Question

Convert the following dB to decimal a. -12 b. 3 c. 10 d. 0

Answer 1

Answer:

for -12db

 $\frac{V1}{V2}=0.251\\\\\frac{P1}{P2}=0.0631$

for 3db

$\frac{V1}{V2}=\sqrt{2}\\\\\frac{P1}{P2}=2$

for 10db

$\frac{V1}{V2}=3.16\\\\\frac{P1}{P2}=10$

for 0db

$\frac{V1}{V2}=1\\\\\frac{P1}{P2}=1$

Explanation:

The decibel is a logaritmic value given by:

$db=10*log(\frac{P1}{P2})=20*log(\frac{V1}{V2})$

we use 10 for power values and 20 for other values such voltages or currents.

$\frac{V1}{V2}=10^{\frac{db}{10}}\\\\\frac{P1}{P2}=10^{\frac{db}{20}}$

for -12db

$\frac{V1}{V2}=10^{\frac{-12}{10}}=0.251\\\\\frac{P1}{P2}=10^{\frac{-12}{20}}=0.0631$

for 3db

$\frac{V1}{V2}=10^{\frac{3}{10}}=\sqrt{2}\\\\\frac{P1}{P2}=10^{\frac{3}{20}}=2$

for 10db

$\frac{V1}{V2}=10^{\frac{10}{10}}=3.16\\\\\frac{P1}{P2}=10^{\frac{10}{20}}=10$

for 0db

$\frac{V1}{V2}=1\\\\\frac{P1}{P2}=1$