A decibel (dB) is one tenth of a bel (B), i.e. 1B = 10dB. The bel is the logarithm of the arrangement amid two ability quantities of 10:1, and amid two acreage quantities in the arrangement \sqrt{10}: 1 .14 A acreage abundance is a abundance such as voltage, current, complete pressure, electric acreage strength, acceleration and allegation density, the aboveboard of which in beeline systems is proportional to power. A ability abundance is a ability or a abundance anon proportional to power, e.g. activity density, acoustic acuteness and beaming intensity.
The adding of the arrangement in decibels varies depending on whether the abundance getting abstinent is a ability abundance or a acreage quantity.
Two signals that alter by one decibel accept a ability arrangement of 1.258925411794167 (or 10^\frac{1}{10}\,) and an amplitude arrangement of 1.122018454301963 (or \sqrt{10}^\frac{1}{10}\,).15
edit Ability quantities
When apropos to abstracts of ability or intensity, a arrangement can be bidding in decibels by evaluating ten times the base-10 logarithm of the arrangement of the abstinent abundance to the advertence level. Thus, the arrangement of a ability amount P1 to addition ability amount P0 is represented by LdB, that arrangement bidding in decibels, which is affected application the formula:
L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,
The base-10 logarithm of the arrangement of the two ability levels is the amount of bels. The amount of decibels is ten times the amount of bels (equivalently, a decibel is one-tenth of a bel). P1 and P0 accept to admeasurement the aforementioned blazon of quantity, and accept the aforementioned units afore artful the ratio. If P1 = P0 in the aloft equation, again LdB = 0. If P1 is greater than P0 again LdB is positive; if P1 is beneath than P0 again LdB is negative.
Rearranging the aloft blueprint gives the afterward blueprint for P1 in agreement of P0 and LdB:
P_1 = 10^\frac{L_\mathrm{dB}}{10} P_0 \, .
Since a bel is according to ten decibels, the agnate formulae for altitude in bels (LB) are
L_\mathrm{B} = \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,
P_1 = 10^{L_\mathrm{B}} P_0 \, .
edit Acreage quantities
When apropos to abstracts of acreage amplitude it is accepted to accede the arrangement of the squares of A1 (measured amplitude) and A0 (reference amplitude). This is because in a lot of applications ability is proportional to the aboveboard of amplitude, and it is adorable for the two decibel formulations to accord the aforementioned aftereffect in such archetypal cases. Thus the afterward analogue is used:
L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{A_1^2}{A_0^2}\bigg) = 20 \log_{10} \bigg(\frac{A_1}{A_0}\bigg). \,
The adequation of 10 \log_{10} \frac{a^2}{b^2} and 20 \log_{10} \frac{a}{b} is one of the accepted backdrop of logarithms.
The blueprint may be rearranged to give
A_1 = 10^\frac{L_\mathrm{dB}}{20} A_0 \,
Similarly, in electrical circuits, blown ability is about proportional to the aboveboard of voltage or accepted if the impedance is captivated constant. Taking voltage as an example, this leads to the equation:
G_\mathrm{dB} =20 \log_{10} \left (\frac{V_1}{V_0} \right ) \quad \mathrm \quad
where V1 is the voltage getting measured, V0 is a defined advertence voltage, and GdB is the ability accretion bidding in decibels. A agnate blueprint holds for current.
edit Examples
dB power arrangement amplitude ratio
100 10 000 000 000 100 000
90 1 000 000 000 31 620
80 100 000 000 10 000
70 10 000 000 3 162
60 1 000 000 1 000
50 100 000 316 .2
40 10 000 100
30 1 000 31 .62
20 100 10
10 10 3 .162
0 1 1
-10 0 .1 0 .316 2
-20 0 .01 0 .1
-30 0 .001 0 .031 62
-40 0 .000 1 0 .01
-50 0 .000 01 0 .003 162
-60 0 .000 001 0 .001
-70 0 .000 000 1 0 .000 316 2
-80 0 .000 000 01 0 .000 1
-90 0 .000 000 001 0 .000 031 62
-100 0 .000 000 000 1 0 .000 01
An archetype calibration assuming ability ratios x and amplitude ratios √x and dB equivalents 10 log10 x. It is easier to butt and analyze 2- or 3-digit numbers than to analyze up to 10 digits.
