By John Siau
April 10, 2014
It's on your iPhone, your Android and your computer. It's even on those CDs you put on a shelf somewhere. Audio that goes to 11.
If 10 is the clip point of digital audio, you actually have digital recordings that go to 11. Nigel Tufnel of Spinal Tap was on to something in 1984 when he explained that his Marshal amps "go to 11". If you have never seen "This is Spinal Tap" I suggest watching this short clip before reading on. Nigel's brilliant discussion sets the stage for this application note.
But, it's not just Spinal Tap recordings that "go to 11"; every recording you own may also "go to 11"! How is this possible? If 10 is the clip point of digital audio, how can there possibly be an 11? And, if we use Nigel's logic; if 10 is good, why isn't 11 better?
As strange as it sounds, audio that "goes to 11" is hidden in between digital samples. This is especially true when the recorded samples just reach "10". Digital systems take a snapshot of the audio signal thousands of times per second. These snapshots or "samples" represent the audio signal at an instant in time. In between successive samples, the audio is always changing. Digital sampling systems often miss short audio peaks which occur between these samples. These peaks often "go to 11", but are entirely missed by the sampling system.
Nevertheless, the short peaks between samples are not lost! These peaks that "go to 11" can be reconstructed from the surrounding digital samples. The DAC (digital to analog converter) in an audio system is equipped with digital reconstruction filters that can recover these inter-sample peaks. These filters work wonderfully until the digital processing overflows. Peaks that hit "9" or "10" will not cause an overflow, but peaks that "go to 11" may cause an overflow.
If you attempt to divide 1 by 0 on your calculator, the digital processing will overload and an error message will be displayed. Likewise, if the digital processing in your audio system overloads, bad things happen. Overflows that occur in digital reconstruction filters can produce a burst of distortion that persists for many samples. This distortion is non-musical and foreign to the natural sounds around us. These overloads often add an unnatural harshness to the digital playback system. But this does not mean that digital audio is fundamentally flawed. Some DACs can reproduce signals that "go to 11" without clipping. Benchmark's DAC2 is one such device.
Benchmark scanned over 5000 CD tracks to determine the severity of the inter-sample peaks in commercially available music. We discovered that most tracks contained peaks that were 1 or 2 dB above a full-scale "10". A peak that is 1 dB above full scale is 1.1 times as high as a full scale sample. A +1 dB inter-sample over is audio that goes to exactly 11! Nigel was right!
But back to our survey of CD tracks: we discovered some tracks had peaks that were 3.1 dB higher than full scale. This is 1.4 times as high as a full scale "10", and is audio that goes to 14 on Nigel's scale. You may own some recordings that go to 14, and you most certainly own many recordings that "go to 11".
Another twist to this situation is that MP3 compression seems to increase the occurrence of peaks that exceed full scale. This can make MP3 files sound worse than they should.
Once these problems were identified, Benchmark was able to implement a solution. The DAC2 reduces the signal level of the digital signal by 3.5 dB before it enters the digital interpolation and reconstruction filters in the DAC. This gain reduction is made up by increasing the analog gain after the D/A converter chip. The result is a DAC that not only "goes to 11", it is a DAC that "goes to 15". A peak of +3.5 dB is 1.5 times full scale (or "15" on Nigel's scale).
The Benchmark DAC2 goes to 15! Nigel should be impressed.
Myth - "Damping Factor Isn't Much of a Factor"
Myth - "A Damping Factor of 10 is High Enough"
Myth - "All Amplifiers Have a High-Enough Damping Factor"
These myths seem to trace back to a well-know paper written by Dick Pierce. His analysis shows that a damping factor of 10 is virtually indistinguishable from a damping factor of 10,000 when it comes to damping the motion of a loudspeaker cone. This analysis has been examined and repeated in many more recent articles, such as a well-written post on Audiofrog.com by Andy Wehmeyer. Articles such as these are often cited as evidence that amplifier damping factor doesn't matter. The mathematical analyses are correct, but the conclusions are incomplete and misleading!
How fast things can change!
It is March 23, 2020 and we are currently battling the worldwide COVID-19 pandemic.
This application note will be a departure from normal. I will make a few observations about the current situation and then look at the nuts and bolts of how we reconstructed our operations in less than 48 hours. Benchmark is 100% operational, but nothing looks the same as it did last week.
- John Siau
As an engineer I like to use "rules of thumb" to make quick estimates that help to explain the physical world around me.
These rules of thumb are easy-to-remember approximations that eliminate the need for complicated and needlessly precise calculations.
If you feel discombobulated by the complexities of high school physics, there is hope! I encourage you to step back and take a fresh approach.
If you learn a few simple rules of thumb, you can unravel mysteries of the physical world, amaze your friends, and yourself.
In this paper I will present 15 simple rules that I find useful when working with music and audio.
- John Siau