WTF is a DAC? – ecoustics.com
Every smartphone, tablet, laptop, computer, TV, and streaming device utilizes a DAC (digital-to-analog converter) that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.
Inside of your smartphone and TV, the internal DAC does convert digital video signals to analog video signals; for those who thought that a DAC is only used for audio.
Back in the old days, everything was analog, then one day somebody said “what if we could manipulate audio with a PC?” and the world changed. The first thing that had to happen was, analog audio signals had to be converted to digital in order to get audio into the computer.
This task is handled by an analog-to-digital converter (ADC). The digital form could then be manipulated but in order for the person doing the work to be able to hear the changes, the digital signal had to be converted back to analog and sent to a headphone or speaker.
This second task is handled by a digital-to-analog-converter (DAC). Computer soundcards usually contain both an ADC and DAC in order to bring audio into the system as well as output audio to speakers or headphones.
Likewise, smartphones use ADCs to convert the caller’s voice to a digital signal which is then converted through the DAC into the analog signal that you hear through the phone’s speakers.
Analog → Digital → Analog
We can think of analog and digital as languages and the ADC and DAC converters as translators between the two languages. Analog signals allow for human understanding of the sound while digital signals allow for storage, transmission, and manipulation of the data inside the computer.
The two languages are very different though, analog is a continuous waveform while digital uses fixed increment samples.
When an analog source is converted to digital, the ADC takes a set number of samples per second and records the voltage of each sample. For example, the standard for Compact Disc Audio known as “Red Book” uses 44,100 samples per second and has 65,535 possible values for voltage (16-bits). This is commonly referred to as 16-bit/44.1kHz.
Math Alert: 216 – 1 = 65,535
Each time the ADC records a sample, it assigns a value for voltage between 0 (no signal) and 65,535 (highest voltage possible) with each step in-between representing an increase of 15μV over the previous step.
Tip: The term lossless audio often refers to digital music that is encoded/decoded at 16-bit/44.1kHz. The term lossless also refers to a compression algorithm that makes a perfect digital copy at a reduced file size. It does so in such a way that the original file can be reconstructed exactly as it was.
Increases in bit-depth (24-bits, 32-bits and beyond) allow for more steps with smaller voltage increases between each, while increases in sampling rate allow for more samples to be taken per second.
Analog proponents argue that because digital is sampled at fixed intervals and has fixed voltage steps, there is always a possibility that the highest peak or lowest low fell between two samples and was thus missed or wasn’t exactly a step above or below the previous and was thus adjusted to fit.
Digital enthusiasts argue that any difference in the digital version and the analog is well beyond the range of human hearing as sampling frequencies of 768,000 samples per second are now possible and bit-depths or 32 and 64 which allow for voltage steps in the nano-Volt or even pico-Volt ranges have basically nullified the analog argument. We’ll leave this topic for others to fight over.
Tip: Hi-Res Audio (High resolution audio) generally describes digital audio that is either encoded/decoded at bit depths greater than 16-bits or at sampling rates higher than 44,100 times a second (44.1kHz).
A future article will discuss this in detail.
The ADC takes an analog signal and converts it to a set of bits to be used digitally. How we manipulate that digital signal is a topic for another article (or several) but for now let’s look at getting the digital signal back out of the device.
A DAC takes a digital input (bits) and creates an analog output signal (voltage) but how it goes about it can be very different depending on the DAC in use.
R-2R Ladder DAC
The oldest and simplest (at least to understand) is the R-2R Ladder DAC which uses a series of resistors to control the flow of current. An R-2R DAC has an input per bit and each connects to a series of resistors that operate as switches to allow a designated amount of current to pass.
Each bit contributes a weighted amount to the combined output thus reproducing the original signal. As an example, our 16-bit sample from a compact disc would have 16 discrete inputs with each input accepting only a single bit from each sample. That input then passes through a resistor array and the output is combined with the signals produced by other bits to create a single output of the appropriate current.
