Analog & Digital Audio Dynamic Range

Many years ago I prepared a chart to help teach and explain digital audio signal levels and how they relate to analog signal levels, both in the studio and in consumer equipment. I have re-created the chart as a .pdf file for dlb Research Digital & Analog Signal Levels Compared. Referring to this chart will be helpful in this and many of the discussions here.

The right side of the chart shows the digital audio dynamic from clipping to the noise floor for a 24 bit PCM sampled audio signal. This is the standard number of bits that can be represented in the SPDIF and AES digital audio standards and what is typically used in exchange between equipment. Of course, 32 bit samples are possible and used in many digital audio workstations, but they are typically not exchanged between equipment in daily use. 32 bits of resolution can be useful in certain signal processing applications, but for a final delivery medium 24 bits is more than sufficient as we shall see.

Roughly speaking, each bit of resolution corresponds to 6 dB of dynamic range (20 x log (2)). 16 bits of resolution will therefore yield roughly 96 dB of dynamic range. There is a fudge factor that makes the real calculation 98.09 dB as can be seen from the chart. 20 bits of resolution yields 122.17 dB of dynamic range. These are mathematical calculations and represent a perfect world.

In practice, building real analog equipment that has true 20 bit resolution is quite difficult. So while we may be able to handle the digital numbers with complete accuracy, we cannot create the music and convert it to a sampled and quantized format (and back) with much more than 20 bits of resolution. This is a very important point that is rarely mentioned.

We have made tremendous strides since the beginning of digital audio which started out in the 14 to 16 bit range. We are just now getting to the point where we can actually design a complete analog-to-digital-to-analog signal path that equals what was relatively easy to do in the analog world 25 years ago.

This is a difficult concept so perhaps a story will help. Dr. Thomas G. Stockham, who I call the father of Digital Audio in the US was one of my college professors. I would often talk to him after class to learn more about my own audio passion. He told a very interesting story about the first orchestra recording he ever did. (I can only paraphrase of course)

"We traveled to Boston to record the symphony. When we arrived we found out that the analog reference level of their mixing console was different that what we designed our analog to digital converter to receive. We didn't have adjustable gain so we went ahead and made some recordings that day. Overnight, we were able to get the parts we needed to make the adjustments so that the second day of recordings the levels matched correctly.

"When we measured things, the first days recordings had the equivalent of only 14 bits of resolution, while the second day we had the full 16 bits of resolution that we planned for. The very next week, we took the equipment to the AES convention and demonstrated the digital recording technology. Without exception, the listeners commented that the 14 bit recordings were noisy and the 16 bit ones weren't."

This story really impressed me. It showed that 16 bits was actually barely enough resolution for playback, and certainly the levels had to be carefully matched if digital audio was to equal the dynamic range of the original analog sound.

Today we have IC converters that can reach more than 120 dB dynamic range according to their data sheets. But do they really have 120 dB of resolution over the entire range of frequencies and levels? A few years ago I designed a system that reached 114 dB of dynamic range from analog input to analog output. But that was only a single static measurement. Distortion levels are much higher than than at full scale when things get loud.

In coming articles we hope to show that it is actually quite difficult to achieve 20 bit resolution and that almost no professional equipment let alone consumer even comes close. We will also explore dithering and rounding in depth and discuss bandwidth and the frequency domain, which is another story completely.

Copyright © 2007 David L. Bytheway