dCS Ring DAC - A Technical Explanation
Apr 27, 2021 at 8:44 AM Post #46 of 111

mwilson

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I just love these declarations of dCS being impossible to sound good (I think I read that on the Chord thread), of Chord using delta-sigma which others do better, of other DACs, of components that just should have used this or that technology instead of the one actually implemented, that the direction is just crap.

I have a neighbor who's an elite sports analyst, and is 100% spot-on come Monday mornings on what the teams should have done on the field the evening prior. I pity those teams that didn't hire him as head coach; they'd have won every single game, every season if only he were there to provide sage advice. Talk about missed opportunities! So my question is, where were you guys and gals when those companies posted "for hire" ads? Surely your knowledge, which is clearly superior to that of their actual engineers, would have saved all of us the agony of having to listen to subpar equipment.
 
Apr 27, 2021 at 9:02 AM Post #47 of 111

mammal

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I pity those teams that didn't hire him as head coach; they'd have won every single game, every season if only he were there to provide sage advice.
Where I am from, we once won a sports event and a journalist asked our coach how did we do it. Guess what was his elaborate strategy - "score at least one more point than your opponent", haha.
 
Apr 27, 2021 at 11:12 AM Post #48 of 111

sajunky

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Where I am from, we once won a sports event and a journalist asked our coach how did we do it. Guess what was his elaborate strategy - "score at least one more point than your opponent", haha.
What he says doesn't matter. It could be a good luck or a business manipulation behind the scene. The later one happens very frequent and only in very few cases come to a light.
 
Apr 27, 2021 at 2:52 PM Post #49 of 111

Vitaly2017

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Waittttt a minute!

If we need daps or dac/amps to produce double the frequencie range ( 40 000 ) in order for us too hear the real dynamic range at 20 000.

So if my device does 20 to 40 000 but my headphones only does 5 to 23 000 am I limited?

I kinda though no cause the output of the adc becomes 20 000 to get back to the human audible range so the headphones are fine then after all????


"
Sample Rates

If the human ear can only hear up to 20,000Hz, is there any reason to use sample rates higher than 20,000Hz? As it happens, yes. One of the most important aspects of digital audio is the Nyquist Theorem, which specifies that the digital audio samples need to be taken at a minimum of twice the highest frequency one is trying to record in the original analogue audio. As the upper limit of human hearing is widely accepted as 20,000Hz, digital audio needs to be sampled at at least 40,000Hz to be able to reproduce the full range of human hearing. For reasons that will be discussed later (related to the digital filtering inside a Digital to Analogue Converter), full range recordings are sampled slightly higher than this, with CD audio being sampled at 44,100Hz. The rate at which these samples is taken is referred to as the sample rate, defining how many samples are used per second. "
 
Apr 28, 2021 at 2:33 AM Post #50 of 111

technobear

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Waittttt a minute!

If we need daps or dac/amps to produce double the frequencie range ( 40 000 ) in order for us too hear the real dynamic range at 20 000.

So if my device does 20 to 40 000 but my headphones only does 5 to 23 000 am I limited?

I kinda though no cause the output of the adc becomes 20 000 to get back to the human audible range so the headphones are fine then after all????


"
Sample Rates

If the human ear can only hear up to 20,000Hz, is there any reason to use sample rates higher than 20,000Hz? As it happens, yes. One of the most important aspects of digital audio is the Nyquist Theorem, which specifies that the digital audio samples need to be taken at a minimum of twice the highest frequency one is trying to record in the original analogue audio. As the upper limit of human hearing is widely accepted as 20,000Hz, digital audio needs to be sampled at at least 40,000Hz to be able to reproduce the full range of human hearing. For reasons that will be discussed later (related to the digital filtering inside a Digital to Analogue Converter), full range recordings are sampled slightly higher than this, with CD audio being sampled at 44,100Hz. The rate at which these samples is taken is referred to as the sample rate, defining how many samples are used per second. "

You are being confused by lazy use of the unit 'Hertz' or 'Hz', a measure of frequency.

