Shannon's Formula: Solve S/N for Simple RF Data Link

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Discussion Overview

The discussion revolves around understanding Shannon's Formula in the context of a simple RF data link application. Participants explore the calculation of the signal-to-noise ratio (S/N) and its implications for bandwidth and channel capacity.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about calculating the S/N ratio given specific parameters such as usable RF power, bandwidth, and noise floor.
  • Several participants provide the formula for SNR in decibels, suggesting that SNR can be derived from the power levels of the signal and noise.
  • There is a discussion about the components of Shannon's Formula, including the maximum theoretical capacity of a channel (c) and the bandwidth (B), with some participants clarifying the relationship between these variables.
  • One participant questions the origin of the variables C and B in the context of the formula, indicating a need for further clarification.
  • Another participant mentions that the theoretical capacity may not be achievable in practice, highlighting a potential gap between theory and application.
  • A participant seeks guidance on the best modulation scheme for achieving high bit rates with minimal bandwidth, expressing concerns about power consumption and spectral efficiency in their application.

Areas of Agreement / Disagreement

Participants generally agree on the formulation of Shannon's Formula and its components, but there remains uncertainty regarding the practical application of these concepts, particularly in calculating the S/N ratio and selecting modulation schemes. No consensus is reached on the best approach for the specific RF data link application.

Contextual Notes

Participants reference various assumptions related to power levels, bandwidth, and noise characteristics without fully resolving how these factors interact in the specific context of the RF data link.

dnyberg2
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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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SNR (dB) = 10 log (Ps / Pn) = Ps (dB) - Pn (dB)

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

Does that help?
 
Zryn said:
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
 
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)
 
Zryn said:
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.
 
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?
 
Zryn said:
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?
 
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"
 
Last edited by a moderator:
Zryn said:
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"

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...
 
Last edited by a moderator:

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