At which signal-to-noise ratio does the allocated bandwidth of a channel is equal to its maximum reliable data transmission rate specified by its channel capacity?

Question

1) -3 dB

2) 0 dB

3) 3 dB

4) 10 dB

Answer 1

Answer 2) 0 dB, is correct, as illustrated by:

The Shannon-Hartley channel capacity theorem:

C=B⋅log₂(1+SNR),

where C stands for the channel capacity or maximum net bit rate (bits/sec), B stands for the channel bandwidth (Hz), and SNR stands for the linear signal-to-noise power ratio.

If C=B ⇒ log₂(1+SNR)=1 ⇒ 1+SNR=2⇒SNR=1

expressing the SNR in dB ⇒SNR_dB=10⋅log₁₀(1)=0 dB