Let's state it differently:

As the upper limit of human hearing is widely accepted as 20,000Hz, digital audio needs to be sampled at at least 40,000 samples per second to be able to reproduce the full range of human hearing. For reasons that will be discussed later (related to the digital filtering inside a Digital to Analogue Converter), full range recordings are sampled slightly higher than this, with CD audio being sampled at 44,100 samples per second. The rate at which these samples is taken is referred to as the sample rate, defining how many samples are used per second.
 
Apr 28, 2021 at 2:00 PM Post #51 of 111

dCS James

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Part 2 – Basics of Pulse Density Modulation (DSD)​

As opposed to PCM audio where the ADC sampling process takes the absolute value of the analogue voltage coming in to it at any given point, Pulse Density Modulation (PDM) instead works based on the time between two samples dictating whether the wave is increasing or decreasing in amplitude. If the samples are closer together, the wave is increasing in amplitude. If they are further apart, the amplitude of the waveform is decreasing. The absolute value of the waveform is not known per se when looking at an individual sample (as it would be with PCM), but put together the samples produce a good representation of the original waveform.

The caveat with this method is that the ‘dynamic resolution’ (the amount of information about the amplitude which is stored in any one sample of the audio) is incredibly low, being 1 bit, so the samples need to be taken at a much higher rate than with PCM audio. Where PCM typically samples at 44,100 samples a second, DSD works at a minimum of 64 times this rate, around 2,800,000 samples per second.

This process of encoding digital audio creates a lot more noise. This is due to both the low bit depth (which at 1-bit creates more quantisation noise) and the higher sample rate (essentially turning things on and off at a much higher rate creates noise). In order to make the format usable, the data is noise-shaped to clear the quantisation noise out of the audio band into the ultrasonic region (above 20kHz), where it cannot be heard.

1619622946424.png


The result is near 24-bit performance in the audio band (0 – 20kHz) and a signal bandwidth that extends beyond 100kHz. The price for the 1-bit approach is a very large amount of noise in the ultrasonic region (20kHz – 1.4MHz), but this is not normally heard as a noticeable background noise. This method of digitally encoding music is what is used in the format Digital Stream Direct (DSD). This format of 1-bit conversion is the basis of Bitstream Sigma-Delta Digital to Analogue Converters (which will be covered in a later post).

There are further developments into DSD audio, whereby higher and higher rates are used. The original rate, referred to as DSD/64 or Single Speed DSD, runs at 64x the rate of CD audio. DSD/128 or Double Speed DSD runs at 128x CD audio rates, and so on for DSD/256 and DSD/512.

DSD files, even at the standard DSD/64 rate are large. The data rate is 5644.8 kbps for 2-channel stereo.

This post is on the shorter side, but with the basic formats covered we can get on to the fun stuff. The next post will be on the basics of digital to analogue conversion, starting with Ladder DACs.

Part 3: Introduction to D/A Conversion
 
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Apr 30, 2021 at 11:05 AM Post #53 of 111

SoundAndMotion

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Hi folks,

James here from dCS.
Hi James,

I appreciate what you're trying to do, and how tough it can be. You are trying to bring some novices up to speed, so you can present your Ring DAC later, but you also have people who already understand the background material really well. Some in the latter group are just looking for something to criticize, while others, like me, are looking at your pedagogic techniques to see if anything is worth stealing :beyersmile::beerchug:

I've presented my work to colleagues, high-schoolers, 4th graders and kindergartners (different presentations, of course). My suggestion, which you can obviously ignore, is to choose a target audience and stick to it. Parts 1 & 2 seem targeted to different groups.
Just my $0.02 and worth every penny..
 
