How DACs Work
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Let's start at the beginning. Digital music is an easily transported intermediate form between an analog original and an analog copy. An ideal system creates a copy at the end that is identical to the original. That has yet to happen, but over the last 20 years we are getting closer and closer. The two critical components of this process are the Analog-to-Digital Converter (ADC) at the studio and the Digital-to-Analog Converter (DAC) in your listening room. Let's start with a look at a diagram of the ADC process.
The Studio Side - ADC
ADCs work by repeatedly measuring the amplitude (volume) of an incoming electrical pressure sound wave (an electrical voltage), and outputting these measurements as a long list of binary bytes. In this way, a mathematical "picture" of the shape of the wave is created. Do not worry about bits and bytes. For our purposes, these are simply numbers, and the "bit depth" is just an indication of the accuracy of the number, kind of like 6.24 is more accurate than 6.2.
So what is this waveform we are recording and trying to recreate? The single cycle wave form in our example is the analog or copied result of all the frequencies from all the instruments that occurred in the air in the recording studio and naturally combined in the air and came piling into the single point microphone diaphragm in a certain order yielding one analog sound naturally produced as our eardrum would hear it. This uncountably large number of frequencies from all the instruments and their harmonics and the resulting room reflections (sound stage cues), naturally combined in the air and the naturally "coded" complex waveform that is the original truth of the music at that moment is what we are trying to copy accurately.
Join the dot pictures
Remember join-the-dot pictures? To produce a good image you must have sufficient dots to capture the detail of the shape AND the dots must be positioned accurately.
Quality in a join-the-dots picture depends on ...
Number of Dots = Sample Rate
The number of dots is the sample rate, or the number of samples taken per second. The more samples taken, the easier it is to recreate the original. But these samples need to be made accurately. The jitter of the clock is the variation in time of each cycle. Shifting the time of the sample records the wrong level. Therefore the accuracy of the digital clock, which governs when samples occur, is paramount. If the clock is not accurate, jitter will occur and the audio quality will suffer.
Accurate Measurement of Amplitude
Measuring amplitude is like measuring with an elastic ruler. If the smallest divisions on the ruler are 1 cm than each measurement must be rounded to the nearest cm. The accuracy of the ruler is also important. Any stretch of the ruler will give a false reading. So why not use much smaller divisions? For a CD, these are defined by the Redbook standards and cannot be changed.
What's Lost is Lost
At this point we have lost two big things. We have lost the exact analog level of each sample. Because of the limited resolution of each bit step, we have lost the exact amplitude of each point. The amount a sample measurement has been rounded up or down is known as the quantization error and produces quantization distortion. At loud signal levels quantization errors manifests themselves as noise (similar to analog noise), but at low signal levels they can manifest themselves as unwanted audible distortion. The other thing that is lost is the shape of the curve between each point. It is gone forever, again a Redbook limitation. But as you will see, we work very hard in the DAC to try to get as much of this missing information back.
Now its Digital and Portable.
The sample rate was defined and the ADC has done its job and locked into the data all its error, but the data is now just a large file of numbers, and these can be changed into innumerable formats and transported around the world and is finally presented to your listening room, to your DAC.
The Playback Side - DAC
A DAC works by reading the digital data in a file and attempting to recreate a copy of the original analog signal recorded. We face many of the same problems faced in the recording process. Basically a DAC as three jobs:
Digital Filter - Fills in the Blanks
The digital filter is the computer algorithm that looks at the digital audio in the past, and the digital audio in the future and tries to figure out what was going on with the music, and tries to shape the final analog output to match as closely as possible that original waveform, now missing for ever. At this point you may have some questions:
Sample Timing - The Clock
We talk a lot about clocks. We are not talking about devices to tell us what time it is, but a device that outputs a pulse or cycle at a fixed interval or time. If you counted them up you could tell time, but we use them to create an absolute reference which is the same at the recording and playback ends.
Normally DACs do not contain clocks. The clock is associated with the device that reads the digital media. So CD transports have clocks, DVD players have clocks, Computers have clocks. The clock is sent to the DAC along with the digital data. This method allowed DACs to be very low cost but this approach severely handicaps the DACs performance. Unfortunately today all but a handful of high-end DACs still follow this method.
