1、INTERNATIONAL TELECOMMUNICATION UNIONITU-T B.12TELECOMMUNICATIONSTANDARDIZATION SECTOROF ITUMEANS OF EXPRESSIONUSE OF THE DECIBEL AND THE NEPER INTELECOMMUNICATIONSITU-T Recommendation B.12(Extract from the Blue Book)NOTES1 ITU-T Recommendation B.12 was published in Fascicle I.3 of the Blue Book. Th
2、is file is an extract from theBlue Book. While the presentation and layout of the text might be slightly different from the Blue Book version, thecontents of the file are identical to the Blue Book version and copyright conditions remain unchanged (see below).2 In this Recommendation, the expression
3、 “Administration” is used for conciseness to indicate both atelecommunication administration and a recognized operating agency. ITU 1988, 1993All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic ormechanical, including photocopying an
4、d microfilm, without permission in writing from the ITU.Fascicle I.3 - Rec. B.12 1Recommendation B. 121)Fascicle I.3 - Rec. B.12USE OF THE DECIBEL AND THE NEPER IN TELECOMMUNICATIONS2)The CCITT,considering(a) the frequent use by the CCIR and CCITT of the decibel and the neper for expressing quantiti
5、es;(b) the IEC Publication 27-3 (1974) on logarithmic quantities and units;(c) the collaboration of CMV with Technical Committee No. 25 of the IEC which permits coordination witha view to establishing further Recommendations;(d) International Standard ISO 31;(e) the convenience of using only one uni
6、t to express in logarithmic form the numerical values ofinternational specifications and the results of measurements in exchanges at the international level;(f) the use in radiocommunications of the decibel alone to express the results of measurements inlogarithmic form;(g) the need, within the ITU,
7、 to publish a guide on this subject;recommendsthat symbols used for the logarithmic expression of quantities that directly or indirectly refer to power shouldbe chosen with the guidance of Annex A.ANNEX A(to Recommendation B.12)Use of the “decibel” and the “neper”A.1 Definition of the decibelA.1.1 T
8、he bel (symbol B) expresses the ratio of two powers by the decimal logarithm of this ratio. This unit is notoften used, having been replaced by the decibel (symbol dB) which is one-tenth of a bel.A.1.2 The decibel may be used to express the ratio of two field quantities, such as voltage, current, so
9、und pressure,electric field, charge velocity or density, the square of which in linear systems is proportional to power. To obtain thesame numerical value as a power ratio, the logarithm of the field quantity ratio is multiplied by the factor 20, assumingthat the impedances are equal.The relationshi
10、p between a current or voltage ratio and that of the corresponding power ratio is impedancedependent. Use of the decibel when the impedances are not equal is not appropriate unless adequate information isgiven concerning the impedances involved._1)A similar text will be submitted to the CCIR as a re
11、vision of Recommendation 574-2.2)In this Recommendation, the notation letter lg is used for the decimal logarithm in accordance with ISO 31 (Part XI) and usagewithin the IEC (Publication 27-3). The notation log10is also used within ISO and the IEC.2 Fascicle I.3 - Rec. B.12For example, if P1and P2 a
12、re two powers, their ratio expressed in decibels is:10 lg PP12If P1and P2represent the powers dissipated by currents I1and I2in resistances R1and R2:10 lg PP12= 10 lg IRIR121222= 20 lg II12+ 10 lg RR12A.1.3 The decibel may also be used to express the ratio of two values of a quantity connected with
13、power by a well-defined relationship. In this case, the logarithm of this ratio must be multiplied by a factor representing the relationshipwhich connects the quantity with a power, and a term representing a multiplying factor may be added to it.The corresponding formulae, together with an example,
14、are given in Appendix I, 1.2.A.2 Definition of the neperThe neper (symbol Np) expresses the ratio of two field quantities such as voltage or current, the square ofwhich is proportional to power by the natural logarithm of this ratio. The value of a power ratio in nepers is one half ofthe natural log
15、arithm of the power ratio. The values in nepers of the ratio of two field quantities and of thecorresponding powers are equal only if the impedances are equal.One neper corresponds to the value of e of a field quantity ratio and to the value e2of a power quantity ratio.Sub-multiples such as the deci
16、neper (dNp) are also used.In some disciplines, nepers may be used to express the logarithm of a power ratio without the factor . Anexample is optical depth or attenuation in radiometry. Such usage is deprecated in telecommunications in order to avoidambiguity. Under this definition, the neper would
17、in fact be equal to 4.34 dB, instead of 8.68 dB as is traditionally thecase.A.3 Use of the decibel and neperCountries can continue to use either the neper or the decibel for measurement purposes within their ownterritory and, to avoid conversion of values, countries which prefer to do so may continu
18、e to use the neper betweenthemselves by bilateral agreement.For the international exchange of information concerning transmission measurement and related values and forthe international specification of limits for such values, the only logarithmic expression to be used is the decibel.For theoretical
19、 or scientific calculations, where ratios are expressed in terms of naperian logarithms, the neperwill always be used, implicitly or explicitly.As a result of some calculations on complex quantities, a real part in nepers and an imaginary part in radians areobtained. Factors may be applied for conve
20、rting to decibels or degrees.The conversion values between the neper and the decibel are as follows:1 Np = (20 lg e)dB 8.686 dB1 dB = (0.05 ln 10)Np 0.1151 NpA.4 Rules for the use of the symbols where dB is includedConcerning the symbols that include the symbol dB, the following rules should be used
21、 as far as possible:A.4.1 The symbols dB without additional indicationThe symbol dB without additional indication should be used to indicate a difference between two power levelsor a ratio of two powers, two power densities, or two other quantities clearly connected with power.Fascicle I.3 - Rec. B.
