Mostrar código-fonte de Decibel

{{short description|Unidade logarítmica que expressa o rácio entre uma quantidade física e um valor de referência}}
[[Imagem:Decibel NIOSH.jpg|thumb|250px|Exemplos de níveis sonoros, avaliados em decibel, de várias fontes sonoras e actividades (extraído da aplicação ''NIOSH Sound Level Meter'')]]
O '''decibel''' (símbolo: '''dB''') é uma [[unidade de medida]] relativa, [[Dimensão|adimensional]], correspondente à décima parte de um [[Bel (unidade)|bel]] (símbolo: B), que expressa o [[Razão (matemática)|rácio]] de uma [[grandeza física]] (geralmente [[energia]] ou [[intensidade (física)|intensidade]]) em relação a um [[Referencial|nível de referência]] especificado ou implícito, expressa numa [[escala logarítmica]] de base 10 (log<sub>10</sub>). Um valor em dB expressa a relação entre dois valores de um [[nível de potência]] ou de um [[nível de campo]] (ou nível de [[potência-raiz]]) numa [[escala logarítmica]]. Dois sinais cujos [[Nível (quantidade logarítmica)|níveis]] difiram em 1,0 dB têm uma relação de potência de 10<sup>1/10</sup> (aproximadamente 1,26) ou uma relação de potência-raiz de 10<sup>{{frac|20}}</sup> (aproximadamente 1,12).<ref>''IEEE Standard 100 Dicionário de Termos Standards IEEE,''Sétima Edição, The Institute of Electrical and Electronics Engineering, New York, 2000; ISBN 0-7381-2601-2; página 288</ref><ref>{{citar livro|último=Mark |author-first=James E. |título=Physical Properties of Polymers Handbook |publicado=Springer |data=2007 |página=1025 |bibcode=2007ppph.book.....M |citação=[…] the decibel represents a reduction in power of 1.258 times […]}}</ref><ref>{{citar livro|último=Yost |author-first=William |título=Fundamentals of Hearing: An Introduction |url=https://archive.org/details/fundamentalsofhe00yost |publicado=Holt, Rinehart and Winston |edição=Second |data=1985 |página=[https://archive.org/details/fundamentalsofhe00yost/page/206 206] |isbn=978-0-12-772690-8 |citação=[…] a pressure ratio of 1.122 equals + 1.0 dB […]}}</ref>

==Definição==
O '''bel''' (símbolo: B) é uma [[unidade de medida]] [[Dimensão|adimensional]], que compara a [[Intensidade (física)|intensidade]] de um sinal a um nível de referência. Recebe este nome em homenagem ao [[físico]] [[Alexander Graham Bell]]. O cálculo é mais frequente em [[decibel]].{{harvref|Hewitt|2015|p=762}}

A unidade bel é usada para caracterizar o [[Logaritmo comum|logaritmo decimal]] da [[razão (matemática)|razão]] entre duas quantidades similares de [[energia]] ou [[potência]] <math>P_1 </math> e <math>P_2 </math>:<ref name="EN27">{{citar livro|título=Formelzeichen für die Elektrotechnik – Teil 3: Logarithmische und verwandte Größen und ihre Einheiten}}</ref>

:<math>Q_{(P)} = \log \frac{P_1}{P_2} \,\mathrm B= 10\,\log \frac{P_1}{P_2} \,\mathrm{dB}.</math>

Para <math>Q_{(P)}</math>, por exemplo, o valor 1 B resulta quando a razão de potência é <math>{P_1}/{P_2}=10 </math>. O decibel, por sua vez, é formado com o acréscimo do [[Sistema_Internacional_de_Unidades#Prefixos_oficiais_do_SI|prefixo]] d ([[deci]]):

:<math>1\,\mathrm{dB} = \frac1{10}\,\mathrm{B}.</math>

O decibel pode expressar uma alteração no valor (por exemplo, +1&nbsp;dB ou &minus;1&nbsp;dB) ou um valor absoluto. No último caso, o valor numérico expressa a proporção de um valor para um valor de referência fixo; quando usado dessa forma, o símbolo da unidade geralmente é sufixado com códigos de letras que indicam o valor de referência. Por exemplo, para o valor de referência de 1&nbsp;[[volt]], um sufixo comum é "[[#Voltagem|V]]" (por exemplo, "20&nbsp;dBV")<ref name = "clqgmk">{{citation |url=http://designtools.analog.com/dt/dbconvert/dbconvert.html |publicado=Analog Devices |título=Utilities : V<sub>RMS</sub> / dBm / dBu / dBV calculator |acessodata=2016-09-16}}</ref><ref>[http://physics.nist.gov/cuu/pdf/sp811.pdf Thompson and Taylor 2008, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811] {{Webarchive|url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |data=2016-06-03 }}.</ref>

As normas [[ISO 80000]]-8<ref>[https://www.iso.org/obp/ui/#iso:std:iso:80000:-8:ed-2:v1:en ISO 80000-8:2020(en) Quantities and units — Part 8: Acoustics].</ref> e [[IEC 60027|60027-3]] descrevem as definições para grandezas físicas e quantidades, entre as quais o decibel. De acordo com essas definições, o decibel (1&nbsp;dB) é uma décima parte do bel. O bel (B), por sua vez, é definido como 0,5&nbsp;log(10) [[neper]]: {{nowrap|1=1 B = 0,5 log(10) Np}}. Por sua vez, o [[neper]] é definido como a mudança em [[nível (quantidade logarítmica)|nível]] de uma quantidade de potência-raiz quando a quantidade de potência-raiz muda por um fator de [[e (constante matemática)|''e'']], ou seja, {{nowrap|1=1 Np = ln(e) = 1}}, relacionando, assim, todas as unidades como o [[logaritmo natural]] não-dimensional das relações potência-raiz-quantidade, {{nowrap|1=1 dB = 0.115&nbsp;13… Np = 0.115&nbsp;13…}}.  Finalmente, o nível de uma quantidade é o logaritmo da razão entre o valor dessa quantidade e um valor de referência do mesmo tipo de quantidade. Essas definições permitem estabelecer as seguintes igualdades:
:<math>
1\text{ dB} = 0,1 \text{ B}
</math>
<math>
1\text{ B} = \frac{1}{2}  \log_{e}\!\left(\frac{Q}{Q_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{Q}{Q_0}\right)\,\text{dB}
</math> <br>
onde <math>Q</math> é a quantidade medida e <math>Q_0</math> o valor de referência.

Portanto, o bel representa o logaritmo de uma razão entre duas grandezas de potência de 10:1, ou o logaritmo de uma proporção entre duas grandezas de potência-raiz de {{radic|10}}:1.<ref>{{citar livro|título=International Standard CEI-IEC 27-3 |capítulo=Letter symbols to be used in electrical technology |em=Part 3: Logarithmic quantities and units |publicado=International Electrotechnical Commission}}</ref> Logo, duas quantidades cujos níveis diferem em um decibel têm uma relação de potência de 10<sup>1/10</sup>, o que corresponde aproximadamente a 1,25893, e uma amplitude (quantidade potência-raiz) cujo rácio é 10<sup>{{frac|20}}</sup> (aproximadamente 1,12202).<ref>{{citar livro|author-last=Mark |author-first=James E. |título=Physical Properties of Polymers Handbook |publicado=Springer |data=2007 |página=1025 |bibcode=2007ppph.book.....M |citação=[…] the decibel represents a reduction in power of 1.258 times […]}}</ref><ref>{{citar livro|author-last=Yost |author-first=William |título=Fundamentals of Hearing: An Introduction |url=https://archive.org/details/fundamentalsofhe00yost |acessourl=registro |publicado=Holt, Rinehart and Winston |edição=Second |data=1985 |página=[https://archive.org/details/fundamentalsofhe00yost/page/206 206] |isbn=978-0-12-772690-8 |citação=[…] a pressure ratio of 1.122 equals + 1.0 dB […]}}</ref>

O bel é raramente usado sem um [[Sistema_Internacional_de_Unidades#Prefixos_oficiais_do_SI|prefixo do SI]] que não seja ''[[deci-|deci]]'', sendo preferível, por exemplo, usar ''centésimos de um decibel'' em vez de ''milibel''. Assim, cinco milésimos de um bel seriam normalmente escritos como 0,05&nbsp;dB, e não como 5&nbsp;mB.<ref>Fedor Mitschke, ''Fiber Optics: Physics and Technology'', Springer, 2010 {{ISBN|3642037038}}.</ref>

Em consequência da definição atrás apresentada, o método de expressar uma razão como um nível em decibel depende da propriedade medida ser uma ''grandeza de potência'' ou uma ''grandeza de potência-raiz'', pelo que tal distinção deve ser sempre tida em conta.

A definição do decibel originou-se na medição da perda de transmissão e potência na [[telefonia]] do início do século XX no [[Bell System]] dos Estados Unidos. O ''bel'' foi assim designado em homenagem a [[Alexander Graham Bell]], mas o bel raramente é usado. Em vez disso, o decibel é usado para uma ampla variedade de medições em ciência e [[engenharia]], mais frequentemente em [[acústica]], [[eletrónica]] e [[teoria de controlo]]. Na eletrónica, os [[Ganho (eletrónica)|ganhos]] dos amplificadores, a [[atenuação]] dos sinais e a [[relação sinal-ruído]] são grandezas frequentemente expressas em decibéis.

Dois tipos principais de escala em decibel são de uso comum: (1) as derivadas de uma relação de potência; e (2) as derivadas de níveis de potência-raiz. Ao expressar uma relação de potência, cada nível é definido como dez vezes o [[Logaritmo comum|logaritmo na base 10]],<ref> {{citar livro | título = Padrão IEEE 100: um dicionário de padrões e termos IEEE | edição = 7º |publicado= The Institute of Electrical and Electronics Engineering |local= New York |ano= 2000 | isbn = 978-0-7381-2601-2 |página= 288}} </ref><ref>{{citar livro|título=IEEE Standard 100: a dictionary of IEEE standards and terms |edição=7th |publicado=The Institute of Electrical and Electronics Engineering |local=New York |ano=2000 |isbn=978-0-7381-2601-2 |página=288}}</ref> ou seja, uma mudança na ''potência'' por um fator de 10 corresponde a uma mudança de nível de 10&nbsp;dB. Ao expressar grandezas de potência-raiz, uma mudança na ''amplitude'' por um fator de 10 corresponde a uma mudança de nível de 20&nbsp;dB. Em consequência, os dois tipos de escalas em decibéis diferem por um fator de dois, de modo que a potência relacionada e os níveis de potência-raiz mudam pelo mesmo valor em sistemas lineares onde a potência seja proporcional ao quadrado da amplitude.

