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# Understanding Digital Audio Levels

A digital audio primer from ABA Academy Director Larry Wilkins

Larry Wilkins

As part of the Alabama Broadcasters Association’s Engineering Academy Continuing Education Series I have begun laying out a series of fundamental tutorials. Here I write on Understanding Digital Audio Levels, Analog vs. Digital Levels — the dBFS Scale.

Digital audio levels are measured differently than analog audio levels. Audio levels in digital are measured in dBFS (decibels relative to full scale).

The highest possible level in digital equipment is 0 dBFS. All other measurements expressed in terms of dBFS will always be less than 0 dB (negative numbers). 0 dBFS indicates the digital word (representing the analog waveform) with all digits = “1,” the highest possible sample.

The lowest possible sample is (16-bit audio): 0000 0000 0000 0001, which equals –96 dBFS. The addition of each bit to the word-length doubles the number of values that can be expressed. 20 log 2 = 6.02. The “6-dB-Per-Bit-Rule” is an approximation for calculating the actual dynamic range for a given word width.

In “real-world” signal processing, quantization is the process by which a number is approximated by a number of finite precision. For example, during analog-to-digital conversion, an infinitely variable signal voltage is represented by a binary number with a fixed number of bits. The difference between two consecutive binary values is called the quantization step, or quantization level. The size of the quantization step defines the effective noise floor of the quantized signal.

A quick estimate of maximum dynamic range capable of being represented by a given word length is dynamic range ~= number of bits x 6 dB.

Therefore the dynamic range for 16-bit system is 96 dB. For 20-bit digital audio it is 120 dB. For 24-bit digital audio it is 144 dB.

The digital world has caused questions about audio level and reference. Considering that we now have an absolute maximum level known as 0 dBFS, it makes sense to calibrate all equipment such that when 0 dBFS occurs at the mixing console, every additional, or downstream piece of gear should be set to match the 0 dBFS level. In this manner, we can faithfully know that the entire system is calibrated, and matched to the output of the mixing console.

As for a nominal operating level the recommended practice is to utilize –12 dBFS as the reference. This would be to observe dynamic peak levels to land at the ­–12 dBFS indication, thereby leaving 12 dB of headroom for the system. Assuming 0 dBFS is to be at the highest audio level before clipping occurs, which corresponds to an analog level of 24 dBu, +4 dBu is the same as –20 dBFS.

While this is generally accepted as the range of digital audio, it is not a hard standard. When digital audio values are converted back to analog, some digital audio equipment provides level selections to shift the analog output levels of 0 VU to –18 dBFS or –14 dBFS.

Lowering the dBFS relationship increases the audio sound levels output from the D/A converter.