22、12 3A.4.2 The symbol dB followed by additional information within parenthesisThe symbol dB followed by additional information within parentheses should be used to express an absolutelevel of power, power flux density or any other quantity clearly connected with power, in relation to a reference valu
23、ewithin the parentheses. In some cases, however, common use may give rise to simplified symbols such as dBm insteadof dB(mW).A.4.3 The symbol dB followed by additional information without parenthesisThe symbol dB followed by additional information without parenthesis should be used to express byconv
24、ention, special conditions such as measurements through specified filters or at a specified point of a circuit.A.5 Loss and gainThe attenuation or loss is a decrease between two points of an electric, electromagnetic or acoustic power. Theattenuation is also the quantitative expression of a power de
25、crease, generally in decibels; this decrease is expressed bythe ratio of the values at two points of a power or of a quantity related to power in a well-defined manner.The gain is the increase between two points of an electric, electromagnetic or acoustic power. The gain is alsothe quantitative expr
26、ession of a power increase, generally in decibels; this increase is expressed by the ratio of thevalues at two points of a power or of a quantity related to power in a well-det-ined manner.The exact designation of the loss or gain in question must be given (e.g. image-attenuation coefficient, insert
27、ionloss, antenna gain) which in fact refers to the precise definitions of the ratio in question (terminal impedances,reference conditions, etc.).A.5.1 Transmission loss (Refs. Recommendation 341, CCIR Volume V and Recommendation 573, term A43, CCIRVolume XIII)This is the ratio, expressed in decibels
28、, of the transmitted power (Pt) to the received power (Pr):L = 10 lg (Pt / Pr) dBA.5.2 Antenna gain (Refs. Radio Regulations, Article 1, No. 154 and Recommendation 573, term E04, CCIR VolumeXIII)This is “the ratio usually expressed in decibels of the power required at the input of a loss free refere
29、nceantenna (P0) to the power supplied to the input of the given antenna (Pa) to produce, in a given direction, the same fieldstrength or the same power flux-density at the same distance”.G = 10 lg (P0 / Pa) dBA.6 LevelsIn many cases, the comparison of a quantity, here called x, with a specified refe
30、rence quantity of the samekind(and dimension), xrefis expressed by the logarithm of the ratio x/xref. This logarithmic expression is often called“the level of x (with respect to xref)” or “the x-level (with respect to x/xref)”. With the general letter symbol for level L,the level of the quantity x m
31、ay be written Lx .Other names and other symbols exist and can be used, x may in itself be a single quantity, e.g. power P, or aratio, e.g. P/A, where A is area, xrefis here supposed to have a fixed value, e.g. 1 mW, 1 W,.1 W/m2, 20 Pa, 1V/m.The level representing the quantity x with reference quanti
32、ty xref may be indicated by the quantity symbol: Lx(with respect to xref), and may be expressed in decibels, when the reference quantity is a power, or a quantity linked topower, in a well defined way.Example:The statement that the level of a certain power, P, is 15 dB above the level corresponding
33、to 1 W can bewritten:4 Fascicle I.3 - Rec. B.12LP(with respect to 1 W) = 15 dB, which means 10 lg (P/1 W) = 153)or 10 lg P (in watts) = 15In many cases it is found practical to use a condensed notation based only on the unit, which in this case wouldbe:LP= 15 dB(1 W)The number “1” in the expression
34、of the reference quantity can be omitted, but this is not recommended incases where confusion may occur. (Such omission has been made in some of the examples below.) In other words,where no number is shown, the number 1 is to be understood.There exist condensed notations for special cases, such as d
35、BW, dBm, dBm0. See A.8 below.Below are given some examples in which the reference level is expressed after the unit in a condensed form. Itmust be observed that the condensed notation is often insufficient for characterizing a quantity, and that then a cleardefinition or another appropriate descript
