I was wondering, how does one derive the radiation pattern for a dipole antenna if you don't assume a sinusoidal forcing function? It seems this assumption kind of ignores the most important question which is the effect of modulation on the radiation of EM waves.

Intuitively, using superposition, it seems you could make an argument with regards to the fourier transform being a super position of sinusoids but I don't know that would work here.

  • $\begingroup$ suggest you post this on the amateur radio SE. lots of antenna experts there. $\endgroup$ May 5, 2018 at 6:37
  • $\begingroup$ Look for the field propagated from a dipole due to a Dirac Delta impulse excitation. Then you would have the impulse response of the dipole and can get other radiation patterns by convolution with other excitations. These in general will be a function of angle and time so the fourier approach does not work except perhaps for cw excitations. $\endgroup$
    – user45664
    May 5, 2018 at 16:25
  • 1
    $\begingroup$ See "Two-way beam patterns from ultrawideband arrays",May 1992 Proceedings of SPIE, DOI10.1117/12.59025 $\endgroup$
    – user45664
    May 5, 2018 at 16:35
  • $\begingroup$ Assuming the Hertzian dipole, why not just take the response to each frequency as the transfer function in the fourier domain? I will check out these other things $\endgroup$ May 5, 2018 at 22:38

1 Answer 1


A non-sinusoidal (but periodic) driving force can be broken down into a Fourier series of (co)sinusoidal terms at multiples of the principal frequency.

Each of these terms will produce electric (far) fields at their frequency, with the $\sin \theta$ polar dependence of a sinusoidally driven dipole, but with a radially-dependent amplitude that depends (linearly) on their fractional contribution to the driving signal and their frequency. There is also a radially- and time-dependent phase.

Since there is no fixed phase relationship at any position between the components of different frequencies, this cannot change the polar dependence of the signal. But of course the higher frequency components become much more important in the radiation field than in the driving signal.

  • $\begingroup$ Yes but what about nonperiodic? A simple example is PAM modulation. $\endgroup$ May 5, 2018 at 7:41
  • $\begingroup$ The antenna is a linear time invariant system in any five direction and range. Use a Fourier transform, therefore, to analyse a nonperiodic excitation such as PAM and then apply to each wavelet the transfer function represented by the antenna. $\endgroup$
    – hyportnex
    May 5, 2018 at 23:30

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