{| class="wikitable" style="width:0; font-size:85%; float: right; margin-left:1em"
|-
! scope="col" style="text-align:right;" |  dB
! scope="col" colspan="2" | Rácio de potências
! scope="col" colspan="2" | Rácio de amplitudes
|-
| style="text-align:right; border:none;" | 100
| style="text-align:right; border:none; padding-right:0" | {{gaps|10|000|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |        {{gaps|100|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  90
| style="text-align:right; border:none; padding-right:0" |  {{gaps|1|000|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |         {{gaps|31|623}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  80
| style="text-align:right; border:none; padding-right:0" |    {{gaps|100|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |         {{gaps|10|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  70
| style="text-align:right; border:none; padding-right:0" |     {{gaps|10|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |          {{gaps|3|162}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  60
| style="text-align:right; border:none; padding-right:0" |      {{gaps|1|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |          {{gaps|1|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  50
| style="text-align:right; border:none; padding-right:0" |        {{gaps|100|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                     316 || style="border:none; padding-left:0;" | .2
|-
| style="text-align:right; border:none;" |  40
| style="text-align:right; border:none; padding-right:0" |         {{gaps|10|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                     100 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  30
| style="text-align:right; border:none; padding-right:0" |          {{gaps|1|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                      31 || style="border:none; padding-left:0;" | .62
|-
| style="text-align:right; border:none;" |  20
| style="text-align:right; border:none; padding-right:0" |                     100 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                      10 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  10
| style="text-align:right; border:none; padding-right:0" |                      10 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                       3 || style="border:none; padding-left:0;" | .162
|-
| style="text-align:right; border:none;" |   6
| style="text-align:right; border:none; padding-right:0" |                       3 || style="border:none; padding-left:0;" | .981 ≈ 4
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .995 ≈ 2
|-
| style="text-align:right; border:none;" |   3
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .995 ≈ 2
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .413 ≈ {{sqrt|2}}
|-
| style="text-align:right; border:none;" |   1
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .259
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .122
|-
| style="text-align:right; border:none;" |   0
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  −1
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .794
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .891
|-
| style="text-align:right; border:none;" |  −3
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .501 ≈ {{frac|2}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .708 ≈ {{sqrt|{{frac|2}}}}
|-
| style="text-align:right; border:none;" |  −6
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .251 ≈ {{frac|4}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .501 ≈ {{frac|2}}
|-
| style="text-align:right; border:none;" | −10
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .1
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.316|2}}
|-
| style="text-align:right; border:none;" | −20
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .01
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .1
|-
| style="text-align:right; border:none;" | −30
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .001
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.031|62}}
|-
| style="text-align:right; border:none;" | −40
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .01
|-
| style="text-align:right; border:none;" | −50
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|01}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.003|162}}
|-
| style="text-align:right; border:none;" | −60
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|001}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .001
|-
| style="text-align:right; border:none;" | −70
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|316|2}}
|-
| style="text-align:right; border:none;" | −80
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|01}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|1}}
|-
| style="text-align:right; border:none;" | −90
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|001}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|031|62}}
|-
| style="text-align:right; border:none;" | −100
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|01}}
|-
| colspan="5" style="text-align:left; background:#f8f8ff;" | Exemplo de uma escala mostrando o rácio de potência ''x'', os rácos de amplitude {{sqrt|''x''}} os dB equivalentes 10&nbsp;log<sub>10</sub>&nbsp;''x''.
|}
===História===
O decibel teve origem nos métodos usados para quantificar a [[perda de sinal]] em circuitos telegráficos e telefónicos. Até meados da década de 1920, a unidade de perda era a designada "Miles of Standard Cable" (MSC), sendo que um 1&nbsp;MSC correspondia à perda de potência que era medida quando o sinal percorria uma [[milha]] (aproximadamente 1,6&nbsp;km) de cabo telefónico padrão a uma frequência de {{val|5000}}&nbsp;[[radiano]]s por segundo (795,8&nbsp;Hz). Tal valor correspondia sensivelmente à menor atenuação detectável por um ouvinte médio. Para este efeito, um cabo de telefone padrão era «''um cabo com resistência uniformemente distribuída de 88&nbsp;ohms por loop-milha e [[shunt (eletrónica)|shunt]] com [[capacitância]] uniformemente distribuída de 0,054&nbsp;[[microfarad]]s por milha»'' (correspondendo aproximadamente a fio de [[bitola]]&nbsp;19).<ref>{{citar livro|último=Johnson |primeiro=Kenneth Simonds |título=Transmission Circuits for Telephonic Communication: Methods of analysis and design |data=1944 |publicado=[[D. Van Nostrand Co.]] |local=New York |página=10}}</ref>

Em 1924, os os membros do Comité Consultivo Internacional em Telefonia de Longa Distância na Europa ('' International Advisory Committee on Long Distance Telephony in Europe'') deram rparecer favorável a uma proposta elaborada pelos [[Bell Labs|Bell Telephone Laboratories]] visando uma nova definição de unidade de atenuação que substituísse o MSC a que deram inicialmente o nome de ''Unidade de Transmissão'' (''Transmission Unit'' ou TU). A nova unidade foi definida de forma que 1&nbsp;TU fosse dez vezes o [[logaritmo de base 10]] da razão entre a potência medida e uma potência de referência.<ref>{{citar livro|título=Sound system engineering |edição=2nd |author-first1=Don |author-last1=Davis |author-first2=Carolyn |author-last2=Davis |publicado=[[Focal Press]] |data=1997 |isbn=978-0-240-80305-0 |página=35 |url={{Google books|plainurl=yes|id=9mAUp5IC5AMC|page=35}}}}.</ref>

A definição foi convenientemente escolhida de modo que 1&nbsp;TU fosse aproximadamente 1& bsp;MSC (como definido, 1&nbsp;MSC era 1,056&nbsp;TU). Em 1928, o Sistema Bell renomeou o TU para «decibel»,<ref>{{citar periódico|periódico=Bell Laboratories Record |título='TU' becomes 'Decibel' |author-first=R. V. L. |author-last=Hartley |autorlink=R. V. L. Hartley |volume=7 |número=4 |publicado=AT&T |páginas=137–139 |data=dezembro de 1928 |url={{Google books|plainurl=yes|id=h1ciAQAAIAAJ}}}}</ref> considerando a nova unidade como sendo um décimo de uma unidade recém-definida para o logaritmo de base 10 do rácio das potências a que, por sugestão do Comité Consultivo Internacional em Telefonia de Longa Distância, deram o nome de «bel». O nome da nova unidade é uma homenagem ao pioneiro das telecomunicações [[Alexander Graham Bell]].<ref>{{citar periódico|author-last=Martin |author-first=W. H. |data=janeiro de 1929 |título=DeciBel—The New Name for the Transmission Unit |periódico=[[Bell System Technical Journal]] |volume=8 |número=1}}</ref> Dada a sua maior adequação aos valores geralmente medidos, o decibel foi a unidade de trabalho proposta, sendo por isso o bel raramente usado.<ref>{{Google books |id=EaVSbjsaBfMC |page=276 |title=100 Years of Telephone Switching}}, Robert J. Chapuis, Amos E. Joel, 2003</ref>

A origem da nomenclatura e a definição inicial do decibel são descritas no anuário de 1931 (''1931 Yearbook'') do [[National Institute of Standards and Technology]] (ao tempo o [[NBS]], National Bureau of Standards) da seguinte forma:<ref>{{citar periódico|título=Standards for Transmission of Speech |periódico=Standards Yearbook |volume=119 |author-first=William H. |último=Harrison |data=1931 |publicado=National Bureau of Standards, U. S. Govt. Printing Office}}</ref>

{{quotation |
Desde os primeiros tempos do telefone, foi reconhecida a necessidade de uma unidade para medir a eficiência de transmissão das instalações telefónicas. A introdução do cabo em 1896 proporcionou uma base estável para uma unidade conveniente e a "milha de cabo padrão" entrou em uso geral pouco depois. Essa unidade foi empregada até 1923, quando uma nova unidade foi adoptada como sendo mais adequada para o trabalho telefónico moderno. A nova unidade de transmissão é amplamente utilizada entre as organizações telefónicas estrangeiras e recentemente foi denominada "decibel" por sugestão do Comité Consultivo Internacional de Telefonia de Longa Distância.

O decibel pode ser definido pela afirmação de que duas quantidades de potência diferem em 1 decibel quando estão na proporção de 10<sup>0,1</sup> e quaisquer duas quantidades de potência diferem em ''N'' decibéis quando estão na proporção de 10<sup>''N''(0,1)</sup>. O número de unidades de transmissão que expressam a proporção de quaisquer duas potências é, portanto, dez vezes o logaritmo comum dessa proporção. Este método de designar o ganho ou perda de potência em circuitos telefónicos permite a adição ou subtração direta das unidades que expressam a eficiência de diferentes partes do circuito&nbsp;...}}

{{anchor|Logit}}Em 1954, [[Joseph Warren Horton]] (do U.S. Navy Underwater Sound Laboratory) argumentou que o uso do decibel como unidade para quantidades diferentes da perda de transmissão levara à confusão e sugeriu o nome ''logit'' para ''magnitudes padrão que se combinam por multiplicação'', para contrastar com o termo ''unidade'' que seria reservado para ''magnitudes padrão que combinam por adição''.<ref>{{citar periódico|primeiro=J. W. |último=Horton |título=The bewildering decibel |periódico=Electrical Engineering |volume=73 |número=6 |páginas=550–555 |ano=1954|doi=10.1109/EE.1954.6438830 |s2cid=51654766 }}
</ref>{{clarify|date=March 2018}}

Em abril de 2003, o [[Comité Internacional de Pesos e Medidas]] (CIPM) considerou uma recomendação para a inclusão do decibel no [[Sistema Internacional de Unidades]] (SI), mas decidiu contra a proposta.<ref>{{citar web |url=http://www.bipm.org/utils/common/pdf/CC/CCU/CCU16.pdf |publicado=Consultative Committee for Units |título=Meeting minutes |em=Section 3}}</ref> No entanto, o decibel é reconhecido por outros organismos internacionais, como a [[International Electrotechnical Commission]] (IEC) e a [[International Organization for Standardization]] (ISO).<ref name="IEC60027-3">{{citar web |url=http://webstore.iec.ch/webstore/webstore.nsf/artnum/028981 |título=Letter symbols to be used in electrical technology |em=Part 3: Logarithmic and related quantities, and their units |id=IEC&nbsp;60027-3, Ed.&nbsp;3.0 |publicado=International Electrotechnical Commission |data=19-07-2002}}</ref> O IEC permite o uso do decibel com grandezas de [[potência-raiz]] e de potência e esta recomendação é seguida por muitos organismos de padronização nacionais, como o [[NIST]] dos Estados Unidos, o que justifica o uso do decibel para relações de voltagem.<ref name=NIST2008>Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", ''Guide for the Use of the International System of Units (SI) 2008 Edition'', NIST Special Publication 811, 2nd printing (November 2008), SP811 [http://physics.nist.gov/cuu/pdf/sp811.pdf PDF]</ref> Apesar do seu uso muito difundido, a utilização de sufixos como referência a valores base (como em [[dBA]] ou [[dBV]]) não são reconhecidos pelo IEC nem pela ISO.