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May 4, 2021 at 8:33 PM Post #54 of 111

manueljenkin

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Part 2 – Basics of Pulse Density Modulation (DSD)​

As opposed to PCM audio where the ADC sampling process takes the absolute value of the analogue voltage coming in to it at any given point, Pulse Density Modulation (PDM) instead works based on the time between two samples dictating whether the wave is increasing or decreasing in amplitude. If the samples are closer together, the wave is increasing in amplitude. If they are further apart, the amplitude of the waveform is decreasing. The absolute value of the waveform is not known per se when looking at an individual sample (as it would be with PCM), but put together the samples produce a good representation of the original waveform.

The caveat with this method is that the ‘dynamic resolution’ (the amount of information about the amplitude which is stored in any one sample of the audio) is incredibly low, being 1 bit, so the samples need to be taken at a much higher rate than with PCM audio. Where PCM typically samples at 44,100 samples a second, DSD works at a minimum of 64 times this rate, around 2,800,000 samples per second.

This process of encoding digital audio creates a lot more noise. This is due to both the low bit depth (which at 1-bit creates more quantisation noise) and the higher sample rate (essentially turning things on and off at a much higher rate creates noise). In order to make the format usable, the data is noise-shaped to clear the quantisation noise out of the audio band into the ultrasonic region (above 20kHz), where it cannot be heard.



The result is near 24-bit performance in the audio band (0 – 20kHz) and a signal bandwidth that extends beyond 100kHz. The price for the 1-bit approach is a very large amount of noise in the ultrasonic region (20kHz – 1.4MHz), but this is not normally heard as a noticeable background noise. This method of digitally encoding music is what is used in the format Digital Stream Direct (DSD). This format of 1-bit conversion is the basis of Bitstream Sigma-Delta Digital to Analogue Converters (which will be covered in a later post).

There are further developments into DSD audio, whereby higher and higher rates are used. The original rate, referred to as DSD/64 or Single Speed DSD, runs at 64x the rate of CD audio. DSD/128 or Double Speed DSD runs at 128x CD audio rates, and so on for DSD/256 and DSD/512.

DSD files, even at the standard DSD/64 rate are large. The data rate is 5644.8 kbps for 2-channel stereo.

This post is on the shorter side, but with the basic formats covered we can get on to the fun stuff. The next post will be on the basics of digital to analogue conversion, starting with Ladder DACs.
A quick question. Does the DCS have choice of an audio optimized pre-ring free apodizing linear interpolation filter, similar to ifi GTO? One step ahead, considering it does MQA full decode, any choices of a spline based interpolation filters?

The stereophile measurements I saw only showed sinc and a min phase filter so far. Also interested to know the digital volume control implementation's precision, if digital, that is.
 
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May 7, 2021 at 8:23 AM Post #55 of 111

dCS James

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A quick question. Does the DCS have choice of an audio optimized pre-ring free apodizing linear interpolation filter, similar to ifi GTO? One step ahead, considering it does MQA full decode, any choices of a spline based interpolation filters?

The stereophile measurements I saw only showed sinc and a min phase filter so far. Also interested to know the digital volume control implementation's precision, if digital, that is.
All of the filters offered within dCS products are audio-optimised. We offer different filters which are each individually optimised for all of the sample rates we support. At 44.1k, we do offer a minimum phase filter that has no pre-ringing.

Each filter is designed using a mixture of techniques to offer various trade-offs (pre-and post-ringing, image rejection, phase linearity etc.). In total, there are 46 sets of filter coefficients just for PCM.

As for linear interpolation, this has a very strict meaning within DSP – a linear interpolator is usually unsuitable for 44.1k material, as it offers poor stop-band performance and a poor audible band frequency response (looks droopy on a frequency spectrum plot).

Our volume control is indeed digital, yes. However, I would say that the whole implementation of the volume control is much more important than just the precision of it – crucially though, it has no measurable degradation of the signal across its entire operating range.
 
