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This is a question I thought about when trying to understand a design of an antenna.

For different kind of waveform of electromagnetic wave propagating through space, how does one modify an antenna thus giving the antenna the best receiving efficiency. Antenna theory seems to always assume electromagnetic waves as perfect sinusoidal wave, conversation on this topic seems to be few and far between.

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Once you understand the sine wave case, you understand almost everything: because everything is sine waves, or at least the sum of sine waves. The superposition principle (linearity) says that the antenna's response to a sum of sine waves will be equal to the sum of the responses to individual sine waves. And 99.9% of the time we're considering signals of bandwidth small enough that all of those component frequencies will be close enough to one another that the antenna's response to them won't vary significantly.

Occasionally you might have to deal with a very high-Q antenna so that you have to deal with the distortion due to limited bandwidth, but that's a specialty topic.

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  • $\begingroup$ So suppose we were to receive radio waves from a dipole antenna, which definitely doesn't look like a perfect sine wave, or radio waves from a point source, which is also not a perfect sine wave, do we have to know every aspects of the wave(including composing frequencies...)when designing an antenna specify for the wave? $\endgroup$
    – Felix
    Jan 9, 2023 at 8:36
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    $\begingroup$ Also,"And 99.9% of the time we're considering signals of bandwidth small enough that all of those component frequencies will be close enough to one another that the antenna's response to them won't vary significantly." in other words, it is possible to build an antenna for one frequency regardless of a waveform? or is sinusodial wave assumed here? $\endgroup$
    – Felix
    Jan 9, 2023 at 8:39
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    $\begingroup$ “So suppose we were to receive radio waves from a dipole antenna, which definitely doesn't look like a perfect sine wave, or radio waves from a point source, which is also not a perfect sine wave” — I think this might be the point of confusion. “Is a sine wave” is a question about the frequency content of a signal, which is unaffected by the shape of the antenna that radiates it. It sounds like you might be thinking of the wave being a plane wave or not — which is an independent property. $\endgroup$
    – Kevin Reid AG6YO
    Jan 9, 2023 at 16:08
  • $\begingroup$ Then how does the frequency content affect the shape of spherical waves generated by for example a dipole Does the shape of plane waves affect the shape of electromagnetic waves and the design of antenna?(Please do remind me if this comment violates the community rules, I’m not sure if this counts as a secondary discussion) $\endgroup$
    – Felix
    Jan 9, 2023 at 18:45
  • $\begingroup$ @Felix In other words we assume an approximate sine wave since the difference from an actual sine wave is too little to matter. $\endgroup$ Jan 17, 2023 at 18:58
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It is a choice - a convention - to use sine waves. But it's a good choice, for several reasons.

Electromagnetic fields, waves and radiation are described by Maxwell's equations. There is nothing sinusoidal about nature, the equations work fine for any shape of waves, but it is easier to derive solutions, facts about nature, if a single frequency sine wave is assumed. Because, for example, $\frac{\mathrm{d}}{\mathrm{d}t}sin(t) = cos(t)$ you can find closed-form solutions for travelling electromagnetic waves, waves penetrating media of different permittivity and permeability, and even simple interaction with wires, without resorting to numerical integration.

There is no limitation caused by the choice of sine waves, if it's convenient, because any other waveform you might need can be made up of the superposition of many sine waves. You can also use an inverse Fourier transform to find the response of an antenna etc in the time domain, and then convolve it with your input waveform.

Finally, as it turns out, most radio communications are so narrow band that for antenna purposes, they are effectively sine waves at one frequency. For example a strong whistle on the mic of an AM transmitter will produce three sine waves, at (say) 27.999, 28.100 and 28.101 MHz, which are all close enough together that we would only analyse one of them. This is expecially true for amateur radio, where wideband transmission is further limited by the rules.


There are some interesting cases where sine waves aren't ideal though:

Ultra-wideband transmitters send actual pulses of EM radiation, with fairly sharp sides. They are band-limited to cover about 3-10 GHz (to reduce interference to traditional communications, especially GNSS). UWB required very special wide band antennas, that do not distort the phase relationship between the different sine waves that make up the impulse, ie. they must preserve the shape of the pulse. They are usually fat monopoles of some kind patent:
enter image description here.

There are even antenna measurement systems that transmit ultra-short impulses, and receive with a fast oscilloscope, to measure the performance of the antenna in the time domain, or at all frequencies at once. These have some advantages, for example you might not need an anechoic chamber as you can simply discard signals beyond a certain time, before the reflections from the ground or walls can reach the receiving antenna.

Also there is one quite powerful kind of electromagnetic simulation called Finite Difference Time Domain that divides space into a fine grid of small cells, and then over many small time steps, solves Maxwell's equations for each cell based the fields present in the adjacent cells in the previous time step. This is completely independent of the actual waveform of the EM radiation, but typically an impulse is used as a stimulus. If you want to see the response at a single frequency, the software uses a Fourier transform to derive it. For example, here is a short pulse of electromagnetic radiation being reflected from a dish antenna, or passing through a dielectric lens. [picture from youtube as linked]
enter image description here

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  • $\begingroup$ For the Finite Difference Time Domain part, from your description there seems to be two different waveforms here, EM radiation and? Also image of EM wave generated by dipole like this is simulated by this method? $\endgroup$
    – Felix
    Jan 10, 2023 at 4:46
  • $\begingroup$ The black circles on the right are the Luneberg lens itself - each line is the boundary between different dielectric materials. $\endgroup$
    – tomnexus
    Jan 10, 2023 at 5:09
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Felix, don't confuse representations of a signal on an oscilloscope screen, or pictures online, or in a book, of analog or digital signals, as waveforms that are changing frequency; they generally are not. The waveform you see in illustrations or on a scope screen are voltage levels of that signal, NOT frequency changes. The frequency is determined by when that waveform crosses the zero mark on the scope screen, not by the amplitude of the waveform; the waveform amplitude is only a representation of voltage level.

And generally, even with signals that are changing frequency as part of a modulation method, like FM, those frequency changes aren't usually enough to require an antenna be designed to be more "wide-banded" than an antenna being used for other modes of communication.

However, if you are talking about circular polarization of a radio signal, that is a discussion in and of itself since that type of magnetic field does have a waveform that is produced and best received by particular antenna designs.

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