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Circuit-slide-18 - Power Flow in Electromagnetic Waves The...

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Power Flow in Electromagnetic Waves The time-dependent power flow density of an electromagnetic wave is given by the instantaneous Poynting vector For time-varying fields it is important to consider the time-average power flow density where T is the period of observation.
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Consider time-harmonic fields represented in terms of their phasors The time-dependent Poynting vector can be expressed as the sum of the cross-products of the components
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The time-average power flow density can be obtained by integrating the previous result over a period of oscillation T . The pre-factors containing field phasors do not depend on time, therefore we have to solve for the following integrals:
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The final result for the time-average power flow density is given by Now, consider the following cross product of phasor vectors
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By combining the previous results, one can obtain the following time average rule We also call complex Poynting vector the quantity NOTE: the complex Poynting vector is not
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