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Is phasor used for Electromagnetic waves, transient of RF module?

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After completing a simulation, I tried plot imag(temw.Ex) and actually got somthing. It seems that even in a transient analysis, the EM waves are still complex, not real. But actually the concept of phase is ill defined for a transient analysis because a wide range of frequencies exist. Also in the help documents, a phasor is said to be used for harmonic field, Electromagnetic waves, frequency domain. So what does a complex field mean in a transient analysis? This also gives rise to another problem. When I specify surface current by Jx=sigma*Ex, should I use real(sigma*temw.Ex) or simply sigma*temw.Ex? Also for a continuous wave source, should I use cos(omega*t) or exp(i*omega*t)?

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