36、ion of the quantity must be given.A.6.1 PowerThe “absolute power level” corresponds to the ratio of P and a reference power, e.g. 1 W.If P= 100 W and the reference power 1 W, we obtain:LP= 10 lg (P/1 W) dB= 10 lg (100 W/1 W) dB= 20 dBwith the condensed notation 20 dB(l W) or 20 dBW, dBW being the ab
37、breviation for: dB(l W). With the referencepower 1 mW and P = 100 W we obtain 50 dB(1 mW), or with the special notation mentioned earlier. 50 dBm, beingthe abbreviation for: dB(1 mW). The notations dBW and dBm are currently used in the CCIR and the CCITT. See A.8 below.A.6.2 Power spectral density (
38、with respect to bandwidth)The logarithmic expression corresponds to the ratio of P/ D , (where D denotes a bandwidth) and a referencequantity, e.g. 1 mW/kHz. P may be a noise power. The logarithm will in this case, as in all other cases, be taken of apure number.An example with a condensed notation
39、is 7 dB(mW/kHz) or that which is the same thing: 7 dB(W/MHz) or7 dB(W/Hz).A.6.3 Power flux-density (with respect to area)The logarithmic expression corresponds to the ratio of P/A, where A is area, and a reference power density, e.g.1 W/m2 A notation in a certain case can be: 40 dB(W/m2)or 10 dB(mW/
40、m2).A.6.4 Power density with respect to temperatureThe logarithmic expression corresponds to the ratio of P / T, where T is temperature, and a reference powerdensity, e.g. 1 mW/K, where K is kelvin.An example is: 45 dB(mW/K)or: 15 dB(W/K)._3)In the ratio (P/1 W), it is evident that both powers must
41、be expressed in the same units.Fascicle I.3 - Rec. B.12 5A.6.5 Spectral power-flux density (power density with respect to area and frequency band)The logarithmic expression corresponds to the ratio of P/ (A D ) and a reference density e.g. 1 W/ (m2Hz).An example is: 18 dB(W/(m2Hz)or: 18 dB(W m2Hz1).
42、A variant sometimes used is, dB(W/(m 24 kHz).A.6.6 Absolute level of electromagnetic fieldThe strength of an electromagnetic field can be expressed by a power flux-density (P/A), by an electric fieldstrength E or by a magnetic field-strength H. The field-strength level LEis the logarithm of the rati
43、o of E and areference field-strength, usually 1 V/m.An example with a condensed notation is:LE= 5 dB(V/m).As the power carried by an electromagnetic field is linked to the square of the field strength, this notationmeans:20 lg E(V/m) = 5.A.6.7 Sound pressure levelThe level corresponds to the ratio o
44、f sound pressure and a reference pressure, often 20 Pa.Example: 15 dB(20 Pa).As acoustic power is linked to the square of sound pressure, this means:20 lg (p / 20 Pa) =154)A.7 Ratios expressing transmission qualityA.7.1 Signal-to-noise ratioThis is either the ratio of the signal power (Ps) to the no
45、ise power (P0), or the ratio of the signal voltage (Us) tothe noise voltage (Un) measured at a given point with specified conditions. It is, expressed in decibels:R = 10 lg (Ps/ Pn) dB or R = 20 lg (Us / Un) dBThe ratio of the wanted signal to the unwanted signal is expressed in the same way. Detail
46、ed definitions aregiven in CCIR Recommendation 573-1, terms F21 and F23.A.7.2 Protection ratioThis is either the ratio of the wanted signal power (Pu) to the maximum permissible interfering signalpower(Pi), or the ratio of the wanted signal field-strength (Eu) to the maximum permissible interfering
47、signal field-strength (Ei). It is expressed in decibels:A = 10 lg (Pu / Pi)dB or A = 20 lg (Eu / Ei)dBMore detailed definitions of protection ratios are given in Recommendation 573-1, terms F22 and F24.A.7.3 Carrier to spectral noise density ratio (C/ N0)This is the ratio Pc / Pn D) where Pcis the c
48、arrier power, Pnthe noise power, D the correspondingfrequency bandwidth. This ratio has a dimension of frequency, it cannot be expressed without caution in terms ofdecibels, for power is not linked with frequency on a well-defined basis.This ratio could be expressed in relation with a reference quan
49、tity such as 1 W/(W/Hz) which clearly indicatesthe origin of the result._4)In the ratio (p/20 Pa), it is evident that both sound pressures must be expressed in the same units.6 Fascicle I.3 - Rec. B.12For example, with Pc= 2 W, Pn= 20 mW, and D = 1 MHz, for the logarithmic expression corresponding toC/N0we have:10 lg PPfcn/ D= 50 dB (W / (W / kHz)This expression is abbreviated to read 50 dB(kHz) which should however be avoided if it is liable to give riseto any misunderstanding.A.7.4 Figure of merit (M)The f