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May 7, 2021 at 8:41 AM Post #56 of 111

dCS James

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Part 3 – Introduction to D/A Conversion​

DACs – Digital to Analogue Converters – are a crucial part of almost all modern headphone setups, in one form or another. They play a vital role in helping to translate the original musical performance of an artist to a listening experience for the end user. The fundamental concept of a DAC is to translate digital audio – whether it is streamed from Spotify or Tidal, stored on a DAP or played from a NAS – into an analogue voltage which is used to drive a transducer like headphones.

When making this digital to analogue conversion, there are two factors to consider: can the converter perfectly reproduce the original amplitude of the wave when it was recorded (in other words, can it output the right voltage), and can it do it at exactly the right time? Whether the converter can reproduce the correct voltage comes down to the DAC circuitry itself, and whether it converts the sample at the right time comes down to the clocking of the system. I will go through the DAC circuitry first, and clocking definitely warrants its own topic which we plan to cover next.

Digital audio is stored in binary format (effectively a series of 1s and 0s) as a series of ‘samples’. As we discussed earlier, the number of consecutive binary digits that are used to represent the original sound wave is called the bit depth. 16-bit audio, for example, has 16 consecutive binary digits, all either 1 or 0. A DAC needs to translate this binary number to an analogue voltage, as that voltage is what drives headphones to produce sound. It does so using a series of current sources – electronic components that each generate an amount of analogue voltage.

One of the most common approaches to D/A conversion is to have one current source always working for one of the digital audio bits exclusively. For example, one current source will always be following what the first bit in the digital audio signal is doing. Another current source will always be following what the second bit in the digital audio signal is doing, and so on for as many current sources as are needed. As the current sources go on, the amount of energy they must generate gets smaller and smaller (it halves for each consecutive current source).

When looking at a diagram of how these components would be laid out, it looks an awful lot like a ladder, hence the informal name these types of DACs have been given – Ladder DACs. To ensure that the voltage generated by each current source is incrementally smaller the further down the chain they are, resistors need to be used between current sources. The values and layout of these resistors gives name to the two prominent types of Ladder DACs – R-2R DACs and Binary Weighted DACs.

One very important distinction to make early on – a dCS DAC (the Ring DAC) is not a Ladder DAC. This difference will be explained later.

R2R DACs

R-2R DACs (a subset of Ladder DAC) use one of two resistor values to control the amount of voltage generated by each current source. Resistors of value R are used between each current source section, and resistors of value 2R are used on each current source. If a particular bit in the audio signal goes high (a 1 instead of a 0), the corresponding switch is enabled and that current source output goes high. The outputs of all current sources are then fed to a summing bus, which provides the overall output of the DAC.

1620390971475.png


Binary Weighted DACs

In Binary Weighted Ladder DACs, resisters of decreasing values are used to create increasingly small steps in power generated by current sources. If the first resistor has a value of R, the next would be 2R, then 4R, then 8R, 16R, and so on for as many steps as required. This hierarchy of resistor values is what gives this approach the Binary Weighted name.

1620391003411.png


The main drawback with both the R-2R and Binary Weighted DAC approaches comes from the fact that resistors (like all electronic components) have an element of error in their values. For example, a gold tolerance resistor guarantees the resistance of the component will be within 5% of its stated value. This means that for the resistors used in a Ladder DAC, the current generated by that section of the DAC could be either lower or higher than needed. The key point here is that a Ladder DAC uses the same current source for a given bit in the audio signal every time, meaning the error is exactly the same every time the bit goes high. Here, the errors in the component values are correlated to the audio signal. This results in an audible linear distortion of the signal, adding in unwanted harmonic components.

The issue with this is the fact that the larger current sources (correlating to the more significant bits in the audio signal) have the same margin of error as the smaller ones. In the case of a 24-bit ladder DAC, a 1% error in the most significant bit (MSB, or the largest current source) would be larger than the entire 7th bit, and 104dB louder than the 24th bit. The MSB needs to be accurate to 0.000006% to allow for 24-bit resolution.

