Explanation about R2R DAC

[AlexMa]

At the current technological level of development, it is impossible to make an accurate R2R matrix with a bit depth of more than 14 bits. The developers' talk about special algorithms is a slyness, when applied to 16-bit matrices, and an outright lie for 24-bit R2R matrices. For a 16-bit matrix, the accuracy of the most significant bit should be 1/2^16/100 * 100 = 0.0000152588%, resistors with such accuracy are not produced, even 0.001% is already very steep and expensive.

 

[jbarrentine]

I did read a blurb about this while looking extensively at the Fiio R2R. Math is essentially alien to me, but someone else pointed out :
"Their own specifications, on the website, say THD+N about 0.025%. For perspective that's about -66dB. That's less than 11 effective bits of precision."

 

[AlexMa]

I did read a blurb about this while looking extensively at the Fiio R2R. Math is essentially alien to me, but someone else pointed out :
"Their own specifications, on the website, say THD+N about 0.025%. For perspective that's about -66dB. That's less than 11 effective bits of precision."

Fiio's website says they use 0.1% tolerance resistors: https://www.fiio.com/k11r2r
That's a surprising admission, but an honest one. The actual conversion accuracy is very low.

R2R DACs are a clear demonstration of the futility of some audio components. These include audiophile routers, external clocks, overly thick and expensive power cables, and many other unnecessary and sometimes harmful things.

 

[VNandor]

I did read a blurb about this while looking extensively at the Fiio R2R. Math is essentially alien to me, but someone else pointed out :
"Their own specifications, on the website, say THD+N about 0.025%. For perspective that's about -66dB. That's less than 11 effective bits of precision."

The conversion between THD+N in % and THD+N in dB is easy. It's 20*log(THDN%/100) so 20*log(0.025/100) which is around -72dB, not -66dB.

The conversion between dB and effective bits is also not hard. It's dB/(20*log2) so 72/(20*log2) which is around 12 bits.

 

[axle_69]

At the current technological level of development, it is impossible to make an accurate R2R matrix with a bit depth of more than 14 bits. The developers' talk about special algorithms is a slyness, when applied to 16-bit matrices, and an outright lie for 24-bit R2R matrices. For a 16-bit matrix, the accuracy of the most significant bit should be 1/2^16/100 * 100 = 0.0000152588%, resistors with such accuracy are not produced, even 0.001% is already very steep and expensive.

I think some R2R DACs measure up to 20-21 bits of linearity. Voltage steps between numbers are not the same due to the limited precision of the resistors but although all resistors do not have the same resistance the resistance is known which means you can still get close to the correct voltage if you change the original number, I'm guessing there is some mapping table and use of different ladders.

 

[AlexMa]

I think some R2R DACs measure up to 20-21 bits of linearity. Voltage steps between numbers are not the same due to the limited precision of the resistors but although all resistors do not have the same resistance the resistance is known which means you can still get close to the correct voltage if you change the original number, I'm guessing there is some mapping table and use of different ladders.

Let's imagine that we are in an absolutely ideal, precise world. Then, if the most significant bit of the R2R ladder controls a voltage of exactly 1 volt, then the 20th bit will control a voltage of about one microvolt. But in our real world, the voltage of the most significant bit with a resistor accuracy of 0.01% can be anything from 0.99 to 1.01 volts, that is, its accuracy will be +/- 10 millivolts. Feel the difference? The least significant bits will generate digital noise against the background of huge steps of the most significant bits with their gigantic errors.
But that's not all. The supply voltage of the chips controlling the R2R ladder must have a pulsation of no more than one nanovolt! Do you really think that is possible?

 

[Deleeh]

2 things the first may sound a bit harsh but unless you have heard yourself better cables,audiophile or tuned routers,DDC and things like that you should not just be biased but be a bit calmer with it.
Because there are enough people who have not only tested but also heard such possibilities.
Even if this topic is divided in the camp, there are some who recognise the difference and others who do not.
Those who do recognise it are also very familiar with their equipment.
The 2 thing is more bits does not automatically mean better, apart from the theory very few people do not hear the number of more bits.
The same would be similar to the sample rate.
More kHz does not automatically mean better, more resolution, texture, depth, bass, treble, midrange.
Here we are accompanied by the science of human hearing, where people do not hear better above 20K Khz, especially when it comes to music.
In fact there is a difference between 16/24 bit as well as in the sampling rate of 48khz and 96khz up to max 192 khz.
Most people don't even hear a difference between 96 and 192 kHz.
Finally, it must also be said that a Delta Sigma sounds different to an R2R Dac or Multibit Dac.
The tonal differences are where you should ideally focus on your personal preferences.
No more, no less.
More does not always mean better, more $ does not have to be better than less $.

