Question

Each time the voltage gain decreases by a factor of 2, the decibel voltage gain

a. increase by 6 dB
b. decrease by 10 dB
c. increase by 10 dB
d. decrease by 6 dB

Answer 1

When the voltage gain decreases by a factor of 2, the decibel voltage gain decreases by 6 dB. This is because decibel levels are based on a logarithmic scale, where a reduction by a factor of 2 in voltage corresponds to a 6 dB decrease.

Step-by-step explanation:

When the voltage gain decreases by a factor of 2, the decibel (dB) voltage gain decreases by 6 dB. Decibels measure the ratio of two powers logarithmically. To show this, consider that for power ratios, a reduction by a factor of 2 corresponds to a reduction of approximately 3 dB:

• 20 · log10(1/2) ≈ -3 dB.

Since power is related to voltage squared (P ≈ V²/R where R is resistance), if the voltage gain is cut in half, the power ratio is reduced by a factor of four. For voltage ratios, the reduction by a factor of 2 is:

• 20 · log10(1/2) ≈ -6 dB.

Therefore, the correct answer is option d. decrease by 6 dB.