Recommendation B.121)
USE 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 quantities;
	(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 with a view to establishing further Recommendations;
	(d)	International Standard ISO 31;
	(e)	the convenience of using only one unit to express in logarithmic form the numerical values of international 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 in logarithmic form;
	(g)	the need, within the ITU, to publish a guide on this subject;
recommends
	that symbols used for the logarithmic expression of quantities that directly or indirectly refer to power should be 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 decibel
A.1.1	The bel (symbol B) expresses the ratio of two powers by the decimal logarithm of this ratio. This unit is not often used, having been replaced by the decibel (symbol dB) which is one–tenth of a bel.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, sound pressure, electric field, charge velocity or density, the square of which in linear systems is proportional to power. To obtain the same numerical value as a power ratio, the logarithm of the field quantity ratio is multiplied by the factor 20, assuming that the impedances are equal.
	The relationship between a current or voltage ratio and that of the corresponding power ratio is impedance dependent. Use of the decibel when the impedances are not equal is not appropriate unless adequate information is given concerning the impedances involved.
	For example, if P1 and P2 are two powers, their ratio expressed in decibels is:
		10 lg 
	If P1 and P2 represent the powers dissipated by currents I1 and I2 in resistances R1 and R2:
		10 lg  = 10 lg    = 20 lg  + 10 lg 
A.1.3	The decibel may also be used to express the ratio of two values of a quantity connected with power by a well–defined relationship. In this case, the logarithm of this ratio must be multiplied by a factor representing the relationship which 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, are given in Appendix I, § I.2.
A.2	Definition of the neper
	The neper (symbol Np) expresses the ratio of two field quantities such as voltage or current, the square of which is proportional to power by the natural logarithm of this ratio. The value of a power ratio in nepers is one half of the natural logarithm of the power ratio. The values in nepers of the ratio of two field quantities and of the corresponding 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 e2 of a power quantity ratio.
	Sub–multiples such as the decineper (dNp) are also used.
	In some disciplines, nepers may be used to express the logarithm of a power ratio without the factor ½. An example is optical depth or attenuation in radiometry. Such usage is deprecated in telecommunications in order to avoid ambiguity. Under this definition, the neper would in fact be equal to 4.34 dB, instead of 8.68 dB as is traditionally the case.
A.3	Use of the decibel and neper
	Countries can continue to use either the neper or the decibel for measurement purposes within their own territory and, to avoid conversion of values, countries which prefer to do so may continue to use the neper between themselves by bilateral agreement.
	For the international exchange of information concerning transmission measurement and related values and for the international specification of limits for such values, the only logarithmic expression to be used is the decibel.
	For theoretical or scientific calculations, where ratios are expressed in terms of naperian logarithms, the neper will 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 are obtained. Factors may be applied for converting to decibels or degrees.
	The conversion values between the neper and the decibel are as follows:
	1 Np = (20 lg e)dB  8.686 dB
	1 dB = (0.05 ln 10)Np  0.1151 Np
A.4	Rules for the use of the symbols where dB is included
	Concerning the symbols that include the symbol dB, the following rules should be used as far as possible:
A.4.1	The symbols dB without additional indication
	The symbol dB without additional indication should be used to indicate a difference between two power levels or a ratio of two powers, two power densities, or two other quantities clearly connected with power.
A.4.2	The symbol dB followed by additional information within parenthesis
	The symbol dB followed by additional information within parentheses should be used to express an absolute level of power, power flux density or any other quantity clearly connected with power, in relation to a reference value within the parentheses. In some cases, however, common use may give rise to simplified symbols such as dBm instead of dB(mW).

A.4.3	The symbol dB followed by additional information without parenthesis
	The symbol dB followed by additional information without parenthesis should be used to express by convention, special conditions such as measurements through specified filters or at a specified point of a circuit.
A.5	Loss and gain
	The attenuation or loss is a decrease between two points of an electric, electromagnetic or acoustic power. The attenuation is also the quantitative expression of a power decrease, generally in decibels; this decrease is expressed by the 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 also the quantitative expression of a power increase, generally in decibels; this increase is expressed by the ratio of the values at two points of a power or of a quantity related to power in a well–defined manner.
