I was looking for an equation that could show the relationship between the range of frequencies of an EM wave, and its Maximum data transfer rate. I know that ranges of shorter wavelengths can have a larger bitrate/symbol rate, but could not find an equation relating the two variables.

Thanks in advance for the help.

EDIT: I refined my wording above. Also, no one answered my question over at amateur radio SE. As for the nyquist rate wiki page, I still could not find the answer I was looking for.

  • $\begingroup$ The bandwidth of a given frequency is zero. $\endgroup$ – Hot Licks Jul 28 '18 at 1:32
  • $\begingroup$ @HotLicks could you clarify what you mean? Did I misspeak? $\endgroup$ – FOG.js Jul 28 '18 at 1:34
  • $\begingroup$ "Bandwidth" refers to the range of adjacent frequencies occupied by some signal. $\endgroup$ – Hot Licks Jul 28 '18 at 1:35
  • $\begingroup$ Oh yes, but I was using the computational definition: "The maximum rate of data transfer across a given path" @HotLicks $\endgroup$ – FOG.js Jul 28 '18 at 1:36
  • $\begingroup$ Right. And the way you transfer data is by varying the carrier frequency. $\endgroup$ – Hot Licks Jul 28 '18 at 1:39

You are looking for the Shannon-Hartley Theorem, which describes the upper bound on the information sent over a noisy channel:

$$ C = B \log_2 ( 1 + S / N ) $$

Where S/N is the signal to noise ratio of the channel, B is the bandwidth in Hz, and C is the information rate in bits/second. This result assumes Gaussian white noise.

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  • $\begingroup$ Thank you so much. I feel silly for not finding the wiki page, but am glad you were able to be such a respectful lifesaver $\endgroup$ – FOG.js Jul 28 '18 at 17:56

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