 

[AlexMa]

2 things the first may sound a bit harsh but unless you have heard yourself better cables,audiophile or tuned routers,DDC and things like that you should not just be biased but be a bit calmer with it.
Because there are enough people who have not only tested but also heard such possibilities.
Even if this topic is divided in the camp, there are some who recognise the difference and others who do not.
Those who do recognise it are also very familiar with their equipment.
The 2 thing is more bits does not automatically mean better, apart from the theory very few people do not hear the number of more bits.
The same would be similar to the sample rate.
More kHz does not automatically mean better, more resolution, texture, depth, bass, treble, midrange.
Here we are accompanied by the science of human hearing, where people do not hear better above 20K Khz, especially when it comes to music.
In fact there is a difference between 16/24 bit as well as in the sampling rate of 48khz and 96khz up to max 192 khz.
Most people don't even hear a difference between 96 and 192 kHz.
Finally, it must also be said that a Delta Sigma sounds different to an R2R Dac or Multibit Dac.
The tonal differences are where you should ideally focus on your personal preferences.
No more, no less.
More does not always mean better, more $ does not have to be better than less $.

I agree with probably everything you said, except that people can't hear the difference between 16 and 24 bits or between sampling rates. I think most people could hear the difference if they wanted to. They just don't need to

 

[Middle Earth]

Are there any DACs that don’t rely on tweaking or twerking ?
I hope this is not another pointless ASR versus subjectivist circular argument
Get what you like and others will do the same and listen to music which is the point
This is supposed to be fun and enjoyable right ?

 

[AlexMa]

Are there any DACs that don’t rely on tweaking or twerking ?
I hope this is not another pointless ASR versus subjectivist circular argument
Get what you like and others will do the same and listen to music which is the point
This is supposed to be fun and enjoyable right ?

Yes, listening to music is fun and interesting. And there are many great audio components for this. But I am somewhat annoyed by the misleading aggressive marketing. A little thought is also good

 

[jbarrentine]

The conversion between THD+N in % and THD+N in dB is easy. It's 20*log(THDN%/100) so 20*log(0.025/100) which is around -72dB, not -66dB.

The conversion between dB and effective bits is also not hard. It's dB/(20*log2) so 72/(20*log2) which is around 12 bits.

so that massive 12 bits instead of 11 bits.

 

[theveterans]

Yes, listening to music is fun and interesting. And there are many great audio components for this. But I am somewhat annoyed by the misleading aggressive marketing. A little thought is also good

Forget about marketing. Go demo some R2R and DS DACs at your home and hear them for yourself

 

[johncarm]

I don't know much about R2R and this thread is new information. But I do own the Gustard R26 (R2R DAC) and love it. Curiously, I heard four different R26's over the course of 2024 and they all sounded different -- two of them quite bad (and the one I kept sounds great). Maybe it's hit or miss when you order one of these, depending on errors in the resistors.

EDIT: I also have a Gustard X30 Pro here. I usually listen to the R26, but just hooked up the X30 Pro and warmed it up. My conclusion is that the R26 sounds more analog and transparent. (So strange to be transparent if it's really creating distortion.)

 

[AlexMa]

I don't know much about R2R and this thread is new information. But I do own the Gustard R26 (R2R DAC) and love it. Curiously, I heard four different R26's over the course of 2024 and they all sounded different -- two of them quite bad (and the one I kept sounds great). Maybe it's hit or miss when you order one of these, depending on errors in the resistors.

EDIT: I also have a Gustard X30 Pro here. I usually listen to the R26, but just hooked up the X30 Pro and warmed it up. My conclusion is that the R26 sounds more analog and transparent. (So strange to be transparent if it's really creating distortion.)

Indeed, buying an R2R DAC is partly a lottery, you may get lucky, but you may not. Over time, the resistor values will change due to aging and diffusion of materials - and this is also unpredictable.
Delta-sigma DACs are also not ideal, they have their drawbacks. In addition, manufacturers overcomplicate flagship chips, which is not always a good thing.
I had different DACs, I gave some away, sold others, sent one to another room, to my vintage system
And the newest DAC I had to design and make myself, since I did not find a suitable ready-made one

 

[johncarm]

Indeed, buying an R2R DAC is partly a lottery, you may get lucky, but you may not. Over time, the resistor values will change due to aging and diffusion of materials - and this is also unpredictable.
Delta-sigma DACs are also not ideal, they have their drawbacks. In addition, manufacturers overcomplicate flagship chips, which is not always a good thing.
I had different DACs, I gave some away, sold others, sent one to another room, to my vintage system
And the newest DAC I had to design and make myself, since I did not find a suitable ready-made one

Whoa. Pretty impressive to design your own DAC. Did you use an FPGA? Or a chipset? Or something else?

Thanks,
Mike