# Electrical engineering dopers: Explain Chu's fundamental antenna size limit, please

So I’m reading this pretty cool fluff piece about a breakthrough in manufacturing teeny-tiny* antennas. The article mentions something about the fundamental size limit, apparently the absolute minimum size, of an antenna. That there is such a limit was determined by L.J. Chu:

Can someone explain the Chu limit in words that I, a music history and musicology major who works with computer networks, can understand? I found some material online and tried to make sense of it, but I sprained my brain and now it needs to rest.

Thanks!

*From the title, I gather that’s the technical term

Are they talking about how an antenna’s dimensions have to be larger than 1/4 (I think) of the wavelength of the energy it’s emitting or receiving?

This is why the classic TV antenna has antenna elements of different lengths; each channel is on a different frequency and has a different wavelength. Thus the long part of the antenna is best at picking up Channel 2 and the short part is best at picking up Channel 13, for example. Channel 13 has a shorter wavelength than Channel 12.

Edit: just read the fluff piece. I think they’re saying “bandwidth” when they mean “frequency”.

You a probably correct. Even with my trivial understanding of the subject, it makes more sense if I mentally substitute “frequency” for “bandwidth.”

Bandwidth is proportional to frequency, though. We’re so used to thinking in terms of bits per second that we’ve forgotten the origin of the term. Bandwidth is, literally, the width of the portion of the frequency band you’re using. Like, if you have the portion of the spectrum from 100 MHz to 110 MHz, that give you a bandwidth of 10 MHz.

But this means that higher frequencies give you more bandwidth, and higher frequencies also correspond to smaller antennas. So I’m not sure what the fundamental limit would be due to.

Bandwidth is not proportional to frequency. Higher frequencies give you room for more bandwidth, but there’s nothing saying you have to take it. You can take your 10 MHz from between 1.250 and 1.260 GHz just as easily as from between 100 MHz and 110 MHz.

Of course, there’s a lower limit. If you’re dealing only with the frequencies under 1 MHz, there’s no way you can use 10 MHz of that, even if you take it all. But once you’re above that lower limit, you can go pretty much anywhere.

antenna element length determines the frequencies it can be used for. antenna element diameter or width determines the bandwidth it can be used for. as antennas go higher in frequency the same size element material (tube, wire, strip) will give greater bandwidth compared to antennas for lower frequencies.

I think they do mean bandwidth. The fluff piece refers twice to “data rate” (once in a quote from one of the people who developed it), and lots of web sites talk about “bandwidth”.

I’m not familiar with the Chu-Harrington limit, but the fundamental issue they are addressing is the fact that it is difficult to make an efficient antenna that is small compared to the wavelength. This is an impedance matching problem. It can be done, but it requires a resonant structure which inherently narrows the bandwidth. The smaller the antenna, the narrower the bandwidth. The sharpness of a resonance is measured by a dimensionless quantity called Q (quality factor). It is proportional to the number of cycles of oscillation for the amplitude to ring down by a factor of two (a tuning fork has a high Q, a wooden fork has a low Q). The reciprocal of the Q is proportional to the fractional bandwidth. I looked up one article on the Chu limit and it concludes that the Q of the optimal small antenna goes up as the reciprocal of the radius of the antenna to the third power, i.e. the useable bandwidth goes down like the radius cubed.

I suppose I properly should have said that bandwidth is proportional to a difference of frequencies. But if you have an antenna that can be tuned to some frequency plus or minus 10%, say, then bandwidth will be proportional to frequency.