ived in one second. The unit is the Hertz. The 8.2.1 The fundamental decibel wavelength is the distance between corresponding points on ad- jacent cycles. The decibel (dB) is basically a unit of comparison of power using a Frequency f and wavelength a are related by Equation 8.5. logarithmic scale, SO that the difference, n, in dBs between two powers is given by Equation 8.8 where P1 and P2 are the two powers (8.5) (all logs are to base 10 unless stated). Hearing 8/5 (8.8) Thus one may speak of a level of (say) +3dBm, which means that the signal in question is 3dB above 1mW, (=2mW). 8.2.2 Other versions of the decibel If P, is less than P. then n is negative. Powers in audio circuits are not easy to measure but voltages are. If V and R are voltage and resistance, then power is given by Equation 8.9, and from this These may be listed as: Equation 8.10 may be obtained. 1. dBmV; the reference is 1mV. (8.9) 2. dBV; the reference is 1 volt. P P=K 3. dBu; this is less obvious and is based on the fact that if 1mW of power is dissipated in 600 ohms the voltage across the 600 ohms is 0.775V. Thus +6dBu is 6dB above 0.775V, (8.10) (=1.55V). 4. dBA; a non-electrical unit which is intended to approximate to an unit of loudness. f R 1 R R2 Equation 8.11 follows. Finally it should be mentioned that dBs are used without any further abbreviations when service areas of transmitters are shown (8.11) with field strength contours. In such instances the reference level is 1uV/m, unless there are statements to the contrary. An alternative to the decibel is the Neper, based on natural logarithms, as given by Equation 8.12. In many audio circuits a common impedance is 600 ohms and Equation 8.11 valid. However there are cases when the impedances Nepers = = log ( voltage ratio) (8.12) at different points in the chain differ from each other and strictly Equation 8.11 should not be used. In fact, though, it is convenient to continue to use this equation and usually the context makes clear It follows that 1dB = 0.115 neper and 1 neper = 8.68