# Shannon's Formula

## Main Question or Discussion Point

I guess its time I try and understand Shannon's Formula as it relates to a simple RF data link application. The part I am having trouble understanding is the S/N in the formula. If I am delivering 1dB of usable RF power at some carrier frequency and have an allowable bandwidth of 870 KHz and the noise floor in this system can be said to be -80dB how in Gods name do I develop the S/N part of the equation? Any help is most welcome.

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Zryn
Gold Member
SNR (dB) = 10 log (Ps / Pn) = Ps (dB) - Pn (dB)

c = B * log10 (1+SNR) / log10 (2)

Does that help?

SNR (dB) = 10 log (Ps / Pn) = Ps (dB) - Pn (dB)

c = B * log10 (1+SNR) / log10 (2)

Does that help?
Where did C and B come from?
The top line makes sense but you lost me with the second line...
Thanks

Zryn
Gold Member
Are you talking about the 'Shannons formula' that relates the maximum theoretical capacity of a channel (c), the bandwidth available (B), and the signal to noise ratio (SNR) ?

c = B * log2 (1+SNR) = B * log10 (1+SNR) / log10 (2)

Are you talking about the 'Shannons formula' that relates the maximum theoretical capacity of a channel (c), the bandwidth available (B), and the signal to noise ratio (SNR) ?

c = B * log2 (1+SNR) = B * log10 (1+SNR) / log10 (2)
Yes. I'm trying to understand how to calculate the S/N ratio for that application.

Zryn
Gold Member
SNR (dB) = 10 log (Ps / Pn) = Ps (dB) - Pn (dB)
This is how you generically figure out the SNR from the power (W or dB).

c = B * log2 (1+SNR) = B * log10 (1+SNR) / log10 (2)
This is Shannons formula, which wasn't expressly written down in the original post, and is just there to make sure we're talking about the same thing.

Does that clarify everything?

This is how you generically figure out the SNR from the power (W or dB).

This is Shannons formula, which wasn't expressly written down in the original post, and is just there to make sure we're talking about the same thing.

Does that clarify everything?
Sure. So c is channels and b is bandwidth?

Zryn
Gold Member
c = Maximum theoretical channel capacity (bits/second). This may not be achievable in reality.

B = Bandwidth (Hz)

Actually, all this and more can be found at http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem" [Broken]

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c = Maximum theoretical channel capacity (bits/second). This may not be achievable in reality.

B = Bandwidth (Hz)

Actually, all this and more can be found at http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem" [Broken]
Thanks for your patience and wisdom. Any idea where I can find a guide to the best modulation scheme that can transmit the highest bit-rates using the least bandwidth with the best spectral density? I find that GFSK looks sexy but still the bandwidth is still relatively substantial and the currently available chipsets are VERY power hungry! I am confined to the ISM band for my application. The present solution is very easy on battery power but a spectral hog. (BAD FCC) My present bit-rate is over 1mbps using a crude on / off keying approach of a very low power class D amplifier...

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