How much increase in decibels corresponds to the doubling of power?

Doubling the power in a signal results in an increase of 3 decibels (dB). This relationship is derived from the logarithmic nature of the decibel scale, which is based on the ratio of two power levels.

When power is measured in decibels, the formula used is:

[ \text{dB} = 10 \log_{10} \left( \frac{P_2}{P_1} \right) ]

In the case of doubling the power (where (P_2 = 2P_1)), the equation becomes:

[ \text{dB} = 10 \log_{10} (2) ]

Calculating ( \log_{10} (2) ) gives approximately 0.301. Therefore, when doubling the power:

[ \text{dB} = 10 \times 0.301 \approx 3.01 \text{ dB} ]

Thus, an increase of approximately 3 dB corresponds to doubling the power of a signal. This reasoning clarifies why the correct answer is an increase of 3 dB for power doubling. In practical terms, this measurement is essential in fields such as telecommunications