The term "dB" is used to describe a ratio between two audio levels. As such; it has no absolute value. Due to the non-linear nature of human hearing, the logarithmic dB scale approximates the relationship of the measured value to the perceived change in acoustic level.
Please note: due to limitations in supported text characters; in the following discussion a value such as "two squared" is described as "2 raised to the power of 2" for clarity.
The decibel may be defined in this manner: two amounts of power differ by 1 decibel when they are in the ratio of 100 raised to the power of one-tenth. The term was used originally in early telephony to measure loss in a standard mile of telephone wire. In honor of Alexander Graham Bell, and to indicate the "decimal" power relationship; the unit was named the "decibel."
The ratio can be expressed as 10 raised to the power of (dB x 0.1); so a 6dB difference between two signals means the larger signal equals the value of the smaller signal multiplied times (10 raised to the power of 0.6) or "ten to the six-tenths power."
In order to give a dB measurement an absolute value; it must have a “zero reference.” One analogy is temperature in “degrees.” Without knowing what “zero degrees” is; we can only talk about the difference between two temperatures (a form of ratio). Unfortunately; the analogy fails when you bring in the differences between Fahrenheit and Centigrade because (unlike the decibel) the “one degree” has different definitions in each system!
One of the more common forms of “absolute” dB scales is Sound Pressure Level or “SPL.” In this case, the “zero reference” is a very small value and the scale only extends in the positive value direction. The zero reference acoustic level is considered to be the “threshold of human perception” and SPL is thus a scale that tells us how much louder a sound level is than the quietest sound one can perceive.
In audio electronics, the “0dBm” standard for power was 1 milliwatt; because most early audio transmission utilized 600 Ohm impedance-matched systems. This power level was achieved when an RMS voltage of 0.775 volts was applied to a 600 Ohm load. In most contemporary audio systems, the signal appears as a voltage waveform; thus the dBu voltage scale is used instead of the dBm power scale. To make this system applicable to pure voltage level measurements; the “dBu” scale is used with the same zero reference of 0.775 Volts.
When the use of VU meters became prevalent in the USA; the VU meter’s “0” was defined as “+4dBm,” and in contemporary systems is defined as “+4dBu.” The designation “VU” is an abbreviation for “Volume Unit” because the VU meter was intended to provide a useful means of relating the metered level of complex audio program to the perceived volume. "0dBVU" = +4dBu = 1.228 Volts rms
The dBV scale is typically used in consumer audio measurements and ratings. The zero reference for dBV is 1 Volt rms.
“+4” versus “-10”
Professional line level is often referred to as “+4” as versus the consumer line level of “-10”; which is source of confusion. This is because “+4” is “+4dBu” and “-10” is “-10dBV;” and the dBu and dBV scales uses different “zero dB” reference voltages! The result is that, rather than the “apparent” difference of 14dB between “+4” and “-10”; the actual difference is closer to 12 dB (11.8dB).
The term dBFS or “dB Full Scale” is used to describe the level of a linear PCM digital audio signal relative to the highest (peak) level that can be encoded, and has no fixed relationship to dBu or "analog level."
0dBFS is sometimes referred to as “digital clipping” level. Because this is the only “fixed” level in digital audio, the dB level scale typically starts at 0dBFS and all other levels below 0dBFS are in “negative dB” (for example -14dBFS).
Depending on the calibration of the AD converter used to encode the audio signal; a wide range of analog input levels can result in the same digital level. Because no signal information is retained once the signal level exceeds 0dBFS; the most important level for calibration purposes is peak level.
In a similar manner, there is no fixed relationship between digital level (relative to 0dBFS) and the analog output level of a DA converter.
Professional level analog audio equipment typically has a peak output level of between +18 and +24dBu. Because the standard for VU meters is “0dBVU = +4dBu,” this results in “0dBVU = -14dBFS” for a peak level of +18dBu and “0dBVU = -20dBFS” for +24dBu. The use of “-14” as a calibration standard for digital audio gear thus means the analog input is calibrated to accept a peak analog level of +18dBu. Lavry converters are set at the factory for a reference level of “-20” where “0dBFS = +24dBu.” Which reference calibration level works best depends on the application. For example; the “-14” level works well for Mastered audio program where the difference between “VU” (or “average”) level and peak level has been controlled with compressors and/or limiters. For recording “live” tracks that are not compressed or limited; the “-20” reference level may be a better choice. There is no standard in the professional audio industry for this calibration; only a range of calibrations that are typically used in recording, mixing, and mastering. The important point is to match the peak analog output level of the source device to “0dBFS” digital level.
Ideally; the analog source should have 1-3 dB of “headroom” (peak output level capability) above the analog input level that results in 0dBFS, so that the analog output does not “clip” or significantly increase in distortion before reaching 0dBFS in the AD converter. For example; if the analog source has a peak output level capability of exactly +24dBu, using “-19” or “-18” as the reference level would achieve this goal.
In some cases there are other consideration; such as preservation of dynamic range. For example; the analog source device has an output level control, and turning it to the “full up” position results in a more noise that setting it to a somewhat lower level. The input of the AD converter should be calibrated so the peak output level with the source output level control at the optimum position results is 0dBFS when the audio reaches peak level. It may take some experimentation to determine this level; and changing the source device may require a change to the calibration to optimize the system with the new device.
In a similar manner, the output level of a DA converter can be adjusted so that the same digital level can result in a wide range of analog levels. The DA converter is typically calibrated to the same peak analog level as the AD converter, so that the digital audio recording system is calibrated for “unity gain.” This results in the playback of the digital audio recording system to be the same level as the analog signal feeding it.
There may also be an advantage to setting the output level of the DA to a lower level for some applications. One example is when feeding a monitor system with high gain. By reducing the level at the output of the DA converter, the monitor Volume control can be operated at a higher, more ideal setting. Lower gain settings can also allow matching of the apparent level when switching between sources.