<!-------------------------

===Power quantities===
When referring to measurements of ''[[Power (physics)|power]]'' quantities, a ratio can be expressed as a [[Level (logarithmic quantity)|level]] in decibels by evaluating ten times the [[base-10 logarithm]] of the ratio of the measured quantity to reference value. Thus, the ratio of ''P'' (measured power) to ''P''<sub>0</sub> (reference power) is represented by ''L''<sub>''P''</sub>, that ratio expressed in decibels,<ref>{{citar livro|título=Microwave Engineering |author-first=David M. |author-last=Pozar |edição=3rd |publicado=Wiley |data=2005 |autorlink=David M. Pozar |isbn=978-0-471-44878-5 |página=63}}</ref> which is calculated using the formula:<ref>IEC 60027-3:2002</ref>

:<math>
L_P = \frac{1}{2} \ln\!\left(\frac{P}{P_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{P}{P_0}\right)\,\text{dB}.
</math>

The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel).  ''P'' and ''P''<sub>0</sub> must measure the same type of quantity, and have the same units before calculating the ratio. If {{nowrap|1=''P'' = ''P''<sub>0</sub>}} in the above equation, then ''L''<sub>''P''</sub> = 0. If ''P'' is greater than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is positive; if ''P'' is less than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is negative.

Rearranging the above equation gives the following formula for ''P'' in terms of ''P''<sub>0</sub> and ''L''<sub>''P''</sub>:
:<math>
P = 10^\frac{L_P}{10\,\text{dB}} P_0.
</math>

=== Root-power (field) quantities ===
{{main|Power, root-power, and field quantities}}
When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of ''F'' (measured) and ''F''<sub>0</sub> (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used:
:<math>
L_F = \ln\!\left(\frac{F}{F_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{F^2}{F_0^2}\right)\,\text{dB} = 20 \log_{10} \left(\frac{F}{F_0}\right)\,\text{dB}.
</math>

The formula may be rearranged to give
:<math>
F = 10^\frac{L_F}{20\,\text{dB}} F_0.
</math>

Similarly, in [[Electronic circuit|electrical circuits]], dissipated power is typically proportional to the square of [[voltage]] or [[Electric current|current]] when the [[Electrical impedance|impedance]] is constant. Taking voltage as an example, this leads to the equation for power gain level ''L''<sub>''G''</sub>:
:<math>
L_G = 20 \log_{10}\!\left (\frac{V_\text{out}}{V_\text{in}}\right)\,\text{dB},
</math>
where ''V''<sub>out</sub> is the [[root-mean-square]] (rms) output voltage, ''V''<sub>in</sub> is the rms input voltage. A similar formula holds for current.

The term ''root-power quantity'' is introduced by ISO Standard [[ISO/IEC 80000|80000-1:2009]] as a substitute of ''field quantity''.  The term ''field quantity'' is deprecated by that standard and ''root-power'' is used throughout this article.

=== Relationship between power and root-power levels ===
Although power and root-power quantities are different quantities, their respective levels are historically measured in the same units, typically decibels.  A factor of 2 is introduced to make ''changes'' in the respective levels match under restricted conditions such as when the medium is linear and the ''same'' waveform is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time.  This relies on the relationship
:<math> \frac{P(t)}{P_0} = \left(\frac{F(t)}{F_0}\right)^2 </math>
holding.<ref>{{citation |autor=I M Mills |autor2=B N Taylor |autor3=A J Thor |título=Definitions of the units radian, neper, bel and decibel |ano=2001 |periódico=Metrologia |volume=38 |página=353 |número=4 |doi=10.1088/0026-1394/38/4/8|bibcode=2001Metro..38..353M }}</ref>  In a nonlinear system, this relationship does not hold by the definition of linearity.  However, even in a [[linear system]] in which the power quantity is the product of two linearly related quantities (e.g. [[voltage]] and [[Electric current|current]]), if the [[Electrical impedance|impedance]] is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes.

For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities ''P''{{sub|0}} and ''F''{{sub|0}} need not be related), or equivalently,
:<math> \frac{P_2}{P_1} = \left(\frac{F_2}{F_1}\right)^2 </math>
must hold to allow the power level difference to be equal to the root-power level difference from power ''P''{{sub|1}} and ''V''{{sub|1}} to ''P''{{sub|2}} and ''V''{{sub|2}}.  An example might be an amplifier with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0&nbsp;dB, but the power gain depends on the changing spectral composition of the waveform being amplified.  Frequency-dependent impedances may be analyzed by considering the quantities [[power spectral density]] and the associated root-power quantities via the [[Fourier transform]], which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently.

===Conversions===
Since logarithm differences measured in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as a unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio.

{| class="wikitable"
|+ Conversion between units of level and a list of corresponding ratios
!Unit !! In decibels !! In bels !! In [[neper]]s !! Power ratio !! Root-power ratio
|-
| 1&nbsp;dB || 1&nbsp;dB || 0.1 B || {{val|0.11513}}&nbsp;Np || 10<sup>{{frac|10}}</sup> ≈ {{val|1.25893}} || 10<sup>{{frac|20}}</sup> ≈ {{val|1.12202}}
|-
| 1 Np || {{val|8.68589}}&nbsp;dB || {{val|0.868589}}&nbsp;B || 1 Np || e<sup>2</sup> ≈ {{val|7.38906}} || [[e (mathematical constant)|e]] ≈ {{val|2.71828}}
|-
| 1 B || 10&nbsp;dB || 1 B || 1.151&nbsp;3 Np || 10 || 10<sup>{{frac|2}}</sup> ≈ 3.162&nbsp;28
|}

===Examples===
The unit dBW is often used to denote a ratio for which the reference is 1&nbsp;W, and similarly dBm for a {{nowrap|1 mW}} reference point.
* Calculating the ratio in decibels of {{nowrap|1 kW}} (one kilowatt, or {{val|1000}} watts) to {{nowrap|1 W}} yields:
::<math>
L_G = 10 \log_{10} \left(\frac{1\,000\,\text{W}}{1\,\text{W}}\right)\,\text{dB} = 30\,\text{dB}.
</math>
* The ratio in decibels of {{nowrap|1={{radic|1&nbsp;000}} V ≈ 31.62 V}} to {{nowrap|1 V}} is
::<math>
L_G = 20 \log_{10} \left(\frac{31.62\,\text{V}}{1\,\text{V}}\right)\,\text{dB} = 30\,\text{dB}.
</math>
{{nowrap|1=(31.62 V / 1 V)<sup>2</sup> ≈ 1 kW / 1 W}}, illustrating the consequence from the definitions above that ''L''<sub>''G''</sub> has the same value, 30&nbsp;dB, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared.
* The ratio in decibels of {{nowrap|10 W}} to {{nowrap|1 mW}} (one milliwatt) is obtained with the formula
::<math>
L_G = 10 \log_{10} \left(\frac{10\text{ W}}{0.001\text{ W}}\right) \text{ dB} = 40 \text{ dB}.
</math>
* The power ratio corresponding to a {{nowrap|3 dB}} change in level is given by
::<math>
G = 10^\frac{3}{10} \times 1 = 1.995\,26\ldots \approx 2.
</math>

A change in power ratio by a factor of 10 corresponds to a change in level of {{nowrap|10 dB}}. A change in power ratio by a factor of 2 or {{frac|2}} is approximately a [[Half-power point|change of 3&nbsp;dB]]. More precisely, the change is ±{{val|3.0103}}&nbsp;dB, but this is almost universally rounded to 3&nbsp;dB in technical writing.  This implies an increase in voltage by a factor of {{nowrap|{{sqrt|2}} ≈}} {{val|1.4142}}.  Likewise, a doubling or halving of the voltage, and quadrupling or quartering of the power, is commonly described as 6&nbsp;dB rather than ±{{val|6.0206}}&nbsp;dB.

Should it be necessary to make the distinction, the number of decibels is written with additional [[significant figures]].  3.000&nbsp;dB corresponds to a power ratio of 10<sup>{{frac|3|10}}</sup>, or {{val|1.9953}}, about 0.24% different from exactly 2, and a voltage ratio of {{val|1.4125}}, 0.12% different from exactly {{sqrt|2}}.  Similarly, an increase of 6.000&nbsp;dB corresponds to the power ratio is {{nowrap|10<sup>{{frac|6|10}}</sup> ≈}} {{val|3.9811}}, about 0.5% different from 4.

==Properties==
The decibel is useful for representing large ratios and for simplifying representation of multiplied effects such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive.

===Reporting large ratios===
The [[logarithmic scale]] nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a manner similar to [[scientific notation]]. This allows one to clearly visualize huge changes of some quantity. See ''[[Bode plot]]'' and ''[[Semi-log plot]]''.  For example, 120&nbsp;dB SPL may be clearer than "a trillion times more intense than the threshold of hearing".{{carece de fontes|data=fevereiro de 2021}}

===Representation of multiplication operations===
Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of [[amplifier]] stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, {{nowrap|log(''A'' × ''B'' × ''C'') }}= log(''A'') + log(''B'') + log(''C''). Practically, this means that, armed only with the knowledge that 1&nbsp;dB is a power gain of approximately 26%, 3&nbsp;dB is approximately 2× power gain, and 10&nbsp;dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example:
*:A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10&nbsp;dB, 8&nbsp;dB, and 7&nbsp;dB respectively, for a total gain of 25&nbsp;dB. Broken into combinations of 10, 3, and 1&nbsp;dB, this is:
*:: 25&nbsp;dB = 10&nbsp;dB + 10&nbsp;dB + 3&nbsp;dB + 1&nbsp;dB + 1&nbsp;dB
*:With an input of 1 watt, the output is approximately
*:: 1&nbsp;W × 10 × 10 × 2 × 1.26 × 1.26  ≈ 317.5&nbsp;W
*: Calculated precisely, the output is 1&nbsp;W × 10<sup>{{frac|25|10}}</sup> ≈ 316.2&nbsp;W. The approximate value has an error of only +0.4% with respect to the actual value, which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation.

