Solving Shannon’s Theorem for SNR in dB

• The equation for dB is:

dB = 10 log10 P/N

dB/10 = log10 P/N

P/N = 10 dB/10

• Substituting into Shannon’s Theorem:

bps = BW log2 (1 + P/N)

bps = BW log2 (1 + 10 SNR/10)

bps/BW = log2 (1 + 10 SNR/10)

2 bps/BW = 1 + 10 SNR/10

10 SNR/10 = 2 bps/BW - 1

SNR/10 = log10 (2 bps/BW - 1)

SNR = 10 log10 (2 bps/BW - 1)

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