# How to calculate bandwidth of a wire, “air” or other channels?

I'm really curious of how engineers identify what is the frequency range that could be sent through "wire" as channel? Do they put wire in front of them and make test that consists of sending sinusoidal signals through it by gradually increasing frequency, till maybe wire suddenly "burns off" and they measure that as highest frequency of a "wire's bandwidth"? How do they test "air" as channel where EM waves travel?

First of all note that bandwidth may have multiple (but similar) definitions. A practically accepted one defines the bandwidth of a baseband lowpass channel (indeed a filter as an LTI system) as the frequency at which the magnitude of its frequency response falls to $1/\sqrt{2}$ of the value at the frequency $f=0$. This point is conventionally called as the $-3$ dB point, or as the cutoff frequency of the channel (filter).

A physical conducting wire can be electrically modeled (depending on the frequency of application) as an LTI system with relevant parameters of $R$, $L$, and $C$, according to its resistance, inductance and capacitance respectively. Such a model therefore will define an LTI filter with a frequency response magnitude which will have theoretical $-3$ dB point(s). In practice the bandwidth of the filter could indeed be measured by a set up similar to what you have defined.

The air as a channel means either the empty space (vacuum) or the atmosphere. The former case ideally has an infinite electromagnetic bandwidth which is practically limited by the ability to create EM waves and the physical space's intrinsinc space-time and energy-mass characterization. The latter has a much narrower bandwidth determined by the electromagnetic characterisation of atmospheric air composition and its different layers, furthermore the sperical shape of Earth and the conducting soil also affects the channel characterisation. It's well known that the channel bandwidth of atmosphere depends on frequency, especially the ionosphere layer.

• Part 1 Well, if we assume that bandWIDTH intuitively means something like B=fmax-fmin, than in "standard" drawings of frequency response of filters you've mentioned like in this picture: upload.wikimedia.org/wikipedia/commons/thumb/6/60/… P.S. See Part 2 below this answer – Krushe Dec 27 '17 at 14:31
• Part 2 Why do we choose bandwidth to be cutoff frequency - 0? Because, every frequency component above the cutoff frequency will be attenuated, and it is not usable. So, no point in considering that part. That's my opinion! I presume that no two wires are identical, so they don't have same cutoff frequency. Hence, in practial cases do we have (use) something called "average cutoff frequency"? – Krushe Dec 27 '17 at 14:32
• Part 3 There is missing part between image and "P.S. See Part 2...": bandwidth would mean B=Fcutoff-0=Fcutoff which basicaly means that bandwith is cutoff frequency. – Krushe Dec 27 '17 at 14:38
• yes that's true! frequencies outise the of bandwidth are useless. The wire bandwidths depend on their length , diameter and intrinsinc conductivity. – Fat32 Dec 27 '17 at 14:43
• So, how in practise we know for every wire it's cutoff frequency? I mean, it would be a lot of job to calculate for every wire in our network it's cutoff frequency. Hence, in practial cases do we have (use) something called "average cutoff frequency" and we choose that as our reference point? – Krushe Dec 27 '17 at 15:06

Technically, a wire is not a pipe, electrical currents ideally flow on the wire instead of through a wire.

All of it is EM. The differences are the boundary values imposed on the fields and the properties of the material. A improperly terminated cable is useless regardless of the bandwidth limit of the cable.

A TE or HE wave guide have a critical frequency that a field needs to be above, not below, to propagate. These modes are also dispersive .

In most cases there are mathematical models that are used that predict propagation behavior but models only capture first and perhaps second order effects so measurement, empiricism, and experience eliminates a lot of speculation.

• The skin currents are ok but not all currents are there? Otherwise I just wonder, why do we waste the volumetric bulk of the wire instead of wrapping a thin layer of copper ower a cheaper and lighter something ? – Fat32 Dec 27 '17 at 18:06
• Heat conducts as well – Stanley Pawlukiewicz Dec 27 '17 at 18:08
• cannot comment on the heating in detail, but possible. – Fat32 Dec 27 '17 at 18:12