14CHAPTER 1. AMPLIFIERS AND ACTIVE DEVICES• Gains and losses may be expressed in terms of a unitless ratio, or in the unit of bels (B)or decibels (dB). A decibel is literally a deci-bel: one-tenth of a bel.• The bel is fundamentally a unit for expressing powergain or loss. To convert a powerratio to either bels or decibels, use one of these equations:• AP(Bel) = log AP(ratio)AP(db) = 10 log AP(ratio)• When using the unit of the bel or decibel to express a voltageor currentratio, it must becast in terms of an equivalent powerratio. Practically, this means the use of differentequations, with a multiplication factor of 2 for the logarithm value corresponding to anexponent of 2 for the voltage or current gain ratio:•AV(Bel) = 2 log AV(ratio)AV(dB) = 20 log AV(ratio)AI(Bel) = 2 log AI(ratio)AI(dB) = 20 log AI(ratio)• To convert a decibel gain into a unitless ratio gain, use one of these equations:•AV(ratio) = 10AV(dB)2020AI(ratio) = 10AI(dB)AP(ratio) = 10AP(dB)10• A gain (ampliﬁcation) is expressed as a positive bel or decibel ﬁgure. A loss (attenuation)is expressed as a negative bel or decibel ﬁgure. Unity gain (no gain or loss; ratio = 1) isexpressed as zero bels or zero decibels.• When calculating overall gain for an ampliﬁer system composed of multiple ampliﬁerstages, individual gain ratios are multipliedto ﬁnd the overall gain ratio. Bel or deci-bel ﬁgures for each ampliﬁer stage, on the other hand, are addedtogether to determineoverall gain.1.6Absolute dB scalesIt is also possible to use the decibel as a unit of absolute power, in addition to using it as anexpression of power gain or loss. A common example of this is the use of decibels as a measure-ment of sound pressure intensity. In cases like these, the measurement is made in reference tosome standardized power level deﬁned as 0 dB. For measurements of sound pressure, 0 dB isloosely deﬁned as the lower threshold of human hearing, objectively quantiﬁed as 1 picowattof sound power per square meter of area.A sound measuring 40 dB on the decibel sound scale would be 104 times greater than thethreshold of hearing. A 100 dB sound would be 1010 (ten billion) times greater than the thresh-old of hearing.