If the gain of an amplifier is 18 dB, what is the gain after reducing the power by one-half?

• A. 15 dB
• B. 9 dB
• C. 36 dB
• D. 0.5 dB

Answer: (A)

To determine the gain of the amplifier after the power is reduced by one-half, we first need to understand the relationship between power changes and the corresponding changes in decibels (dB).

In the context of decibels, a power decrease of half corresponds to a decrease of approximately 3 dB. The formula for calculating the power gain in dB is given by:

[

\text{Gain (dB)} = 10 \log_{10} \left( \frac{P_{out}}{P_{in}} \right)

]

In this scenario, we start with a gain of 18 dB. If the power is halved, the new gain can be calculated as follows:

1. Subtract the 3 dB from the original gain of 18 dB:

[

18 \text{ dB} - 3 \text{ dB} = 15 \text{ dB}

]

This calculation reflects the fact that when the power is decreased by one-half, the gain in decibels decreases by 3 dB.

Thus, the gain of the amplifier after reducing the power by one-half is 15 dB. This logic aligns with standard conventions