	The exact designation of the loss or gain in question must be given (e.g. image–attenuation coefficient, insertion loss, 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, CCIR Volume XIII)
	This is the ratio, expressed in decibels, of the transmitted power (Pt) to the received power (Pr):
L = 10 lg (Pt/Pr)			dB
A.5.2	Antenna gain (Refs. Radio Regulations, Article 1, No. 154 and Recommendation 573, term E04, CCIR Volume XIII)
	This is “the ratio usually expressed in decibels of the power required at the input of a loss free reference antenna (P0) to the power supplied to the input of the given antenna (Pa) to produce, in a given direction, the same field strength or the same power flux–density at the same distance”.
G = 10 lg (P0/Pa)			dB
A.6	Levels
	In many cases, the comparison of a quantity, here called x, with a specified reference quantity of the same kind (and dimension), xref is 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 xref)”. With the general letter symbol for level L, the level of the quantity x may 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 a ratio, e.g. P/A, where A is area, xref is here supposed to have a fixed value, e.g. 1 mW, 1 W, 1 mW/m2, 20 mPa, 1 mV/m.
	The level representing the quantity x with reference quantity 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 to power, in a well defined way.
	Example:
	The statement that the level of a certain power, P, is 15 dB above the level corresponding to 1 W can be written:
	LP (with respect to 1 W) = 15 dB, which means 10 lg (P/1 W) = 153) 
or 10 lg P (in watts) = 15
	In many cases it is found practical to use a condensed notation based only on the unit, which in this case would be:
LP = 15 dB(1 W)
	The number “1” in the expression of the reference quantity can be omitted, but this is not recommended in cases 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 dBW, 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. It must be observed that the condensed notation is often insufficient for characterizing a quantity, and that then a clear definition or another appropriate description of the quantity must be given.
A.6.1	Power
	The “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 dB
with the condensed notation 20 dB(1 W) or 20 dBW, dBW being the abbreviation for: dB(1 W). With the reference power 1 mW and P = 100 W we obtain 50 dB(1 mW), or with the special notation mentioned earlier. 50 dBm, being the 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 (with respect to bandwidth)
	The logarithmic expression corresponds to the ratio of P/Df (where Df denotes a bandwidth) and a reference quantity, 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 a pure number.
	An example with a condensed notation is 7 dB(mW/kHz) or that which is the same thing: 7 dB(W/MHz) or 7 dB(mW/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/m2).
A.6.4	Power density with respect to temperature
	The logarithmic expression corresponds to the ratio of P/T, where T is temperature, and a reference power density, e.g. 1 mW/K, where K is kelvin.
An example is:	45 dB(mW/K)
		or:	15 dB(W/K).
A.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 . Df) and a reference density e.g. 1 W/(m2 . Hz).
An example is:	–18 dB(W/(m2 · Hz))
		or:		–18 dB(W · m–2 · Hz–1).
A variant sometimes used is, dB(W/(m2 · 4 kHz)).

A.6.6	Absolute level of electromagnetic field
	The strength of an electromagnetic field can be expressed by a power flux–density (P/A), by an electric field strength E or by a magnetic field–strength H. The field–strength level LE is the logarithm of the ratio of E and a reference field–strength, usually 1 mV/m.
	An example with a condensed notation is:
	LE = 5 dB(mV/m).
	As the power carried by an electromagnetic field is linked to the square of the field strength, this notation means:
	20 lg E(mV/m) = 5.
A.6.7	Sound pressure level
	The level corresponds to the ratio of sound pressure and a reference pressure, often 20 mPa.
	Example: 15 dB(20 mPa).
	As acoustic power is linked to the square of sound pressure, this means:
	20 lg (p/20 mPa) = 154) 
A.7	Ratios expressing transmission quality
A.7.1	Signal–to–noise ratio
	This is either the ratio of the signal power (Ps) to the noise power (P0), or the ratio of the signal voltage (Us) to the 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)		dB
	The ratio of the wanted signal to the unwanted signal is expressed in the same way. Detailed definitions are given in CCIR Recommendation 573–1, terms F21 and F23.
