If output power increases by a factor of 4, how many decibels is this?

If output power increases by a factor of 4, how many decibels is this?

• A. 4 dB
• B. 12 dB
• C. 2 dB
• D. 6 dB

Answer: (D)

When you express a change in power in decibels, use dB = 10 log10(P2/P1). If the power increases by a factor of 4, P2/P1 = 4, so dB = 10 log10(4) = 10 × 0.60206 ≈ 6.02 dB. So the increase is about 6 dB. The other values correspond to different power ratios: 4 dB is a smaller factor, 12 dB is a much larger factor, and 2 dB corresponds to an even smaller factor. (If you were dealing with voltage or current rather than power, you’d use 20 log10 instead.)

When you express a change in power in decibels, use dB = 10 log10(P2/P1). If the power increases by a factor of 4, P2/P1 = 4, so dB = 10 log10(4) = 10 × 0.60206 ≈ 6.02 dB. So the increase is about 6 dB. The other values correspond to different power ratios: 4 dB is a smaller factor, 12 dB is a much larger factor, and 2 dB corresponds to an even smaller factor. (If you were dealing with voltage or current rather than power, you’d use 20 log10 instead.)