All of these examples crop dimensionless answers in dB because they are about ratios bidding in decibels.
To account the arrangement of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels, use the formula
G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{1000~\mathrm{W}}{1~\mathrm{W}}\bigg) \equiv 30~\mathrm{dB} \,
To account the arrangement of \sqrt{1000~\mathrm{W}} \approx 31.62~\mathrm{V} to 1~\mathrm{V} in decibels, use the formula
G_\mathrm{dB} = 20 \log_{10} \bigg(\frac{31.62~\mathrm{V}}{1~\mathrm{V}}\bigg) \equiv 30~\mathrm{dB} \,
Notice that ({31.62\,\mathrm{V}}/{1\,\mathrm{V}})^2 \approx {1\,\mathrm{kW}}/{1\,\mathrm{W}}, illustrating the aftereffect from the definitions aloft that GdB has the aforementioned value, 30~\mathrm{dB}, behindhand of whether it is acquired from admiral or from amplitudes, provided that in the specific arrangement getting advised ability ratios are according to amplitude ratios squared.
To account the arrangement of 1 mW (one milliwatt) to 10 W in decibels, use the formula
G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{0.001~\mathrm{W}}{10~\mathrm{W}}\bigg) \equiv -40~\mathrm{dB} \,
To acquisition the ability arrangement agnate to a 3 dB change in level, use the formula
G = 10^\frac{3}{10} \times 1\ = 1.99526... \approx 2 \,
A change in ability arrangement by a agency of 10 is a 10 dB change. A change in ability arrangement by a agency of two is about a 3 dB change. More precisely, the agency is 103/10, or 1.9953, about 0.24% altered from absolutely 2. Similarly, an access of 3 dB implies an access in voltage by a agency of about \scriptstyle\sqrt{2}, or about 1.41, an access of 6 dB corresponds to about four times the ability and alert the voltage, and so on. In exact agreement the ability arrangement is 106/10, or about 3.9811, a about absurdity of about 0.5%.
The adding of the arrangement in decibels varies depending on whether the abundance getting abstinent is a ability abundance or a acreage quantity.
Two signals that alter by one decibel accept a ability arrangement of 1.258925411794167 (or 10^\frac{1}{10}\,) and an amplitude arrangement of 1.122018454301963 (or \sqrt{10}^\frac{1}{10}\,).15
edit Ability quantities
When apropos to abstracts of ability or intensity, a arrangement can be bidding in decibels by evaluating ten times the base-10 logarithm of the arrangement of the abstinent abundance to the advertence level. Thus, the arrangement of a ability amount P1 to addition ability amount P0 is represented by LdB, that arrangement bidding in decibels, which is affected application the formula:
L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,
The base-10 logarithm of the arrangement of the two ability levels is the amount of bels. The amount of decibels is ten times the amount of bels (equivalently, a decibel is one-tenth of a bel). P1 and P0 accept to admeasurement the aforementioned blazon of quantity, and accept the aforementioned units afore artful the ratio. If P1 = P0 in the aloft equation, again LdB = 0. If P1 is greater than P0 again LdB is positive; if P1 is beneath than P0 again LdB is negative.
Rearranging the aloft blueprint gives the afterward blueprint for P1 in agreement of P0 and LdB:
P_1 = 10^\frac{L_\mathrm{dB}}{10} P_0 \, .
