A little background: I am simulating the response of an antenna to a pulse. The pulse has a wide frequency range, but the antenna only responds to a fairly narrow frequency. I can extract voltage and current from the antenna: they look like sinusoidal signals quickly decaying in time.
I now want to calculate the power spectral density (PSD) of that received signal. If I calculate the FFT of my voltage and current signals I see a nice isolated peak at the resonance frequency, so I would expect the power to also be concentrated around that frequency.
My first attempt was simply to multiply the voltage and current in time domain and then calculating the PSD of that. It did not work, the peak of the PSD happens at a frequency roughly double the expected one and at the desired frequency there is actually a "notch". I suspect that it is because by simply multiplying current and voltage I have effectively modulated one onto the other, therefore mixing their frequencies.
I can get a PSD that seem to make sense if instead I multiply the voltage and current in frequency domain and then calculate the PSD from the resulting spectrum.
So my questions are:
- Why can't I just calculate power as v*i in time domain?
- Does multiplying voltage and current spectra to then calculate the PSD make sense?