A.7.2	Protection ratio
	This is either the ratio of the wanted signal power (Pu) to the maximum permissible interfering signal power (Pi), or the ratio of the wanted signal field–strength (Eu) to the maximum permissible interfering signal field–strength (Ei). It is expressed in decibels:
A = 10 lg (Pu/Pi)		dB	or	A = 20 lg (Eu/Ei)		dB
	More 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/Df) – where Pc is the carrier power, Pn the noise power, Df the corresponding frequency bandwidth. This ratio has a dimension of frequency, it cannot be expressed without caution in terms of decibels, for power is not linked with frequency on a well–defined basis.
	This ratio could be expressed in relation with a reference quantity such as 1 W/(W/Hz) which clearly indicates the origin of the result.
	For example, with Pc = 2 W, Pn = 20 mW, and Df = 1 MHz, for the logarithmic expression corresponding to C/N0 we have:
		10 lg = 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 rise to any misunderstanding.
A.7.4	Figure of merit (M)
	The figure of merit (M) characterizing a receiving radio station is a logarithmic expression which is related to the antenna gain G (in decibels) and the overall noise temperature T (in kelvins) in the following way:
		M = dB (W/(W . K))
	The decibel notation may be abbreviated to read dB(K–1) which should however be avoided if it is liable to give rise to misunderstanding.
A.8	Special notations
	Examples of special notations, the use of which may be continued are given below. These notations are often made in addition to other notations.
	For absolute power level (see Appendix I, § I.1.1)
dBW:	absolute power level with respect to 1 watt, expressed in decibels;
dBm:	absolute power level with respect to 1 milliwatt, expressed in decibels;
dBm0:	absolute power level with respect to 1 milliwatt, expressed in decibels, referred to a point of zero relative level;
dBm0p:	absolute psophometric power level (weighted for telephony) with respect to 1 milliwatt, expressed in decibels, referred to a point of zero relative level;
dBm0s:	absolute power level with respect to 1 milliwatt, expressed in decibels, referred to a point of zero relative level in sound programme transmission;
dBm0ps:	absolute psophometric power level (weighted for sound–programme transmission) with respect to 1 milliwatt, expressed in decibels, referred to a point of zero relative level in sound programme transmission.
	For absolute level of an electromagnetic field (see Appendix I, § I.2.1):
	dBm or dBu:	absolute level of the electromagnetic field with respect to 1mV/m, expressed in decibels.
	For absolute voltage level including the audio–frequency noise level (see Appendix I, §§ I.2.2 and I.2.3):
dBu:	absolute voltage level with respect to 0.775 V, expressed in decibels;
dBu0:	absolute voltage level with respect to 0.775 V, referred to a point of zero relative level;
dBu0s:	absolute voltage level with respect to 0.775 V, referred to a point of zero relative level in sound–programme transmission;
dBqps:	absolute weighted voltage level measured according to Recommendation 468, CCIR Volume X–1, in sound–programme transmission;
dBq0ps:	absolute weighted voltage level measured according to Recommendation 468, CCIR Volume X–1, referred to a point of zero relative level in sound–programme transmission;
dBq0s:	absolute unweighted voltage level measured according to Recommendation 468, CCIR Volume X–1, in sound–programme transmission with respect to 0.775 V referred to a point of zero relative level.
	For relative power level (see Appendix I, § I.1.2):
	dBr:		decibels (relative);
	For relative voltage level in sound–programme transmission (see Appendix I, § I.2.4):
dBrs:	relative power level expressed in decibels, referred to another point in sound–programme transmission.
	For absolute acoustic pressure level:
	dBA (or dBB, dBC):	weighted acoustic pressure level with respect to 20 mPa, mentioning the weighting curve used (curves A, B or C, see IEC Publication 123).
	For antenna gain in relation to an isotropic antenna:
	dBi.
	For antenna gain in relation to a half–wave dipole:
	dBd.
	Note 1 – In the case of the ratio “energy per bit to spectral noise density”, E/N0, which is used in digital transmission, the ratio is made between two quantities homogeneous with spectral power density, and this ratio may normally be expressed in decibels, like power ratios (see § A.1 above). However, it is necessary to ensure that the units used for the expression of both terms in the ratio are equivalent: for example, joule (J) for energy and watts per hertz (W/Hz) for spectral noise density.
	Note 2 – Appendix I gives the principles for the use of the term decibel in telecommunication.
	The examples given in the present Recommendation are illustrations of these principles.
