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# Lecture 5 phasor notations

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### Lecture 5 phasor notations

1. 1. PHASOR NOTATIONS
2. 2. Phasor Representation of a Time- Harmonic Field • A phasor is a complex number representing the amplitude and phase of a sinusoid of known frequency.    jAetcosA  time domain frequency domain phasor
3. 3. Phasor Representation of a Time- Harmonic Field • Phasors are an extremely important concept in the study of classical electromagnetics, circuit theory, and communications systems. • Maxwell’s equations in simple media, circuits comprising linear devices, and many components of communications systems can all be represented as linear time-invariant (LTI) systems. • The eigen functions of any LTI system are the complex exponentials of the form: tj e 
4. 4. Phasor Representation of a Time- Harmonic Field • Given the phasor (frequency-domain) representation of a time-harmonic vector field, the time-domain representation of the vector field is obtained using the recipe:     tj erEtrE  Re, 
5. 5. Phasor Representation of a Time- Harmonic Field • Phasors can be used provided all of the media in the problem are linear  no frequency conversion. • When phasors are used, integro-differential operators in time become algebraic operations in frequency, e.g.:    rEj t trE    ,