Lecture 5 phasor notations
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Phasors are complex numbers that represent the amplitude and phase of sinusoidal signals and are useful for analyzing linear time-invariant systems. Phasors allow representations of electromagnetic fields, circuit elements, and communication systems as sinusoidal signals. By using phasors, time-domain differential operators can be converted to algebraic operations in the frequency domain, simplifying analyses of linear problems where frequency components do not mix.
Lecture 5 phasor notations
- 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. 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. 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. 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 ,