One further issue Ladder DACs suffer from is Zero Crossing Point Distortion. Given that each current source has a potential correlated error associated with it, what happens when say in a 16-bit DAC we go from reproducing an amplitude of 32767 to 32768? The DAC changes from having the first (most significant) bit low and the following 15 bits high, to having the first bit high and the following 15-bits low. This is called the Zero Crossing point. The size of the errors associated with each current source / bit here – specifically the fact that the sum of the 15 errors with 32767 and the one error with 32768 – are both very large compared to the least significant bit (LSB). This means that the change from 32767 to 32768 in the DAC can be much bigger than one LSB. The result of this is linear distortion, which is extremely undesirable.

The solution to the issues posed by the linear distortion of a Ladder DAC is to remove the link between the original signal and the physical resistor value errors associated with specific sample values. How exactly this can be achieved will be discussed in the next post, where I will explore the architecture of the dCS Ring DAC.

Part 4: The Ring DAC
 
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May 7, 2021 at 9:04 AM Post #57 of 111

manueljenkin

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All of the filters offered within dCS products are audio-optimised. We offer different filters which are each individually optimised for all of the sample rates we support. At 44.1k, we do offer a minimum phase filter that has no pre-ringing.

Each filter is designed using a mixture of techniques to offer various trade-offs (pre-and post-ringing, image rejection, phase linearity etc.). In total, there are 46 sets of filter coefficients just for PCM.

As for linear interpolation, this has a very strict meaning within DSP – a linear interpolator is usually unsuitable for 44.1k material, as it offers poor stop-band performance and a poor audible band frequency response (looks droopy on a frequency spectrum plot).

Our volume control is indeed digital, yes. However, I would say that the whole implementation of the volume control is much more important than just the precision of it – crucially though, it has no measurable degradation of the signal across its entire operating range.
Thank you very much. I'm sorry I used the wrong name. I was meaning linear-time invariant filters, not linear interpolation filters. There can be adaptive filters that are non LTI.
 
May 7, 2021 at 10:31 AM Post #58 of 111

sajunky

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The issue with this is the fact that the larger current sources (correlating to the more significant bits in the audio signal) have the same margin of error as the smaller ones. In the case of a 24-bit ladder DAC, a 1% error in the most significant bit (MSB, or the largest current source) would be larger than the entire 7th bit, and 104dB louder than the 24th bit. The MSB needs to be accurate to 0.000006% to allow for 24-bit resolution.

One further issue Ladder DACs suffer from is Zero Crossing Point Distortion. Given that each current source has a potential correlated error associated with it, what happens when say in a 16-bit DAC we go from reproducing an amplitude of 32767 to 32768? The DAC changes from having the first (most significant) bit low and the following 15 bits high, to having the first bit high and the following 15-bits low. This is called the Zero Crossing point. The size of the errors associated with each current source / bit here – specifically the fact that the sum of the 15 errors with 32767 and the one error with 32768 – are both very large compared to the least significant bit (LSB). This means that the change from 32767 to 32768 in the DAC can be much bigger than one LSB. The result of this is linear distortion, which is extremely undesirable.
The first things, a numbers are taken out of reality. Do you want 24-bits, really? A typical background noise (uncorelated) :) of the standard room is between 35dB and 40dB. Typically users set a volume to such level that the lowest details can be heard comfortably. Lets say it is an average 37dB, then add to it 104dB, you get 141dB, enough to blow your hearing in a second. Someone talked about it already, but you don't listen.

16 bits CD quality translate to 96dB, add to it a room noise, it translate to 133dB. All modern recordings use dithering, it further extend that range.

Secondly there is a loophole in your knowledge about R2R conversion or your tutorial is completely biased, basically not worth reading. You didn't hear about sign-magnitude encoding which is in a common use with R2R ladders (for a number of years) and do not suffer from zero crossing distortions, didn't you?
 
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