IEVref:103-07-12ID:
Language:enStatus: Standard
Term: instantaneous complex value
Synonym1: rotating phasor
[Preferred]
Synonym2: complex representation, <of a sinusoidal quantity>
[Preferred]
Synonym3:
Symbol:
Definition: for a sinusoidal quantity a(t)= A ^ cos(ω t+ ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacaGGOaGaam iDaiaacMcacqGH9aqpceWGbbGbaKaajugabiGacogacaGGVbGaai4C aOGaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaS qaaKqzadGaaGimaaWcbeaakiaacMcaaaa@4817@ , complex quantity

a _ (t)= A ^ [cos(ω t+ ϑ 0 )+j sin(ω t+ ϑ 0 )]= A ^ exp[j(ω t+ ϑ 0 )]= A ^ exp(jω t)exp(j ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaamaaabaGaamyyaa aacaGGOaGaamiDaiaacMcacqGH9aqpceWGbbGbaKaajugGbiaacUfa jugqbiGacogacaGGVbGaai4CaOGaciikaiabeM8a3jaayIW7caWG0b Gaey4kaSIaeqy0dO0aaSbaaSqaaKqzaeGaaGimaaWcbeaakiaacMca cqGHRaWkjugqbiGacQgakiaaysW7jugqbiaacohacaGGPbGaaiOBaO GaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaSqa aKqzaeGaaGimaaWcbeaakiaacMcajugGbiaac2facqGH9aqpkiqadg eagaqcaKqzafGaciyzaiaacIhacaGGWbqcLbyaciGGBbqcLbuaciGG QbGcciGGOaGaeqyYdCNaaGjcVlaadshacqGHRaWkcqaHrpGsdaWgaa WcbaqcLbqacaaIWaaaleqaaOGaaiykaKqzagGaaiyxaiabg2da9OGa bmyqayaajaqcLbuaciGGLbGaaiiEaiaacchakiGacIcajugqbiGacQ gakiabeM8a3jaayIW7caWG0bGaaiykaKqzafGaciyzaiaacIhacaGG WbGcciGGOaqcLbuaciGGQbGccqaHrpGsdaWgaaWcbaqcLbqacaaIWa aaleqaaOGaaiykaaaa@8771@

where j is the imaginary unit, A ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiqadgeagaqcaaaa@3628@ is complex amplitude, ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3baa@371F@ is angular frequency, and ϑ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9aknaaBaaale aajugabiaaicdaaSqabaaaaa@385A@ is initial phase

Note 1 to entry: The instantaneous value of the quantity is the real part of its complex representation.


Publication date:2009-12
Source
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO
2017-08-25: Corrected <mstyle displaystyle='true'> tag; missing quotation mark. LMO
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