R-2R DACs are often touted as being the best since in theory they reproduce exactly the original signal. The reality is unless every resistor is perfectly matched, the outcome isn’t exactly the original signal and matching the hundreds of resistors needed to build a 16-bit DAC let alone a 32-bit or 64-bit model is no easy task.
As a matter of fact, some manufacturers found it near impossible to get parts with tight enough tolerances to make consistently good R2R DACs and began to look at alternatives that were less time consuming and costly to implement.
As manufacturing tolerances have improved, so have R-2R DACs but even today the precision resistors are quite expensive to manufacture and still imperfect.
Denafrips and HoloAudio both manufacture excellent R-2R DACs that feature these types of configurations and parts quality but that also comes with a lofty price tag.
Binary-Weighted Resistor DAC
Another similar DAC is the binary-weighted resistor DAC. This can be thought of as kind of a star shaped version of the R-2R ladder where each input meets at a single point and is then fed through a single resistor that sums up the resistances. The more significant bits of the input will produce greater output current than the lesser bits (weighting).
This method uses fewer parts, but still suffers from some of the same issues as the R-2R design in that any variance in the resistors used will skew the output.
The most common DAC today is the Delta-Sigma DAC and if the R-2R DAC was easy to explain but near impossible to implement perfectly, the Delta-Sigma is the opposite, although a perfect implementation shouldn’t be confused with perfect signal reproduction.
First, we’ll need to break down the Delta-Sigma process into 3 parts; the modulator, the bitstream, and the low-pass filter. Our input signal is passed first to the modulator where it is translated into a bitstream and passed to the low-pass filter before exiting as analog output.
The modulator’s sole purpose is to produce a bitstream which can be thought of as translating our high-bit count low-frequency signal into a low-bit count much higher frequency signal.
Essentially, what happens is rather than encoding the signal itself, the modulator aims to encode the difference (Delta) between samples and then adds the output of a 1-bit DAC (Sigma) to the sample to help reduce error. The process is called Pulse Proportion modulation.
Once the modulator has produced the bitstream (our low-bit rate, high-frequency signal), it is fed to a low-pass filter that strips off all the upper-frequency noise introduced by the modulator and leaves us with just an analog output that mirrors the original input fairly closely.
I say fairly closely as higher order Delta-Sigma modulators will produce signals that are closer to the original with less artifacts and noise than a first order modulator can produce.
Going to a higher order modulator has its own problems though as using multiple integrators in a Delta-Sigma modulator will cause phase turn so modulators above the 2nd order use additional low pass filters or noise shapers instead of integrators to further improve the signal clarity without causing phase issues.
Fortunately, Delta-Sigma is usually implemented within a single chip so most of us mere mortals don’t have to understand all the inner workings to utilize the technology.
The Schiit Audio Modi 3E is an example of Delta-Sigma SAC.
PCM vs. DSD
This also helps us understand the difference in PCM (Pulse Code Modulated) files like FLAC or MP3 and Direct Stream Digital (DSD) Files. PCM files are low-frequency high-bit depth files of the type we’ve been discussing when using our Compact Disc references above. DSD files take a somewhat opposite approach using super high frequency low-bit depth files stored in Delta-Sigma encoding.
Because DSD files are stored as a bitstream, the Delta-Sigma modulator is not needed to decode them and they can be passed straight to the low-pass filter thus avoiding the possibility of introducing additional errors in the Delta-Sigma process.
Remember though, that a similar ADC process was used to produce the DSD file so not all sources of potential error are removed by using DSD instead of PCM encoding.
Also worth noting, is that most file types are PCM encoded, including WAV, FLAC, MP3, ALAC, and MQA and what differs is wrapper around that data. Some files like MQA may require additional processes to occur before being passed to the DAC itself for final processing of the PCM encoded signal and in many cases today, we see those operations taking place on additional circuits prior to the DAC itself.
So when you see an iFi Audio product that says it support MQA but uses a Burr-Brown DAC that only supports PCM encoded files, now you know how they are able to do it.
The XMOS chipset does the initial unpacking and cleanup and then passes PCM to the Burr-Brown for final decoding.
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