# Radiation Pattern for a Dipole Antenna with non-sinusodial forcing voltage

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.

• suggest you post this on the amateur radio SE. lots of antenna experts there. – niels nielsen May 5 '18 at 6:37
• 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. – user45664 May 5 '18 at 16:25
• See "Two-way beam patterns from ultrawideband arrays",May 1992 Proceedings of SPIE, DOI10.1117/12.59025 – user45664 May 5 '18 at 16:35
• 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 – FourierFlux May 5 '18 at 22:38

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.