However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of [[slide rule]]s than to modern digital processing, and is cumbersome and difficult to interpret.<ref name="Hickling">R. Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048</ref><ref>Hickling, R. (2006). Decibels and octaves, who needs them?. Journal of sound and vibration, 291(3-5), 1202-1207.</ref>
Quantities in decibels are not necessarily [[Dimensional homogeneity|additive]],<ref>Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p. [{{Google books |plainurl=yes |id=rrpEuUOkT3UC |page=7}} 7]</ref><ref>Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13</ref>  thus being "of unacceptable form for use in [[dimensional analysis]]".<ref>J. C. Gibbings, ''Dimensional Analysis'', [{{Google books |plainurl=yes |id=Q6iflrgVaWcC |page=37}} p.37], Springer, 2011 {{ISBN|1849963177}}.</ref>
Thus, units require special care in decibel operations. Take, for example, [[carrier-to-noise-density ratio]] ''C/N<sub>0</sub>'' (in hertz), involving carrier power ''C'' (in watts) and noise [[power spectral density]] ''N<sub>0</sub>'' (in W/Hz). Expressed in decibels, this ratio would be a subtraction (''C/N<sub>0</sub>'')<sub>dB</sub> = ''C''<sub>dB</sub> - ''N''<sub>0dB</sub>. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz.

==={{anchor|Addition}}Representation of addition operations===
{{Details|Logarithmic addition}}
According to Mitschke,<ref>{{citar livro|título=Fiber Optics |publicado=Springer |data=2010}}</ref> "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations:<ref>R. J. Peters, ''Acoustics and Noise Control'', Routledge, 12 November 2013, 400 pages, p.&nbsp;13</ref><blockquote>if two machines each individually produce a [[sound pressure]] level of, say, 90&nbsp;dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93&nbsp;dB, but certainly not to 180&nbsp;dB!; suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87&nbsp;dBA but when the machine is switched off the background noise alone is measured as 83&nbsp;dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83&nbsp;dBA background noise from the combined level of 87&nbsp;dBA; i.e., 84.8&nbsp;dBA.; in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. [...] Compare the logarithmic and arithmetic averages of [...] 70&nbsp;dB and 90&nbsp;dB: [[logarithmic average]] = 87&nbsp;dB; [[arithmetic average]] = 80&nbsp;dB.</blockquote>

Addition on a logarithmic scale is called [[logarithmic addition]], and can be defined by taking exponentials to convert to a linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations:
:<math>87\,\text{dBA} \ominus 83\,\text{dBA} = 10 \cdot \log_{10}\bigl(10^{87/10} - 10^{83/10}\bigr)\,\text{dBA} \approx 84.8\,\text{dBA}</math>
:<math>
\begin{align}
M_\text{lm}(70, 90) &= \left(70\,\text{dBA} + 90\,\text{dBA}\right)/2 \\
&= 10 \cdot \log_{10}\left(\bigl(10^{70/10} + 10^{90/10}\bigr)/2\right)\,\text{dBA} \\
&= 10 \cdot \left(\log_{10}\bigl(10^{70/10} + 10^{90/10}\bigr) - \log_{10} 2\right)\,\text{dBA}
\approx 87\,\text{dBA}.
\end{align}
</math>
Note that the [[logarithmic mean]] is obtained from the logarithmic sum by subtracting <math>10\log_{10} 2</math>, since logarithmic division is linear subtraction.

===Fractions===
[[Attenuation]] constants, in topics such as [[optical fiber]] communication and [[radio propagation]] [[path loss]], are often expressed as a [[Fraction (mathematics)|fraction]] or ratio to distance of transmission. In this case, dB/m represents decibel per meter, dB/mi represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of [[dimensional analysis]], e.g., a 100-meter run with a 3.5&nbsp;dB/km fiber yields a loss of 0.35&nbsp;dB = 3.5&nbsp;dB/km × 0.1&nbsp;km.

==Uses==

===Perception===
The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see [[Weber–Fechner law]]), making the dB scale a useful measure.<ref>{{Google books |id=1SMXAAAAQBAJ |page=268 |title=Sensation and Perception}}</ref><ref>{{Google books |id=BggrpTek5kAC |page=SA19-PA9 |title=Introduction to Understandable Physics, Volume 2}}</ref><ref>{{Google books |id=ukvei0wge_8C |page=356 |title=Visual Perception: Physiology, Psychology, and Ecology}}</ref><ref>{{Google books |id=-QIfF9q6Q_EC |page=407 |title=Exercise Psychology}}</ref><ref>{{Google books |id=oUNfSjS11ggC |page=83 |title=Foundations of Perception}}</ref><ref>{{Google books |id=w888Mw1dh_EC |page=304 |title=Fitting The Task To The Human}}</ref>

===Acoustics===
The decibel is commonly used in [[acoustics]] as a unit of [[sound pressure level]]. The reference pressure for sound in air is set at the typical threshold of perception of an average human and there are [[Sound pressure#Examples of sound pressure|common comparisons used to illustrate different levels of sound pressure]]. As sound pressure is a root-power quantity, the appropriate version of the unit definition is used:
:<math>
L_p = 20 \log_{10}\!\left(\frac{p_{\text{rms}}}{p_{\text{ref}}}\right)\,\text{dB},
</math>
where ''p''<sub>rms</sub> is the [[root mean square]] of the measured sound pressure and ''p''<sub>ref</sub> is the standard reference sound pressure of 20 [[micropascal]]s in air or 1 micropascal in water.<ref>ISO 1683:2015</ref>

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.<ref>C. S. Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047</ref>

The human ear has a large [[dynamic range]] in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is equal to or greater than 1 trillion (10<sup>12</sup>).<ref>{{citar web |título=Loud Noise Can Cause Hearing Loss |url=https://www.cdc.gov/nceh/hearing_loss/what_noises_cause_hearing_loss.html |website=cdc.gov |data=7-10-2019 |publicado=Centers for Disease Control and Prevention |acessodata=30-07-2020}}</ref> Such large measurement ranges are conveniently expressed in [[logarithmic scale]]: the base-10 logarithm of 10<sup>12</sup> is 12, which is expressed as a sound pressure level of 120&nbsp;dB re 20&nbsp;[[Pascal (unit)|μPa]].

Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by [[frequency weighting]] ([[A-weighting]] being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.<ref name=Pierre>{{citation |url= http://storeycountywindfarms.org/ref3_Impact_Sound_Pressure.pdf |autor=Richard L. St. Pierre, Jr. and Daniel J. Maguire |título=The Impact of A-weighting Sound Pressure Level Measurements during the Evaluation of Noise Exposure |data=julho de 2004 |acessodata=2011-09-13}}</ref>

{{further|Sound pressure#Examples of sound pressure}}

===Telephony===
The decibel is used in [[telephony]] and [[Audio signal|audio]].  Similarly to the use in acoustics, a frequency weighted power is often used.  For audio noise measurements in electrical circuits, the weightings are called [[psophometric weighting]]s.<ref name="Reeve">{{citar livro|último=Reeve |primeiro= William D. |ano= 1992 |título= Subscriber Loop Signaling and Transmission Handbook – Analog |edição= 1st |publicado=IEEE Press |isbn= 0-87942-274-2}}</ref>

===Electronics===
In electronics, the decibel is often used to express power or amplitude ratios (as for [[Gain (electronics)|gains]]) in preference to [[arithmetic]] ratios or [[percent]]ages. One advantage is that the total decibel gain of a series of components (such as [[amplifier]]s and [[Attenuator (electronics)|attenuators]]) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium ([[free space optical communication|free space]], [[waveguide]], [[coaxial cable]], [[fiber optics]], etc.) using a [[link budget]].

The decibel unit can also be combined with a reference level, often indicated via a suffix, to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "[[dBm]]".  A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater (about 1.259&nbsp;mW).

In professional audio specifications, a popular unit is the [[dBu]].  This is relative to the [[root mean square]] voltage which delivers 1&nbsp;mW (0&nbsp;dBm) into a 600-ohm resistor, or {{sqrt|1&nbsp;mW&times;600&nbsp;Ω }}≈ 0.775&nbsp;V<sub>RMS</sub>.  When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are [[#dBu or dBv|identical]].

===Optics===
In an [[optical link]], if a known amount of [[Optics|optical]] power, in [[dBm]] (referenced to 1&nbsp;mW), is launched into a [[Optical fiber|fiber]], and the losses, in dB (decibels), of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities.<ref>{{citar livro|título= Fiber optic installer's field manual  | author-first = Bob |author-last=Chomycz|publicado= McGraw-Hill Professional|ano= 2000| isbn = 978-0-07-135604-6|páginas= 123–126| url = {{Google books |plainurl=yes |id=B810SYIAa4IC |page=123 }} }}</ref>

In spectrometry and optics, the [[absorbance|blocking unit]] used to measure [[optical density]] is equivalent to −1&nbsp;B.

===Video and digital imaging===
In connection with video and digital [[image sensor]]s, decibels generally represent ratios of video voltages or digitized light intensities, using 20&nbsp;log of the ratio, even when the represented intensity (optical power) is directly proportional to the voltage generated by the sensor, not to its square, as in a [[CCD imager]] where response voltage is linear in intensity.<ref>{{citar livro|título= The Colour Image Processing Handbook|autor= Stephen J. Sangwine and Robin E. N. Horne|publicado= Springer|ano= 1998| isbn = 978-0-412-80620-9|páginas= 127–130| url = {{Google books |plainurl=yes |id=oEsZiCt5VOAC |page=127 }} }}</ref>
Thus, a camera [[signal-to-noise ratio]] or [[dynamic range]] quoted as 40&nbsp;dB represents a ratio of 100:1 between optical signal intensity and optical-equivalent dark-noise intensity, not a 10,000:1 intensity (power) ratio as 40&nbsp;dB might suggest.<ref>{{citar livro|título= Introduction to optical engineering|autor= Francis T. S. Yu and Xiangyang Yang|publicado= Cambridge University Press|ano= 1997| isbn = 978-0-521-57493-8|páginas= 102–103| url = {{Google books |plainurl=yes |id=RYm7WwjsyzkC |page=120 }} }}</ref>
Sometimes the 20&nbsp;log ratio definition is applied to electron counts or photon counts directly, which are proportional to sensor signal amplitude without the need to consider whether the voltage response to intensity is linear.<ref>{{citar livro|título= Image sensors and signal processing for digital still cameras|capítulo= Basics of Image Sensors|autor= Junichi Nakamura| editor = Junichi Nakamura|publicado= CRC Press|ano= 2006| isbn = 978-0-8493-3545-7|páginas= 79–83  |capítulourl= {{Google books |plainurl=yes |id=UY6QzgzgieYC |page=79 }} }}</ref>

However, as mentioned above, the 10&nbsp;log intensity convention prevails more generally in physical optics, including fiber optics, so the terminology can become murky between the conventions of digital photographic technology and physics. Most commonly, quantities called "dynamic range" or "signal-to-noise" (of the camera) would be specified in 20&nbsp;log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value.

