can be noted: *The initial displacement of  $\backslash cos(\; 2\; \backslash pi\; f\; t\; +\; \backslash theta\; )\backslash ,$  is different from the sine function, yet they appear to have the same "phase". *The time-variant angle  $2\; \backslash pi\; f\; t\; +\; \backslash theta,\backslash ,$  or its modulo $2\backslash pi$ value, is also commonly referred to as "phase". Then it is not an initial condition, but rather a continuously-changing condition. The term instantaneous phase is used to distinguish the time-variant angle from the initial condition. It also has a formal definition that is applicable to more general functions and unambiguously defines a functions initial phase at t0.  I.e., sine and cosine inherently have different initial phases. When not explicitly stated otherwise, cosine should generally be inferred. (also see Phasor (electronics)#Introduction

Phase shift

Image:Phase shift.svg $\backslash theta$ is sometimes referred to as a phase-shift, because it represents a "shift" from zero phase. But a change in $\backslash theta$ is also referred to as a phase-shift For infinitely long sinusoids, a change in $\backslash theta$ is the same as a shift in time, such as a time-delay. If $x(t)\backslash ,$ is delayed (time-shifted) by $\backslash beginmatrix\}\; \backslash frac1\}4\}\; \backslash endmatrix\}\backslash ,$ of its cycle, it becomes: :| |$x(t\; -\; \backslash beginmatrix\}\; \backslash frac1\}4\}\; \backslash endmatrix\}T)\; \backslash ,$ |$A\backslash cdot\; \backslash sin(2\; \backslash pi\; f\; (t\; -\; \backslash beginmatrix\}\; \backslash frac1\}4\}\; \backslash endmatrix\}T)\; +\; \backslash theta)\; \backslash ,$ |- | |$A\backslash cdot\; \backslash sin(2\; \backslash pi\; f\; t\; -\; \backslash beginmatrix\}\backslash frac\backslash pi\; \}2\}\; \backslash endmatrix\}\; +\; \backslash theta\; ),\backslash ,$ |} whose "phase" is now $\backslash theta\; -\; \backslash beginmatrix\}\backslash frac\backslash pi\; \}2\}\; \backslash endmatrix\}.$   It has been shifted by $\backslash beginmatrix\}\backslash frac\backslash pi\; \}2\}\; \backslash endmatrix\}$.

Phase difference

Image:Sine waves same phase.svg Image:Sine waves different phase.svg Image:Phase-shift illustration.png of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts. (The illustration on the right ignores the effect of diffraction whose effect increases over large distances).]] Two oscillators that have the same frequency and different phases have a phase difference and the oscillators are said to be out of phase with each other. The amount by which such oscillators are out of step with each other can be expressed in degree (angle) from 0° to 360°, or in radian from 0 to 2π. If the phase difference is 180 degrees (π radians), then the two oscillators are said to be in antiphase If two interacting wave meet at a point where they are in antiphase, then destructive Interference (wave propagation) will occur. It is common for waves of electromagnetic (light, RF), acoustic (sound) or other energy to become superposed in their transmission medium. When that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes. Time is sometimes used (instead of angle) to express position within the cycle of an oscillation. *A phase difference is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time. But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds (different frequencies), the phase difference is undefined and would only reflect different starting positions. Technically, phase difference between two entities at various frequencies is undefined and does not exist. *Time zones are also analogous to phase differences.

In-phase and quadrature (I&Q) components

The term in-phase is also found in the context of communication signals: :$A(t)\backslash cdot\; \backslash sin2\backslash pi\; ft\; +\; \backslash phi(t)]\; I(t)\backslash cdot\; \backslash sin(2\backslash pi\; ft)\; +\; Q(t)\backslash cdot\; \backslash underbrace\backslash cos(2\backslash pi\; ft)\}\_\backslash sin\backslash left(2\backslash pi\; ft\; +\; \backslash frac\backslash pi\}2\}\; \backslash right)\}$ and: :$A(t)\backslash cdot\; \backslash cos2\backslash pi\; ft\; +\; \backslash phi(t)]\; I(t)\backslash cdot\; \backslash cos(2\backslash pi\; ft)\; \backslash underbrace2\}\backslash right)\},$ where $\backslash \; f\backslash ,$ represents a carrier frequency and :$I(t)\backslash \; \backslash stackrel\backslash textdef\}\}\}\backslash \; A(t)\backslash cdot\; \backslash cos\backslash left(\backslash phi(t)\backslash right),\; \backslash ,$ :$Q(t)\backslash \; \backslash stackrel\backslash textdef\}\}\}\backslash \; A(t)\backslash cdot\; \backslash sin\backslash left(\backslash phi(t)\backslash right).\backslash ,$ $A(t)\backslash ,$ and $\backslash phi(t)\backslash ,$ represent possible modulation of a pure carrier wave, e.g.:  $\backslash sin(2\backslash pi\; ft).\backslash ,$  The modulation alters the original $\backslash sin\backslash ,$ component of the carrier, and creates a (new) $\backslash cos\backslash ,$ component, as shown above. The component that is in phase with the original carrier is referred to as the in-phase component The other component, which is always 90° ($\backslash beginmatrix\}\; \backslash frac\backslash pi\}2\}\; \backslash endmatrix\}$ radians) "out of phase", is referred to as the Quadrature phase

Phase coherence

coherence (physics) is the quality of a wave to display well defined phase relationship in different regions of its domain of definition. In physics, quantum mechanics ascribes waves to physical objects. The wave function is complex and since its square modulus is associated with the probability of observing the object, the complex character of the wave function is associated to the phase. Since the complex algebra is responsible for the striking interference effect of quantum mechanics, phase of particles is therefore ultimately related to their quantum behavior.

Phase compensation

Image:Phi compen cct.JPG Phase compensation is the correction of phase error(i.e., the difference between the actually needed phase (waves) 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 to keep a phase margin. A phase compensator subtracts out an amount of phase shift from a signal which is equal to the amount of phase shift added by switching one or more additional amplifier stages into the amplification signal path.

See also

*Instantaneous phase *Lissajous curve *Phase cancellation *Polarity (physics) *Polarization (waves)

External links

*http://www.kwantlen.ca/science/physics/faculty/mcoombes/P2421_Notes/Phasors/doublesine.gif Relationship of phase difference and time-delay] *http://www.sengpielaudio.com/calculator-timedelayphase.htm Phase angle, phase difference, time delay, and frequency] *http://www.tedpavlic.com/teaching/osu/ece209/lab3_opamp_FO/lab3_opamp_FO_phase_shift.pdf ECE 209: Sources of Phase Shift] — Discusses the time-domain sources of phase shift in simple linear time-invariant circuits. * http://phy.hk/wiki/englishhtm/phase.htm Phase Difference] Java Applet Category:Wave mechanics ar:طور موجة ca:Fase (ona) cs:Fáze (vlna) da:Fase (svingning) de:Phase (Schwingung) et:Faas el:Φάση (τριγωνομετρία) es:Fase (onda) eo:Fazo fa:فاز (موج) fr:Phase (onde) gl:Fase dunha onda ko:위상 it:Fase (segnali) he:מופע lt:Fazė hu:Fáziseltolódás nl:Fase (golf) ja:位相 no:Bølgefase pl:Faza fali pt:Fase (física) ru:Фаза колебаний sl:Fazna razlika su:Fase (galura) sv:Fas (matematik) tr:Faz (dalga) uk:Фаза (коливання) vi:Pha sóng zh:相位