	Note 3 – In Appendix II is given the principle of the notation recommended by the IEC for expressing the level of a quantity with respect to a specified reference. The notations used in the present Recommendation are applications of this principle.
APPENDIX I
(to Recommendation B.12)
Use of the term decibel in telecommunication
I.1	Use of the decibel for ratios of quantities directly connected with power
I.1.1	Absolute power level
	The absolute power level is the ratio, generally expressed in decibels, between the power of a signal at a point in a transmission channel and a specified reference power.
	It should be specified in every case whether the power is real or apparent.
	It is necessary for the reference power to be indicated by a symbol:
–	when the reference power is one watt, the absolute power level is expressed in “decibels relative to one watt” and the symbol “dBW” is used;
–	when the reference power is one milliwatt, the absolute power level is expressed in “decibels relative to one milliwatt” and the symbol “dBm” is used.
I.1.2	Relative power level and related concepts
I.1.2.1	Definition
	The relative power level is the ratio, generally expressed in decibels, between the power of a signal at a point in a transmission channel and the same power at another point in the channel chosen as reference point, generally at the origin of the channel.
	It should be specified in every case whether the power is real or apparent.
	Unless otherwise specified, the relative power level is the ratio of the power of a sinusoidal test signal (at 800 or 1000 Hz) at a point in the channel to the power of that signal at the transmission reference point.
I.1.2.2	Transmission reference point
	In the old transmission plan, the CCITT had defined “the zero relative–level point” as being the two–wire origin of a long distance circuit (point 0 of Figure I–1/B.12).
	In the presently recommended transmission plan the relative level should be –3.5 dBr at the virtual switching point on the sending side of a four–wire international circuit (point V of Figure I–2/B.12). The “transmission reference point” or “zero relative level point” (point T of Figure I–2/B.12) is a virtual two–wire point which would be connected to V through a hybrid transformer having a loss of 3.5 dB. The conventional load used for the computation of noise on multi–channel carrier systems corresponds to an absolute mean power level of –15 dBm at point T.
I.1.2.3	Meaning of “dBm0”
	If a measuring signal with an absolute power level LM (in dBm) is applied at point T, the absolute power level of signal appearing at a point X, where the relative level is LXR (in dBr), will be LM + LXR (in dBm).
	Conversely, if a signal at X has an absolute power level LXA (in dBm), it is often convenient to “refer it to zero relative level point” by computing L0 (in dBm0) by the formula:
L0 = LXA – LXR
	This formula may be used, not only for signals, but also for noise (weighted or unweighted), which helps in the computation of a signal–to–noise ratio.
	Note – More detailed explanations for § I.1.2.1 and I.1.2.2 above are given in Recommendations G.101 (§ 5) and G.223 published in Volume III.
Fig. I–1 B.12 and Fig. I–2/B.12/ T1203260-90 = 6 cm

I.1.3	Power density
	Definition: Quotient of a power by another quantity, for example, an area, a bandwidth, a temperature.
	Note 1 – The quotient of a power by an area is called “power flux–density” (“puissance surfacique”) and is commonly expressed in “watts per square metre” (symbol: W . m–2 or W/m2).
	The quotient of a power by a frequency bandwidth is called “power spectral density” and can be expressed in “watts per hertz” (symbol: W . Hz–1 or W/Hz). It can also be expressed with a unit involving a bandwidth characteristic of the technique concerned, for example, 1 kHz or 4 kHz in analogue telephony, 1 MHz in digital transmission or in television; the power spectral density is then expressed in “watts per kilohertz” (W/kHz) or in “watts per 4 kHz” (W/4 kHz) or even in “watts per megahertz” (W/MHz).
	The quotient of a power by a thermo–dynamic temperature, used particularly in the case of noise powers, has no specific name. It is usually expressed as “watts per kelvin” (symbol: W . K–1 or W/K).
	Note 2 – In some cases a combination of several types of power densities can be used, for example a “spectral power flux–density” which is expressed as “watts per square metre and per hertz” (symbol: W . m–2 . Hz–1 or W/(m2 . Hz)).
I.1.4	Absolute power density level
	Definition: Expression in logarithmic form, usually in decibels, of the ratio between the power density at a given point and a reference power density.