Photographers typically use an alternative base-2 log unit, the [[F-number#Stops.2C f-stop conventions.2C and exposure|stop]], to describe light intensity ratios or dynamic range.

=={{anchor|Suffixes}}Suffixes and reference values==
Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1&nbsp;milliwatt.

In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative.

This form of attaching suffices to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC):<ref name=NIST2008>Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", ''Guide for the Use of the International System of Units (SI) 2008 Edition'', NIST Special Publication 811, 2nd printing (November 2008), SP811 [http://physics.nist.gov/cuu/pdf/sp811.pdf PDF]</ref> A change in level of 1 dB always corresponds to a power ratio of approximately 1 : 1.259. The suffix merely indicates the method of measurement, not a different scaling or type of unit. The [[IEC 60027-3]] standard recommends the following format:<ref name="IEC60027-3"/> ''L''<sub>''x''</sub> (re ''x''<sub>ref</sub>) or as ''L''<sub>''x''/''x''<sub>ref</sub></sub>, where ''x'' is the quantity symbol and ''x''<sub>ref</sub> is the value of the reference quantity, e.g., ''L''<sub>''E''</sub>&nbsp;(re&nbsp;1&nbsp;μV/m)&nbsp;=&nbsp;20&nbsp;dB or  ''L''<sub>''E''/(1&nbsp;μV/m)</sub>=&nbsp;20&nbsp;dB for the [[electric field strength]] ''E'' relative to 1&nbsp;μV/m reference value.
If the measurement result 20 dB is presented separately, it can be specified using the information in parentheses, which is then part of the surrounding text and not a part of the unit: 20 dB (re: 1&nbsp;μV/m) or 20 dB (1&nbsp;μV/m).

Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for [[A-weighting|A-weighted]] sound pressure level). The suffix is often connected with a [[hyphen]], as in "dB{{nbhyph}}Hz", or with a space, as in "dB&nbsp;HL", or enclosed in parentheses, as in "dB(sm)", or with no intervening character, as in "dBm" (which is non-compliant with international standards).

===Voltage===
Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, or use the factor of 20 instead of 10, as discussed above.

[[File:Relationship between dBu and dBm.png|thumb|upright=1.25|A schematic showing the relationship between [[dBu]] (the [[voltage source]]) and [[dBm]] (the power dissipated as [[heat]] by the 600&nbsp;Ω [[resistor]])]]

;dBV: dB(V<sub>[[root mean square|RMS]]</sub>)&nbsp;– [[volt]]age relative to 1&nbsp;volt, regardless of impedance.<ref name = "clqgmk">{{citation |url=http://designtools.analog.com/dt/dbconvert/dbconvert.html |publicado=Analog Devices |título=Utilities : V<sub>RMS</sub> / dBm / dBu / dBV calculator |acessodata=2016-09-16}}</ref> This is used to measure microphone sensitivity, and also to specify the consumer [[Line level|line-level]] of {{nowrap|−10 dBV}}, in order to reduce manufacturing costs relative to equipment using a {{nowrap|+4 dBu}} line-level signal.<ref>{{citar livro|url=https://books.google.com/books?id=TIfOAwAAQBAJ&q=%22%E2%88%9210+dBV%22+%221+kHz%22|título=The Audio Expert: Everything You Need to Know About Audio|último=Winer|primeiro=Ethan|publicado=Focal Press|ano=2013|isbn=978-0-240-82100-9|páginas=107}}</ref>

;dBu or dBv: [[root mean square|RMS]] [[volt]]age relative to {{nowrap|<math>V = \sqrt{600 \, \Omega \cdot 0.001\,\text{W}} \approx 0.7746\,\text{V}</math>}} (i.e. the voltage that would dissipate 1 mW into a 600&nbsp;Ω load). An [[root mean square|RMS]] voltage of 1&nbsp;V therefore corresponds to <math>20\cdot\log_{10}\left ( \frac{1\,V_\text{RMS}}{\sqrt{0.6}\,V} \right )=2.218\,\text{dBu}.</math><ref name="clqgmk" /> Originally dBv, it was changed to dBu to avoid confusion with dBV.<ref>{{citar web|url=http://stason.org/TULARC/entertainment/audio/pro/3-3-What-is-the-difference-between-dBv-dBu-dBV-dBm-dB.html|título=3.3&nbsp;– What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements?|primeiro=Stas Bekman: stas (at)|último=stason.org|website=stason.org}}</ref>  The "v" comes from "volt", while "u" comes from the volume ''unit'' used in the [[VU meter]].<ref>{{citation |url=https://www.youtube.com/watch?v=b02P4f3CBuM |título=Creation of the dBu standard level reference |autor=Rupert Neve |autorlink=Rupert Neve}}</ref>{{paragraphbreak}}dBu can be used as a measure of voltage, regardless of impedance, but is derived from a 600&nbsp;Ω load dissipating 0&nbsp;dBm (1&nbsp;mW). The reference voltage comes from the computation {{nowrap|<math>V = \sqrt{R \cdot P}</math>}} where <math>R</math> is the resistance and <math>P</math> is the power.{{paragraphbreak}} In [[professional audio]], equipment may be calibrated to indicate a "0" on the VU meters some finite time after a signal has been applied at an amplitude of {{nowrap|+4 dBu}}. Consumer equipment typically uses a lower "nominal" signal level of {{nowrap|−10 dBV}}.<ref>{{citar web|autor=deltamedia.com |url=http://www.deltamedia.com/resource/db_or_not_db.html |título=DB or Not DB |publicado=Deltamedia.com |acessodata=2013-09-16}}</ref> Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons.  A switch or adjustment that covers at least the range between {{nowrap|+4 dBu}} and {{nowrap|−10 dBV}} is common in professional equipment.

;dBm0s
:Defined by Recommendation ITU-R V.574.; dBmV: dB(mV<sub>[[root mean square|RMS]]</sub>) – [[volt]]age relative to 1&nbsp;millivolt across 75&nbsp;Ω.<ref>{{citar livro|título=The IEEE Standard Dictionary of Electrical and Electronics terms|edição=6th  |anooriginal=1941|ano=1996|publicado=IEEE|isbn=978-1-55937-833-8 }}</ref> Widely used in [[cable television]] networks, where the nominal strength of a single TV signal at the receiver terminals is about 0&nbsp;dBmV. Cable TV uses 75&nbsp;Ω coaxial cable, so 0&nbsp;dBmV corresponds to −78.75&nbsp;dBW (−48.75&nbsp;dBm) or approximately 13&nbsp;nW.

;dBμV or dBuV: dB(μV<sub>[[root mean square|RMS]]</sub>)&nbsp;– [[volt]]age relative to 1&nbsp;microvolt.  Widely used in television and aerial amplifier specifications. 60&nbsp;dBμV&nbsp;= 0&nbsp;dBmV.

===Acoustics===
Probably the most common usage of "decibels" in reference to sound level is dB&nbsp;SPL, [[sound pressure level]] referenced to the nominal threshold of human hearing:<ref>{{citar livro|título= Audio postproduction for digital video|autor= Jay Rose|publicado= Focal Press|ano= 2002| isbn = 978-1-57820-116-7|página= 25| url = {{Google books |plainurl=yes |id=sUcRegHAXdkC |page=25 }} }}</ref>  The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dB&nbsp;SIL and dB&nbsp;SWL) use the factor of 10.
;dB&nbsp;SPL: dB&nbsp;SPL ([[sound pressure level]]) – for sound in air and other gases, relative to 20&nbsp;micropascals (μPa), or {{val|2|e=-5|u=Pa}}, approximately the quietest sound a human can hear.  For [[Underwater acoustics|sound in water]] and other liquids, a reference pressure of 1&nbsp;μPa is used.<ref>Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.</ref>{{paragraphbreak}} An RMS sound pressure of one pascal corresponds to a level of 94&nbsp;dB&nbsp;SPL.
;dB&nbsp;SIL: dB [[sound intensity level]] – relative to 10<sup>−12</sup>&nbsp;W/m<sup>2</sup>, which is roughly the [[threshold of human hearing]] in air.
;dB&nbsp;SWL: dB [[sound power level]] – relative to 10<sup>−12</sup>&nbsp;W.
;dBA, dBB, and dBC: These symbols are often used to denote the use of different [[weighting filter]]s, used to approximate the human ear's [[Stimulus (psychology)|response]] to sound, although the measurement is still in dB&nbsp;(SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dB<sub>A</sub> or [[A-weighting|dB(A)]]. According to standards from the International Electro-technical Committee ([[IEC 61672|IEC 61672-2013]])<ref>{{citar livro|título=IEC 61672-1:2013 Electroacoustics - Sound Level meters - Part 1: Specifications |data=2013 |publicado=International Electrotechnical Committee |local=Geneva}}</ref> and the American National Standards Institute, [[ANSI S1.4]],<ref>[[ANSI]] [https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.4.1983.pdf S1.4-19823 Specification for Sound Level Meters], 2.3 Sound Level, p. 2–3.</ref> the preferred usage is to write L<sub>A</sub>&nbsp;= x&nbsp;dB.  Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A{{nbhyph}}weighted measurements. Compare [[dBc]], used in telecommunications.
;dB&nbsp;HL: dB hearing level is used in [[audiogram]]s as a measure of hearing loss. The reference level varies with frequency according to a [[minimum audibility curve]] as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.{{carece de fontes|data=março de 2008}}
;dB&nbsp;Q: sometimes used to denote weighted noise level, commonly using the [[ITU-R 468 noise weighting]]{{carece de fontes|data=março de 2008}}
;dBpp: relative to the peak to peak sound pressure.<ref>Zimmer, Walter MX, Mark P. Johnson, Peter T. Madsen, and Peter L. Tyack. "Echolocation clicks of free-ranging Cuvier’s beaked whales (Ziphius cavirostris)." The Journal of the Acoustical Society of America 117, no. 6 (2005): 3919–3927.</ref>
;dBG: G{{nbhyph}}weighted spectrum<ref>http://oto2.wustl.edu/cochlea/wt4.html</ref>

===Audio electronics===
See also dBV and dBu above.

