What is Decibels? and how to measure them

To show a signal loss or gained strength, the scientist used the unit called decibel(dB)

A decibel value in, strictly speaking, it is a ratio b/w two values

A bel is named after Alexander Graham Bell

Remember: if the decibel value is negative then the signal lost its strength similarly if the decibel value is positive then the signal got amplified or strengthened

Decibels definition: decibel is a meter to express a ratio b/w two signals power ( $p_0$ and $p_1$ )

dB= deci-Bel

bel= $log_{10}(p_o/p_i)$

A deci-bel (dB) is one-tenth of a bel

$\begin{equation*}deci-bel(dB)=10 log_{10} \frac{p_o}{p_i}\end{equation*}$

Where $p_o$ is the output power and $p_i$ is the input power

Decibel measurement

Consider a signal is passed through an amplifier with power 10 w and received 20w power as output calculate whether it is gain or loss of signal strength

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$\begin{equation*}Gain=10 log_{10} \frac{20}{10} =3.01dB\end{equation*}$

Consider a signal is passed through a transmission medium (cable) with power 20 w and received 10w power as output calculate whether it is gain or loss of signal strength

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$\begin{equation*}Loss=10 log_{10} \frac{10}{20} =-3.01dB\end{equation*}$

decibel levels chart

Units of sound intensity : the intensity of sound can be expressed as power per unit area(Watts/ $cm^2$ )

Example	Decibels	Watts/ $cm^2$
Painful	140 dB	$10^{-2}$
	130 dB	$10^{-3}$
Discomfort	120 dB	$10^{-4}$
rock concerts	110 dB	$10^{-5}$
	100 dB	$10^{-6}$
limit for industrial noise	90 dB	$10^{-7}$
	80 dB	$10^{-8}$
	70 dB	$10^{-9}$
Normal discussion	60 dB	$10^{-10}$
	50 dB	$10^{-11}$
	40 dB	$10^{-12}$
Whisper	30 dB	$10^{-13}$
	20 dB	$10^{-14}$
Normal breathing	10 dB	$10^{-15}$
	0 dB	$10^{-16}$
	-10 dB	$10^{-17}$
	-20 dB	$10^{-18}$

Decibel scale and Amplitude

floating point PCM Amplitude	dB	16 bit PCM Amplitude
1.0	0	32,768
0.75	-2.4987	24.576
0.5	-6.0206	16,384
0.25	-12.0412	8,192
0.1	-20	3,277
0.05	-26.0206	1,638
0.01	-40	328
0.001	-60.0	33