Which formula defines the signal-to-noise ratio (SNR) in decibels?

Which formula defines the signal-to-noise ratio (SNR) in decibels?

• A. 20 log10(P_signal/P_noise)
• B. 10 log10(P_signal/P_noise)
• C. log10(P_signal/P_noise)
• D. 40 log10(P_signal/P_noise)

Answer: (B)

In decibels, the SNR is defined as 10 times the base-10 logarithm of the power ratio because decibels are a logarithmic scale for power. Since SNR compares signal power to noise power, the appropriate form is 10 log10(P_signal / P_noise). If you were instead dealing with voltages or amplitudes, you’d use 20 log10(V_s / V_n) because power is proportional to the square of the voltage (P ∝ V^2); the extra factor of 2 inside the log translates to the 20 in front when you convert a voltage ratio to decibels. The other options don’t match this power-based definition: 20 log10(P_s / P_n) would misalign with the standard power-to-decibel relation, log10(P_s / P_n) lacks the 10 to place it in decibels, and 40 log10(P_s / P_n) isn’t a recognized form for SNR.

In decibels, the SNR is defined as 10 times the base-10 logarithm of the power ratio because decibels are a logarithmic scale for power. Since SNR compares signal power to noise power, the appropriate form is 10 log10(P_signal / P_noise). If you were instead dealing with voltages or amplitudes, you’d use 20 log10(V_s / V_n) because power is proportional to the square of the voltage (P ∝ V^2); the extra factor of 2 inside the log translates to the 20 in front when you convert a voltage ratio to decibels. The other options don’t match this power-based definition: 20 log10(P_s / P_n) would misalign with the standard power-to-decibel relation, log10(P_s / P_n) lacks the 10 to place it in decibels, and 40 log10(P_s / P_n) isn’t a recognized form for SNR.