;[[dBm]]: dB(mW) – power relative to 1&nbsp;[[milliwatt]]. In audio and telephony, dBm is typically referenced relative to a 600&nbsp;Ω impedance,<ref>{{citar livro|último=Bigelow|primeiro=Stephen|título=Understanding Telephone Electronics|publicado=Newnes|isbn=978-0750671750|página=[https://archive.org/details/isbn_9780750671750/page/16 16]|ano=2001|acessourl=registro|url=https://archive.org/details/isbn_9780750671750/page/16}}</ref> which corresponds to a voltage level of 0.775&nbsp;volts or 775&nbsp;millivolts.
;[[dBm0]]: Power in dBm (described above) measured at a [[zero transmission level point]].
;[[dBFS]]: dB([[full scale]]) – the [[amplitude]] of a signal compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs. Full-scale may be defined as the power level of a full-scale [[Sine wave|sinusoid]] or alternatively a full-scale [[square wave]]. A signal measured with reference to a full-scale sine-wave appears 3&nbsp;dB weaker when referenced to a full-scale square wave, thus: 0&nbsp;dBFS(fullscale sine wave) = −3&nbsp;dBFS(fullscale square wave).
;dBVU: dB volume unit<ref>Tharr, D. (1998). Case Studies: Transient Sounds Through Communication Headsets. Applied Occupational and Environmental Hygiene, 13(10), 691–697.</ref>
;dBTP: dB(true peak) – [[peak amplitude]] of a signal compared with the maximum which a device can handle before clipping occurs.<ref>[[ITU-R BS.1770]]</ref> In digital systems, 0&nbsp;dBTP would equal the highest level (number) the processor is capable of representing.  Measured values are always negative or zero, since they are less than or equal to full-scale.

===Radar===
;[[dBZ (meteorology)|dBZ]]: dB(Z)&nbsp;– decibel relative to Z&nbsp;= 1&nbsp;mm<sup>6</sup>⋅m<sup>−3</sup>:<ref>{{citar web |url=https://www.weather.gov/jetstream/glossary_d |título=Glossary: D's |publicado=National Weather Service |acessodata=2013-04-25 |arquivourl=https://web.archive.org/web/20190808140856/https://www.weather.gov/jetstream/glossary_d |arquivodata=2019-08-08 |urlmorta= não}}</ref> energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20&nbsp;dBZ usually indicate falling precipitation.<ref>{{citar web |url=https://www.weather.gov/jetstream/radarfaq#reflcolor |título=RIDGE Radar Frequently Asked Questions |acessodata=2019-08-08 |arquivourl=https://web.archive.org/web/20190331123302/https://www.weather.gov/jetstream/radarfaq#reflcolor |arquivodata=2019-03-31 |urlmorta= não}}</ref>
;dBsm: dB(m<sup>2</sup>) – decibel relative to one square meter: measure of the [[radar cross section]] (RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dBsm, large flat plates or non-stealthy aircraft have positive values.<ref>{{citar web |url=http://everything2.com/title/dBsm |título=Definition at Everything2 |acessodata=2019-08-08 |arquivourl=https://web.archive.org/web/20190610170944/https://everything2.com/title/dBsm?%2F |arquivodata=10-06-2019 |urlmorta= não}}</ref>

===Radio power, energy, and field strength===
;[[dBc]]: relative to carrier – in [[telecommunication]]s, this indicates the relative levels of noise or sideband power, compared with the carrier power.  Compare dBC, used in acoustics.
;dBpp: relative to the maximum value of the peak power.
;dBJ: energy relative to 1&nbsp;[[joule]]. 1&nbsp;joule&nbsp;= 1&nbsp;watt second&nbsp;= 1&nbsp;watt per hertz, so [[power spectral density]] can be expressed in dBJ.
;[[dBm]]: dB(mW) – power relative to 1&nbsp;[[milliwatt]]. In the radio field, dBm is usually referenced to a 50&nbsp;Ω load, with the resultant voltage being 0.224&nbsp;volts.<ref>{{citar livro|último=Carr|primeiro=Joseph|título=RF Components and Circuits|ano=2002|publicado=Newnes|isbn=978-0750648448|páginas=45–46}}</ref>
;dBμV/m, dBuV/m, or dBμ:<ref name="dBµ">{{citar web|título=The dBµ vs. dBu Mystery: Signal Strength vs. Field Strength?|url=http://radio-timetraveller.blogspot.com/2015/02/the-db-versus-dbu-mystery-signal.html|website=radio-timetraveller.blogspot.com|data=24-02-2015|acessodata=13-10-2016}}</ref> dB(μV/m) – [[electric field strength]] relative to 1&nbsp;[[microvolt]] per [[meter]]. The unit is often used to specify the signal strength of a [[television]] [[broadcast]] at a receiving site (the signal measured ''at the antenna output'' is reported in dBμV).
;dBf: dB(fW) – power relative to 1&nbsp;[[femtowatt]].
;dBW: dB(W) – power relative to 1&nbsp;[[watt]].
;dBk: dB(kW) – power relative to 1&nbsp;[[kilowatt]].
;dBe: dB electrical.
;dBo: dB optical. A change of 1&nbsp;dBo in optical power can result in a change of up to 2&nbsp;dBe in electrical signal power in a system that is thermal noise limited.<ref>Chand, N., Magill, P. D., Swaminathan, S. V., & Daugherty, T. H. (1999). Delivery of digital video and other multimedia services (>&nbsp;1&nbsp;Gb/s bandwidth) in passband above the 155&nbsp;Mb/s baseband services on a FTTx full service access network. Journal of lightwave technology, 17(12), 2449–2460.</ref>

===Antenna measurements===
;dBi: dB(isotropic) – the forward [[Antenna gain|gain of an antenna]] compared with the hypothetical [[isotropic antenna]], which uniformly distributes energy in all directions. [[Linear polarization]] of the EM field is assumed unless noted otherwise.
;dBd: dB(dipole) – the forward gain of an [[antenna (electronics)|antenna]] compared with a half-wave [[dipole antenna]]. 0&nbsp;dBd&nbsp;= 2.15&nbsp;dBi
;dBiC: dB(isotropic circular) – the forward gain of an antenna compared to a [[Circular polarization|circularly polarized]] isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.
;dBq: dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0&nbsp;dBq&nbsp;= −0.85&nbsp;dBi
;dBsm: dB(m<sup>2</sup>) – decibel relative to one square meter: measure of the [[antenna effective area]].<ref>{{citar livro|url={{Google books |plainurl=yes |id=-AkfVZskc64C |page=118 }} |título=EW 102: A Second Course in Electronic Warfare |autor=David Adamy |acessodata=2013-09-16}}</ref>
;dBm<sup>−1</sup>: dB(m<sup>−1</sup>) – decibel relative to reciprocal of meter: measure of the [[antenna factor]].

===Other measurements===
;dB{{nbhyph}}Hz: dB(Hz) – bandwidth relative to one hertz. E.g., 20&nbsp;dB{{nbhyph}}Hz corresponds to a bandwidth of 100&nbsp;Hz. Commonly used in [[link budget]] calculations. Also used in [[carrier-to-receiver noise density|carrier-to-noise-density ratio]] (not to be confused with [[carrier-to-noise ratio]], in dB).
;[[dBFS|dBov or dBO]]: dB(overload) – the [[amplitude]] of a signal (usually audio) compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs.  Similar to dBFS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the level in dBov of a digital system is defined as:
:: <math>L_\text{ov} = 10\log_{10}\left ( \frac{P}{P_0} \right )\ [\text{dBov}]</math>,
: with the maximum signal power <math>P_0=1.0</math>, for a rectangular signal with the maximum amplitude <math>x_\text{over}</math>. The level of a tone with a digital amplitude (peak value) of <math>x_\text{over}</math> is therefore <math>L= -3.01\ \text{dBov}</math>.<ref>ITU-T Rec. G.100.1 The use of the decibel and of relative levels in speechband telecommunications https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.100.1-201506-I!!PDF-E&type=items</ref>
;dBr: dB(relative) – simply a relative difference from something else, which is made apparent in context.  The difference of a filter's response to nominal levels, for instance.
;[[dBrn]]: dB above [[reference noise]].  See also '''dBrnC'''
;dBrnC: '''dBrnC''' represents an audio level measurement, typically in a telephone circuit, relative to a -90 dBm reference level, with the measurement of this level frequency-weighted by a standard C-message weighting filter.  The C-message weighting filter was chiefly used in North America.  The Psophometric filter is used for this purpose on international circuits.  See [[Psophometric weighting]] to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters.<ref>dBrnC is defined on page 230 in "Engineering and Operations in the Bell System," (2ed), R.F. Rey (technical editor), copyright 1983, AT&T Bell Laboratories, Murray Hill, NJ, {{ISBN|0-932764-04-5}}</ref>
;dBK:'''dB(K)'''&nbsp;– decibels relative to 1&nbsp;[[kelvin|K]]; used to express [[noise temperature]].<ref>{{citar livro|url={{Google books |plainurl=yes |id=pjEubAt5dk0C |page=126 }} |título=Satellite Communication: Concepts And Applications |autor=K. N. Raja Rao |data=2013-01-31 |acessodata=2013-09-16}}</ref>
;dB/K: dB(K<sup>−1</sup>)&nbsp;– decibels relative to 1&nbsp;K<sup>−1</sup>.<ref>{{citar livro|url={{Google books |plainurl=yes |id=DVoqmlX6048C |page=79 }} |título=Comprehensive Glossary of Telecom Abbreviations and Acronyms |autor=Ali Akbar Arabi |acessodata=2013-09-16}}</ref>&nbsp;— ''not'' decibels per kelvin: Used for the ''[[G/T]]'' factor, a [[figure of merit]] utilized in [[satellite communications]], relating the [[antenna gain]] ''G'' to the [[receiver (radio)|receiver]] system noise equivalent temperature ''T''.<ref>{{citar livro|url={{Google books |plainurl=yes |id=L4yQ0iztvQEC |page=93 }} |título=The Digital Satellite TV Handbook |autor=Mark E. Long |acessodata=2013-09-16}}</ref><ref>{{citar livro|url={{Google books |plainurl=yes |id=U9RzPGwlic4C |page=SA27-PA14 }} |título=Reference Data for Engineers: Radio, Electronics, Computers and Communications |autor=Mac E. Van Valkenburg  |data=2001-10-19 |acessodata=2013-09-16}}</ref>