	Note – For example, if one watt per square metre is chosen as the reference power flux–density, the absolute power flux–density levels are expressed as “decibels with respect to one watt per square metre” (symbol: dB(W/m2)).
	Similarly, if one watt per hertz is chosen as the spectral reference power density, the absolute spectral power density levels are expressed as “decibels with respect to one watt per hertz” (symbol: dB(W/Hz)).
	If one watt per kelvin is chosen as the reference for power density per unit temperature, the absolute power density levels per temperature unit are expressed as “decibels with respect to one watt per kelvin” (symbol: dB(W/K)).
	This notation can easily be extended to combined densities. For example, the absolute spectral density levels of the flux–density are expressed as “decibels with respect to one watt per square metre and per hertz” for which the symbol is: dB(W/(m2 . Hz)).
I.2	Use of the decibel for ratios of quantities indirectly connected with power
	Current practice has led to an extension of the use of the term decibel to ratios of quantities which are only indirectly connected with power or which are linked to it through the medium of a third quantity. In these various cases, the decibel should be used with the utmost precaution and should always be accompanied by a note indicating the conventions adopted and the sphere of validity of this usage.
	A case extremely common in practice, is where the ratio of two powers P1 and P2 depends solely on the ratio of the values X1 and X2 of another quantity X by an equation in the form:
P1/P2 = (X1/X2)a
a being any real number. The corresponding number of decibels can then be calculated from the ratio:
X1/X2 from the equation:
N = 10 lg (P1/P2) = 10 a lg (X1/X2)			dB
	It should be noted that a quantity X is not always associated with the same value of the number a, and therefore it is not possible, without some other indication, to express in decibels the ratio of two values of the quantity X.
	Most often a is equal to 2, and then the expression in decibels of ratios of currents or voltages or other analogous quantities in other fields, is:
N = 20 lg (X1/X2)				dB
	An example where a is other than 2 is the relationship between cross–polarization (XPD) and the co–polarized path attenuation (CPA) given by the empirical relationship (see CCIR Report 722, Volume V):
XPD = U – V lg (CPA)			dB
I.2.1	Absolute level of the electromagnetic field
	The electromagnetic field set up by a transmitter is of concern to some services. At considerable distances from the antenna this field is generally defined by its electric component E, for which it is often convenient to use a logarithmic scale.
	For a non–guided wave propagated in a vacuum, or in practice in the atmosphere, there is a clearly defined relationship between the electric field E and the power flux–density p:
E2 = Z0 p
Z0, which is the intrinsic impedance of the vacuum, having a fixed numerical value of 120 p ohms. In particular, a field of 1 microvolt per metre corresponds to a power flux–density of –145.8 dB(W/m2).
	The absolute level of the electric field can then be defined by the equation:
		N = 20 lg
E0 being a reference field, generally 1 microvolt per metre. In this case, N represents the absolute field level in “decibels with respect to 1 microvolt per metre”, the symbol for which is “dB(mV/m)”.
	In accordance with International Standard ISO 2955, the symbol “dB(uV/m)” may be used when the character set employed does not comprise Greek letters. This symbol is sometimes further abbreviated to “dBu”. This symbol does however have another use which is defined in § I.3.2.
I.2.2	Absolute voltage level
	The absolute voltage level is the ratio, generally expressed in decibels, of the voltage of a signal at a point in a transmission channel to a specified reference voltage.
	The nature of the voltage in question, e.g. r.m.s. value, should be specified in every case.
	A reference voltage with an r.m.s. of 0.775 volts is generally adopted which corresponds to a 1 milliwatt power dissipated in a resistance of 600 ohms, since 600 ohms represents a rough approximation to the characteristic impedance of certain balanced telephone lines.
I.2.2.1	If the impedance at the terminals of which the voltage U1 is measured, is in fact 600 ohms, the absolute voltage level thus defined, corresponds to the absolute power level with respect to 1 milliwatt, and so the number N exactly represents the level in decibels with respect to 1 milliwatt (dBm).
I.2.2.2	If the impedance at the terminals of which the voltage U1 is measured, is R ohms, N equals the number of dBm increased by the quantity 10 log (R/600).
