How DACs Work

How DACs Work

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 (Horizontal X axis) which has to do with time.
  • Accuracy of the positioning of the dots (Vertical Y axis) which has to do with amplitude or loudness at that instant in time.

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.

  1. Bit Depth (the resolution of the measurement scale). Bit depth in images determines the number of possible colors a pixel can be. In audio it is the scale of the ruler measured in number of bits. A 24 bit recording has a finer scale than a 16 bit recording.
  2. Measurement Accuracy (how accurately the amplitude is measured). Where the bit depth determines the resolution or scale used to measure, accuracy is like the precision or stretch of the ruler. This is generally a hardware function, like the precision of a resistor, not a timing issue.

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.

  • Bit Perfect If the integrity of the file has been maintained, the exact same numerical values that were generated in the ADC are presented to your DAC. If it is, the data is said to be Bit-Perfect.
  • Sample Rate Conversion Unfortunately many times a computer or product which works with digital music from more than one source, finds it much easier to process, if all music is converted into the same sample frequency and same bit depth. This all too common process double the original ADC errors, by resampling the data a second time. Computers normally always output audio at the sample rate and frequency the user specifies, regardless of its original sample rate.

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:

  • Sample Amplitude The DAC creates an analog voltage equivalent to the numeric value read from the file. A DACs ability to do this depends on the type of DAC it is and its accuracy. More about this later.
  • Sample Timing The DAC needs to create this analog voltage not only at the right level, but at the right time. The accuracy of the clock and the amount of clock jitter, used to create these voltage levels is vitally important.
  • Fill In The Blanks The basic DAC creates an analog voltage equivalent to the numeric value read from the file. But we know that there is data missing between each sample, and that the original level may have been a little more or less than the level recorded (quantization error). This is where the science ends and the art begins as we try to guess what the errors were and what is missing between the blanks.

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:

  • How do you look at the future music data? The only way to see the future, is to delay the output. So our digital filter is actually way ahead of the output, and why DACs create audio delay.
  • If the original is missing, how do you know what kind of filtering is right? Even though the original is missing, our sensitive ears and memory know what the human voice and various instruments sounds like. We listen to each new algorithm we write and ask ourselves if the result is more life-like or not. This is the art of the process. We see, knowing the nature of music, if we can fill in the blanks perfectly. This method would not work for random data, but sound generating instruments follow natural rules (because the strings on a guitar have a certain weight and tension and therefore must have a certain resonance, and the overtones that give that guitar it's character all follow the natural rules ).

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.

  • Our Solution - Reclocking - The MSB approach to this problem is to accumulate data from the source in a memory, and then read it from the memory using a super-accurate low-jitter clock, located right in the DAC. This feature is included in all MSB DACs.
  • Even Better - PRO I2S with Master Clock Output - Although reclocking is fantastic, we still have data coming in from an outside source at a different frequency from our internal clock, being clocked by a transport or computer. Having these two slightly different clocks running in the same box is a cause of noise. When we feed our DAC clock back to the source, and synchronize it with the DAC, we eliminate this source of noise and get even better timing accuracy.

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.

Ladder DAC


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?

  • Start with native resolution. Reading the bits natively has been proven by ear to always be best (the Data CD)
  • Digital Process at high resolution We process that data with our own digital filter, at 80 bit resolution with code written in-house to optimize the incredible capability of the MSB DAC modules.
  • Reclock with an accurate low jitter clock. We reclock that data with the lowest jitter in the industry.
  • Convert to analog with a sign magnitude ladder DAC. MSB offers three levels of DAC precision, and the output of the DAC modules is very robust and has more power than is necessary to drive an amplifier so we can offer a very neutral volume control internally by simply using resistors to attenuate the output voltage.

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.