===List of suffixes in alphabetical order===

====Unpunctuated suffixes====
;dBA: see [[dB(A)]].
;dBa: see [[dBrn adjusted]].
;dBB: see [[dB(B)]].
;[[dBc]]: relative to carrier – in [[telecommunication]]s, this indicates the relative levels of noise or sideband power, compared with the carrier power.
;dBC: see [[dB(C)]].
;dBD: see [[dB(D)]].
;dBd: dB(dipole) – the forward gain of an [[antenna (electronics)|antenna]] compared with a half-wave [[dipole antenna]]. 0&nbsp;dBd = 2.15&nbsp;dBi
;dBe: dB electrical.
;dBf: dB(fW) – power relative to 1 [[femtowatt]].
;[[dBFS]]: dB([[full scale]]) – the [[amplitude]] of a signal compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs. Full-scale may be defined as the power level of a full-scale [[Sine wave|sinusoid]] or alternatively a full-scale [[square wave]]. A signal measured with reference to a full-scale sine-wave appears 3&nbsp;dB weaker when referenced to a full-scale square wave, thus: 0&nbsp;dBFS(fullscale sine wave) = −3&nbsp;dBFS(fullscale square wave).
;dBG: [[G-weighted]] spectrum
;dBi: dB(isotropic) – the forward [[Antenna gain|gain of an antenna]] compared with the hypothetical [[isotropic antenna]], which uniformly distributes energy in all directions. [[Linear polarization]] of the EM field is assumed unless noted otherwise.
;dBiC: dB(isotropic circular) – the forward gain of an antenna compared to a [[Circular polarization|circularly polarized]] isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.
;dBJ: energy relative to 1 [[joule]]. 1 joule = 1 watt second = 1 watt per hertz, so [[power spectral density]] can be expressed in dBJ.
;dBk: dB(kW) – power relative to 1 [[kilowatt]].
;dBK:'''dB(K)''' – decibels relative to [[kelvin]]: Used to express [[noise temperature]].
;[[dBm]]: dB(mW) – power relative to 1 [[milliwatt]].
;[[dBm0]]: Power in dBm measured at a zero transmission level point.
;dBm0s: Defined by Recommendation ITU-R V.574.
;dBmV: dB(mV<sub>[[root mean square|RMS]]</sub>) – [[volt]]age relative to 1 millivolt across 75 Ω.
;dBo: dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in system that is thermal noise limited.
;dBO: see dBov
;dBov or dBO: dB(overload) – the [[amplitude]] of a signal (usually audio) compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs.
;dBpp: relative to the peak to peak sound pressure.
;dBpp: relative to the maximum value of the peak power.
;dBq: dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0&nbsp;dBq = −0.85&nbsp;dBi
;dBr: dB(relative) – simply a relative difference from something else, which is made apparent in context.  The difference of a filter's response to nominal levels, for instance.
;[[dBrn]]: dB above [[reference noise]].  See also '''dBrnC'''
;dBrnC: '''dBrnC''' represents an audio level measurement, typically in a telephone circuit, relative to the [[circuit noise level]], with the measurement of this level frequency-weighted by a standard C-message weighting filter.  The C-message weighting filter was chiefly used in North America.
;dBsm: dB(m<sup>2</sup>) – decibel relative to one square meter
;dBTP: dB(true peak) – [[peak amplitude]] of a signal compared with the maximum which a device can handle before clipping occurs.
;dBu or dBv: [[root mean square|RMS]] [[volt]]age relative to {{nowrap|<math>\sqrt{0.6}\,\text{V}\, \approx 0.7746\,\text{V}\, \approx -2.218\,\text{dBV}</math>}}.
;dBu0s: Defined by Recommendation ITU-R V.574.
;dBuV: see dBμV
;dBuV/m: see dBμV/m
;dBv: see dBu
;dBV: dB(V<sub>[[root mean square|RMS]]</sub>) – [[volt]]age relative to 1 volt, regardless of impedance.
;dBVU: dB volume unit
;dBW: dB(W) – power relative to 1 [[watt]].
;dBW·m<sup>−2</sup>·Hz<sup>−1</sup>: [[Jansky#dBW·m−2·Hz−1|spectral density]] relative to 1 W·m<sup>−2</sup>·Hz<sup>−1</sup><ref>{{citar web|url=http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |título=Archived copy |acessodata=2013-08-24 |urlmorta= não|arquivourl=https://web.archive.org/web/20160303223821/http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |arquivodata=2016-03-03 }}</ref>
;[[DBZ (meteorology)|dBZ]]: dB(Z) – decibel relative to Z = 1&nbsp;mm<sup>6</sup>⋅m<sup>−3</sup>
;dBμ: see dBμV/m
;dBμV or dBuV: dB(μV<sub>[[root mean square|RMS]]</sub>) – [[volt]]age relative to 1 microvolt.
;dBμV/m, dBuV/m, or dBμ: dB(μV/m) – [[electric field strength]] relative to 1 [[microvolt]] per [[meter]].

====Suffixes preceded by a space====
;dB HL: dB hearing level is used in [[audiogram]]s as a measure of hearing loss.
;dB Q: sometimes used to denote weighted noise level
;dB SIL: dB [[sound intensity level]] – relative to 10<sup>−12</sup>&nbsp;W/m<sup>2</sup>
;dB SPL: dB SPL ([[sound pressure level]]) – for sound in air and other gases, relative to 20&nbsp;μPa in air or 1&nbsp;μPa in water
;dB SWL: dB [[sound power level]] – relative to 10<sup>−12</sup>&nbsp;W.

====Suffixes within parentheses====
;[[dB(A)]], [[dB(B)]], [[dB(C)]], [[dB(D)]], [[dB(G)]], and [[dB(Z)]]: These symbols are often used to denote the use of different [[weighting filter]]s, used to approximate the human ear's [[Stimulus (psychology)|response]] to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dB<sub>A</sub> or [[A-weighting|dBA]].

====Other suffixes====
;dB-Hz: dB(Hz) – bandwidth relative to one hertz.
;dB/K: dB(K<sup>−1</sup>) – decibels relative to [[multiplicative inverse|reciprocal]] of [[kelvin]]
;dBm<sup>−1</sup>: dB(m<sup>−1</sup>) – decibel relative to reciprocal of meter: measure of the [[antenna factor]].

==Related units==
;mBm:{{anchor|Millibel}} mB(mW) – power relative to 1 [[milliwatt]], in millibels (one hundredth of a decibel). 100&nbsp;mBm = 1&nbsp;dBm. This unit is in the Wi-Fi drivers of the [[Linux]] kernel<ref>{{citar web|url=http://wireless.kernel.org/en/users/Documentation/iw#Setting_TX_power|título=en:users:documentation:iw [Linux Wireless]|website=wireless.kernel.org}}</ref> and the regulatory domain sections.<ref>{{citar web|url=http://penturalabs.wordpress.com/2013/05/16/is-your-wifi-ap-missing-channels-12-13/|título=Is your WiFi AP Missing Channels 12 & 13?|data=16-05-2013|website=wordpress.com}}</ref>



-------------------------------------------->

== Acústica ==
Uma [[Intensidade (acústica)|intensidade sonora]] ''I'' ou [[potência]] ''P'' pode ser expressa em decibels de acordo com a relação:

::<math>
I_\mathrm{dB} = 10 \log_{10} \left(\frac{I}{I_0} \right) \quad \mathrm{ou} \quad P_\mathrm{dB} = 10 \log_{10} \left(\frac{P}{P_0} \right)\,
</math>
em que ''I''<sub>0</sub> e ''P''<sub>0</sub> são as intensidades e potências de referência.

Se ''P''<sub>dB</sub> é 3&nbsp;dB então ''P'' é aproximadamente o dobro de ''P''<sub>0</sub>.

Se ''P''<sub>dB</sub> é 10&nbsp;dB então ''P'' é 10 vezes maior que ''P''<sub>0</sub>.

Se ''P''<sub>dB</sub> é -10&nbsp;dB então ''P'' é 10 vezes menor que ''P''<sub>0</sub>.

Se ''P''<sub>dB</sub> é 20&nbsp;dB então ''P'' é 100 vezes maior que ''P''<sub>0</sub>.

Se ''P''<sub>dB</sub> é -20&nbsp;dB então ''P'' é 100 vezes menor que ''P''<sub>0</sub>.

A [[tensão elétrica]] ''V'', a [[corrente elétrica]] ''I'' ou a [[pressão]] ''p'' podem ser expressas em decibels de acordo com a relação seguinte:

::<math>
X_\mathrm{dB} = 20 \log_{10} \left (\frac{X}{X_0} \right ) </math>

em que ''X'' pode ser a tensão ''V'', a corrente ''I'' ou a pressão ''p'', e ''X''<sub>0</sub> são seus valores de referência. Note que é incorreto utilizar essas medidas se as [[impedância]]s elétricas ou acústicas não são as mesmas nos pontos onde a tensão ou pressão é comparada. Usando essa abordagem o decibel é uma medida de intensidade ou potência relativa.

Se ''V''<sub>dB</sub> é 6&nbsp;dB então ''V'' é o dobro que ''V''<sub>0</sub>.

Se ''V''<sub>dB</sub> é 20&nbsp;dB então ''V'' é 10 vezes maior que ''V''<sub>0</sub>.

Se ''V''<sub>dB</sub> é -20&nbsp;dB então ''V'' é 10 vezes menor que ''V''<sub>0</sub>.

Se ''V''<sub>dB</sub> é 40&nbsp;dB então ''V'' é 100 vezes maior que ''V''<sub>0</sub>.

Se ''V''<sub>dB</sub> é -40&nbsp;dB então ''V'' é 100 vezes menor que ''V''<sub>0</sub>.