I.2.3	Absolute audio–frequency noise level in broadcasting, sound recording or sound–programme transmission
	Measurement of audio–frequency noise in broadcasting, sound recording or sound–programme transmission is made, normally through a weighting network and by following the quasi–peak value method of Recommendation 468 using a reference voltage of 0.775 volt at 1 kHz and a nominal impedance of 600 ohms and expressing the results normally in dBqp.
	Note – The two notations in “dBq” and “dBm” should not be used interchangeably. In sound–programme transmission the notation “dBq” is restricted to level measurements of noise with single or multiple tone bursts whereas the notation “dBm” only applies to sinusoidal signals used for lining up the circuit.
I.2.4	Relative voltage levels in sound–programme transmission
	The relative voltage level at a point in a sound–programme transmission chain is the ratio, expressed in dB, of the voltage level of a signal at that point relative to the voltage level of the same signal at the reference point. This ratio is expressed in “dBrs”, the “r” indicating “relative level” and “s” indicating that the ratio refers to levels in a “sound–programme” system. At the reference point (the point of zero relative level, 0 dBrs) a test signal at the alignment level (see Recommendation 645, CCIR Volume X–1, has a level of 0 dBu. Note that in some broadcasting chains, there may be no point of zero relative level. However, points of measurements and interconnection may still be given a level (in dBrs) relative to hypothetical reference point.
I.3	Use of the decibel, by extension, for ratios of quantities not connected with power
I.3.1	Voltage ratios
	In certain spheres such as audio frequencies, the concept of voltage is sometimes more important than that of power. This is the case, for example, when low output– and high input–impedance two–port networks are associated in tandem. In this way a deliberate departure is made from the impedance matching conditions in order to simplify the formation of these networks. When this is done, only the voltage ratios at different points in the link need to be taken into consideration.
	It is then convenient to express these voltage ratios in a logarithmic scale, e.g. to the base 10, by defining the number N of corresponding units by means of the equation:
		N = K lg
	In this equation the coefficient K is a priori arbitrary. However, by analogy with the operation:
		N = 20 lg
which expresses in decibels the ratio of the I2R loss as in two equal resistances at the terminals of which the voltages U1 and U2 respectively, are applied, one is led to adopt the value 20 for the coefficient K. The number N then expresses in decibels the power ratios which would correspond to the voltage ratios, if the latter were applied to equal resistances, although in practice this is not generally the case.
I.3.2	Absolute voltage level
	If the impedance at the terminals of which the voltage is measured is not specified, the corresponding power level cannot be calculated. However, a number N can be defined conventionally in accordance with § I.3.1 with respect to a reference voltage and can be expressed in decibels. To avoid any confusion, it is essential to specify that an absolute voltage level is concerned and the symbol dBu must be used. The symbol dBu appears to create no confusion with the use defined in § I.2.1 as the absolute level of the electromagnetic field referred to 1 microvolt per metre. If, however, there is any risk of confusion, the expression dB (775 mV) must be written, at least the first time.
APPENDIX II
(to Recommendation B.12)
Notation for expressing the reference of a level
(Part 5 of IEC Publication 27–3)
	A level representing the quantity x with the reference quantity xref may be indicated by:
Lx (with respect to xref) or by Lx/xref.
	Examples
	The statement that a certain sound pressure level is 15 dB above the level corresponding to a reference pressure of 20 mPa can be written as:
Lp (re 20 mPa) = 15 dB or as Lp/20 mPa = 15 dB.
	The statement that the level of a current is 10 Np below 1 ampere can be written as:
L1 (with respect to 1 A) = –10 Np.
	The statement that a certain power level is 7 dB above 1 milliwatt can be written as:
Lp (with respect to 1 mW) = 7 dB.
	The statement that a certain electric field–strength is 50 dB above 1 microvolt per metre can be written as:
LE (with respect to 1 mV/m) = 50 dB.
	In presenting data, particularly in tabular form or in graphical symbols, a condensed notation is often needed for identifying the reference value. Then, the following condensed form, illustrated by application to the above examples, may be used:
   15 dB(20 mPa)
–10 Np(1 A)
     7 dB(1 mW)
   50 dB(1 mV/m).
	The number “1” in the expression of a reference quantity is sometimes omitted. This is not recommended in cases when confusion may occur.
	When a constant level reference is used repeatedly in a given context and explained in the context, it may be omitted.5)