Sample Amplitude - The DAC Accuracy
This critical parameter is equally important. Just as we can hear tiny variations in the clock, we can hear errors in amplitude (moment to moment loudness). The accuracy of a DAC depends on the quality of the DAC components as well as the DAC architecture used. Almost all DACs produced today are Delta Sigma because of the amazing average accuracy obtained over many samples. MSB uses a Ladder DAC, able to achieve similar accuracies, but in every sample and at a greater cost.
Types of DACs and How they Work
A DAC is a circuit that converts digital measures of audio amplitude in discrete steps into a continuous analog electrical equivalent of the sound to be reproduced. The amplitude is a digital number (like a 16 bit word) and the steps occur based on the sampling rate (like 44,100 times per second). This process is very much like an endless conveyer belt with empty one gallon jugs on it, moving by a filling station. The size of the jug is fixed, the rate they pass by is determined by the sampling rate. The goal of the DAC is to fill each jug to exactly the right level specified by the music. There are three techniques used to accomplish this; Delta Sigma, Ladder, and the MSB Sign Magnitude Ladder.
Delta Sigma DACs (Single Bit)
Each sample or jug is filled to the right level with many measuring cups, poured to reach the target level.
A "one bit" measuring cup is either full or empty. With 64 times oversampling, the cup is only 1/64th the volume of the jug. This rather crude cup does not come close to being accurate enough. The cup would need to be 1/16,777,216th the volume of the jug to be accurate.
Line speed is like Sampling Rate (48,000 per second)
By keeping a running tally of the error and by going a little over and a little under in many many samples, a very accurate average is reached, but only with an aggressive filter applied to the output.
A ladder DAC is different in that instead of a single measuring cup (or bit), a whole array of cups are available, from very small to very large.
Any combination of cups can be used to fill each jug to exactly the right level.
No filtering is required but the accuracy is defined by the cumulative error of all the cups used.
MSB Sign Magnitude Ladder DAC
The MSB Sign Magnitude Ladder DAC is like a Ladder DAC but refined in two ways.
Because the jars are typically 1/2 full when finished, we start with very accurately 1/2 filled containers instead of empty ones. From there, we again use the wide range of measuring cups to either add or take away from each jar.
Again each jar is filled exactly so no filtering is needed, but because we only had to add or subtract a little bit our accuracy is higher. Because our hearing is most sensitive to low level sound (sound near the 1/2 full zero crossing) our DAC is most accurate near 1/2 full where we use the smallest and most accurate measuring cups.
What about Upsampling?
Synchronous Upsampling like MSB does just means adding more jars between the existing jars and moving them faster down the line. By looking at many jars before and after the new empty one, we calculate how full to make it. The result is smaller steps as shown in the waveform This is very significant when used with a Delta Sigma DAC but less so with a Ladder DAC.
The Final Word
The original way Sony and Philips converted digital was a ladder DAC, just a handful of resistors that when connected looked like a ladder (hence the name). It was very difficult for Philips to build because it was hard to get the resistors accurate enough, so the original 1541 DAC was inaccurate. Yet it sounded better than the next generation method, the Delta Sigma DAC. (BTW, the 1541 Crown DAC is still sought after today by boutique companies and going for up to $200 each compared to their original cost of $12. It is nice as MSB has a drawer full of them!) The ladder DAC is technically, attractive because it is like a passive process (zero processing of any kind, yes I know the conversion itself is a process), meaning there are no active sampling and averaging processing, only simple resistors that have no speed limit. The MSB ladder is a refinement of the original design. The resistor network is faster - more than 5 MHz. It has a noise floor of 160db - keep in mind that each 3 db is twice as loud. And it is far more accurate with the highest precision resistors made in the world today.
So what is the MSB approach?
Unlike virtually all other digital manufacturers, MSB is a truly unique company designing and building all processes and hardware in-house so we are never limited by components, hardware, chipsets or the software processes of DAC chip manufacturers.
We invite you to listen to MSB and compare the sound to the best you can find at any price. Please contact us for an in-home demo. You will never think about digital playback the same way again.