Embora o [[Comitê Internacional de Pesos e Medidas]] (BIPM) aceite a sua utilização com o sistema [[Sistema Internacional de Unidades|SI]], ele não é uma unidade do SI. Apesar disso, seguem-se as convenções do SI, e a letra ''d'' é grafada em minúscula por corresponder ao prefixo ''deci-'' do SI, e ''B'' é grafado em maiúsculo pois é uma  abreviação da unidade ''[[Bel (unidade)|bel]]'' que é derivada de nome [[Alexander Graham Bell]]. Como o bel é uma medida muito grande para uso diário, o '''decibel (dB)''', que corresponde a um décimo de '''bel (B)''', acabou se tornando a medida de uso mais comum.

=== Vantagens ===
As vantagens do uso do decibel são:
* É mais conveniente somar os valores em decibels em estágios sucessivos de um sistema do que multiplicar os seus fatores de multiplicação.
* Faixas muito grandes de razões de valores podem ser expressas em decibels em uma faixa bastante moderada, possibilitando uma melhor visualização dos valores grandes.
* Na acústica o decibel usado como uma escala logarítmica da razão de intensidade sonora, se ajusta melhor a intensidade percebida pelo ouvido humano, pois o aumento do nível de intensidade em decibels corresponde aproximadamente ao aumento percebido em qualquer intensidade, fato conhecido com a [[Lei de potências de Stevens]]. Por exemplo, um humano percebe um aumento de 90&nbsp;dB para 95&nbsp;dB como sendo o mesmo que um aumento de 20&nbsp;dB para 25&nbsp;dB.
Ver exemplo em *[http://www.phys.unsw.edu.au/~jw/dB.html#soundfiles Sound files to show the size of a decibel].

=== Outras escalas logarítmicas ===
* O [[neper]] é uma unidade similar que usa o [[logaritmo natural]].
* A [[escala Richter]] também usa números expressos em bels.
* Na [[espectrometria]] e na [[óptica]] as unidades de [[absorbância]] são equivalentes a −1&nbsp;B.
* Na [[astronomia]] a [[magnitude aparente]] que mede o brilho das [[estrelas]] também é uma unidade logarítmica, uma vez que da mesma forma que o [[ouvido]] responde de modo logarítmico a [[potência acústica]], o [[olho]] também responde de modo logarítmico a [[intensidade luminosa]].
* Na [[química]], o [[pH]], que mede a acidez e alcalinidade de uma solução aquosa, também é uma escala logarítmica.

== História e uso do bel e decibel ==
O '''bel''' (símbolo '''B''') é uma [[unidade de medida]] de [[razão|razões]]. Ele é principalmente usado nas [[telecomunicações]], [[eletrônica]], e [[acústica]]. Foi inventado por engenheiros do [[Bell Labs]] para quantificar a redução no nível acústico sobre um cabo telefônico padrão com 1 [[milha]] de comprimento. Originalmente era chamado de ''unidade de transmissão'' ou ''TU'', mas foi renomeado entre 1923 e 1924 em homenagem ao fundador do laboratório [[Alexander Graham Bell]].

== Decibel na medida física do som ==
O [[som]] é uma [[oscilação]] na pressão do ar (ou de outro meio elástico) capaz de ser percebida pelo [[ouvido]] humano. O número de oscilações da pressão do ar por unidade de tempo define sua [[frequência]], enquanto a magnitude da [[pressão]] média define a [[potência]] e a [[Intensidade (acústica)|intensidade sonora]]. A frequência é expressa em [[hertz]] (ou ciclos/segundo) e a pressão em [[Pascal (unidade)|pascal]] (ou [[newton]]s/[[metro|m]]<sup>2</sup>), enquanto a potência é a [[energia]] emitida pela fonte sonora por unidade de tempo, expressa em [[joule]]s/s ou [[watt|W]] (estamos usando unidades do [[Sistema Internacional de Unidades|Sistema Internacional]]). A intensidade sonora pode ser definida como potência por unidade de [[área]], expressa em watt/m<sup>2</sup>. Essas escalas para medida de pressão, potência e intensidade das ondas sonoras são escalas lineares.

Contudo, a pressão, a potência e a intensidade dos sons captados pelo ouvido humano cobrem uma ampla faixa de variação. Por exemplo, um murmúrio irradia uma potência de 0,000 000 001 watt (10<sup>−9</sup> W) enquanto o grito de uma pessoa comum tem uma potência sonora de cerca de 0,001 watt; uma [[orquestra|orquestra sinfônica]] chega a produzir 10 watts enquanto um avião a jato emite 100 000 watts de potência ao decolar. Sendo assim, uma escala logarítmica, como o ''decibel'', é mais adequada para medida dessas grandezas físicas. Por este motivo, são usadas as seguintes escalas logarítmicas:

=== Nível de Pressão Sonora ===
<math>dB_{\rm SPL}=20\,\log( P_{\rm ef}/P_o)</math>

<math>P_{\rm ef}</math> = valor eficaz da pressão sonora

<math>P_o=2\times 10^{-5}\, {\rm N/m}^2</math>

=== Nível de Intensidade Sonora ===
<math>dB_{\rm IL} =10\, \log(I/I_o)</math>

I = intensidade acústica
<math>I_o=10^{-12}\, {\rm W/m}^2</math>

=== Nível de Potência Sonora ===
<math>dB_{\rm PWL}=10\, \log(W/W_o)</math>

W = potência acústica

<math>W_o=10^{-12}\, {\rm W}</math>

Os valores de referência, P<sub>o</sub>, I<sub>o</sub> e W<sub>o</sub>, correspondem aos limiares (ou umbrais) de percepção do ouvido humano. Note que o dB no umbral é zero. Nas expressões acima,

SPL = ''sound pressure level (''nível de pressão sonora);

IL = (''sound'') ''intensity level'' (nível de intensidade sonora);

PWL = (''sound'') ''power level'' (nível de potência sonora).

== Decibels ou decibéis? ==
Esta é uma dúvida que muitas pessoas têm. Segundo o "Novo Dicionário Aurélio da Língua Portuguesa" (2ª edição Revista e Atualizada), o plural de ''bel'' é '''bels''', enquanto para o plural de ''decibel'' as duas formas são corretas: '''decibels''' e '''decibéis'''.

Entretanto, no Brasil, o Decreto Federal No. 81.621 de 3 de maio de 1978 (Anexo 3.2), sobre o Quadro Geral de Unidades de Medidas, estabelece que a '''forma legal''' do plural de ''decibel'' é '''decibels'''.<ref name="decreto">{{citar web|URL=http://www.planalto.gov.br/ccivil_03/decreto/1970-1979/D81621.htm |título=DECRETO No 81.621, DE 3 DE MAIO DE 1978. |autor=Ernesto Geisel |data=03-05-1978 |publicado=Presidência da República — Casa Civil |acessodata=20-06-2017}}</ref>

Estas duas são as interpretações populares da questão das unidades e dos seus plurais, mas não estão erradas.<ref>{{citar web|URL=http://www.planalto.gov.br/ccivil_03/decreto/1970-1979/anexo/and81621-78.pdf |título=Quadro geral de unidades |autor= |data=03-05-1978 |publicado=Presidência da República — Casa Civil |acessodata=20-06-2017}}</ref> Uma unidade é um qualificativo, um padrão, não uma quantidade. As unidades não têm portanto plural, nem gênero. Uma "unidade" é UM. Em rigor deve-se portanto dizer 1 decibel (1x1 decibel), 10 decibel 10x1 decibel, dez vezes a unidade padrão decibel), etc. Por outro lado, essa informação pode ser facilmente refutada apresentando os plurais "metros", "horas" e "quilogramas" para as unidades "metro", "hora" e "quilograma". A confusão é comum porque não há plurais nas simbologias das unidades (2 metros = 2 m, 11 horas = 11h e 30 quilogramas = 30&nbsp;kg). Ver definição de [[unidades de medida]].

A regra definida pelas normas internacionais ISO, considera que quando a designação da unidade é proveniente do nome de uma pessoa (exemplo: N=Newton) não se utiliza o plural.

== Ver também ==
* [[Bel (unidade)|Bel]]
* [[Cent (música)]]
* [[dB drag racing]]
* [[Década (escala logarítmica)]]
* [[Escala de magnitude de Richter]]
* [[Magnitude aparente]]
* [[pH]]
* [[Phon]]
* [[Sone]]
* {{Section link|Um terço de oitava|Base 10}}
* [[Volume (som)]]

==Referências==
{{Reflist}}
==Bibliografia==
* {{citar periódico|último=Tuffentsammer |author-first=Karl |título=Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen |língua=de |títulotrad=The decilog, a bridge between logarithms, decibel, neper and preferred numbers |periódico=VDI-Zeitschrift |volume=98 |data=1956 |páginas=267–274}}
* {{citar livro|título=Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! |língua=de |títulotrad=Logarithms, preferred numbers, decibel, neper, phon - naturally related! |author-first=Eugen |último=Paulin |data=2007-09-01 |url=http://www.rechenschieber.org/Normzahlen.pdf |acessodata=2016-12-18 |arquivourl=https://web.archive.org/web/20161218223050/http://www.rechenschieber.org/Normzahlen.pdf |arquivodata=2016-12-18}}
* {{citar livro|url=https://books.google.com.br/books?id=QgKbCgAAQBAJ&pg=PA762&lpg=PA762&dq=Bel+unidade&source=bl&ots=O5GeDovevI&sig=ACfU3U0QkV9yCgmAq910m_1Xa5bzd3bB5A&hl=pt-BR&sa=X&ved=2ahUKEwiE4v60v6vjAhU6GLkGHZVtDxQ4ChDoATACegQICRAB#v=onepage&q=Bel%20unidade&f=false|título=Física conceitual|autor=Hewitt, Paul G.|edição=12|data=2015|editora=Bookman|isbn=9780321909107}}
==Ligações externas==
* [http://www.phys.unsw.edu.au/jw/dB.html O que é um decibel? Com arquivos de som e animações]
* [http://www.sengpielaudio.com/calculator-soundlevel.htm Conversão de unidades de nível sonoro: dBSPL ou dBA para pressão sonora p e intensidade sonora J]
* [https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=9735 Regulamentos da OSHA sobre exposição ocupacional ao ruído]
* [http://learnemc.com/working-with-decibels Trabalhando com Decibéis] (Sinal de RF e intensidades de campo)

{{Decibel}}
{{SI Unidades de base}}
{{Controle de autoridade}}

[[Categoria:Acústica]]
[[Categoria:Escalas logarítmicas de medição]]
[[Categoria:Engenharia de telecomunicações]]
[[Categoria:Unidades de medida]]