Since a bel is according to ten decibels, the agnate formulae for altitude in bels (LB) are
L_\mathrm{B} = \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,
P_1 = 10^{L_\mathrm{B}} P_0 \, .
edit Acreage quantities
When apropos to abstracts of acreage amplitude it is accepted to accede the arrangement of the squares of A1 (measured amplitude) and A0 (reference amplitude). This is because in a lot of applications ability is proportional to the aboveboard of amplitude, and it is adorable for the two decibel formulations to accord the aforementioned aftereffect in such archetypal cases. Thus the afterward analogue is used:
L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{A_1^2}{A_0^2}\bigg) = 20 \log_{10} \bigg(\frac{A_1}{A_0}\bigg). \,
The adequation of 10 \log_{10} \frac{a^2}{b^2} and 20 \log_{10} \frac{a}{b} is one of the accepted backdrop of logarithms.
The blueprint may be rearranged to give
A_1 = 10^\frac{L_\mathrm{dB}}{20} A_0 \,
Similarly, in electrical circuits, blown ability is about proportional to the aboveboard of voltage or accepted if the impedance is captivated constant. Taking voltage as an example, this leads to the equation:
G_\mathrm{dB} =20 \log_{10} \left (\frac{V_1}{V_0} \right ) \quad \mathrm \quad
where V1 is the voltage getting measured, V0 is a defined advertence voltage, and GdB is the ability accretion bidding in decibels. A agnate blueprint holds for current.
edit Examples
dB power arrangement amplitude ratio
100 10 000 000 000 100 000
90 1 000 000 000 31 620
80 100 000 000 10 000
70 10 000 000 3 162
60 1 000 000 1 000
50 100 000 316 .2
40 10 000 100
30 1 000 31 .62
20 100 10
10 10 3 .162
0 1 1
-10 0 .1 0 .316 2
-20 0 .01 0 .1
-30 0 .001 0 .031 62
-40 0 .000 1 0 .01
-50 0 .000 01 0 .003 162
-60 0 .000 001 0 .001
-70 0 .000 000 1 0 .000 316 2
-80 0 .000 000 01 0 .000 1
-90 0 .000 000 001 0 .000 031 62
-100 0 .000 000 000 1 0 .000 01
An archetype calibration assuming ability ratios x and amplitude ratios √x and dB equivalents 10 log10 x. It is easier to butt and analyze 2- or 3-digit numbers than to analyze up to 10 digits.
All of these examples crop dimensionless answers in dB because they are about ratios bidding in decibels.
To account the arrangement of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels, use the formula
G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{1000~\mathrm{W}}{1~\mathrm{W}}\bigg) \equiv 30~\mathrm{dB} \,
To account the arrangement of \sqrt{1000~\mathrm{W}} \approx 31.62~\mathrm{V} to 1~\mathrm{V} in decibels, use the formula
G_\mathrm{dB} = 20 \log_{10} \bigg(\frac{31.62~\mathrm{V}}{1~\mathrm{V}}\bigg) \equiv 30~\mathrm{dB} \,
Notice that ({31.62\,\mathrm{V}}/{1\,\mathrm{V}})^2 \approx {1\,\mathrm{kW}}/{1\,\mathrm{W}}, illustrating the aftereffect from the definitions aloft that GdB has the aforementioned value, 30~\mathrm{dB}, behindhand of whether it is acquired from admiral or from amplitudes, provided that in the specific arrangement getting advised ability ratios are according to amplitude ratios squared.
To account the arrangement of 1 mW (one milliwatt) to 10 W in decibels, use the formula
G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{0.001~\mathrm{W}}{10~\mathrm{W}}\bigg) \equiv -40~\mathrm{dB} \,
To acquisition the ability arrangement agnate to a 3 dB change in level, use the formula
G = 10^\frac{3}{10} \times 1\ = 1.99526... \approx 2 \,
A change in ability arrangement by a agency of 10 is a 10 dB change. A change in ability arrangement by a agency of two is about a 3 dB change. More precisely, the agency is 103/10, or 1.9953, about 0.24% altered from absolutely 2. Similarly, an access of 3 dB implies an access in voltage by a agency of about \scriptstyle\sqrt{2}, or about 1.41, an access of 6 dB corresponds to about four times the ability and alert the voltage, and so on. In exact agreement the ability arrangement is 106/10, or about 3.9811, a about absurdity of about 0.5%.
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