2^24 = 16777216
the resistor string has to have the ability to scale the LSB to 1/16777216 of the total resistor string.
That would require each of the steps to be 0.00000596% of the total.
What accuracy do we require from each step?
the resistor string has to have the ability to scale the LSB to 1/16777216 of the total resistor string.
That would require each of the steps to be 0.00000596% of the total.
What accuracy do we require from each step?
I doubt very much they mean 1ohm and 2ohms, rather that's showing ratios. If you love glitchy sound and non-monotonicity in your DAC, by all means build it but its hardly recommended.
There seems to be some misconceptions about R2R DACs....
First, Dynamic Range, S/N Ratio and S/N+THD, and THD are often mixed together. It's impossible to get 144 dB S/N ratio no matter how many bits as thermal noise will set a lower limit, but you can get easily 144 dB Dynamic Range.... I still believe 24 bit is needed, but to archieve good audio performance at low levels, t.ex. always look at the -60 dB measurements. I also believe that those ultra low levels of THD at -1 dB doesn't really matter, again, look at the -60 dB THD....
The critical thing with many bit R2R DACs is the zero crossing. Digital Audio is usually in binary 2s complement format, in a R2R DAC you just invert the MSB bit. Lets take an 8 bit example:
11111111 - 255 +limit
..
10000011 - 131
10000010 - 130
10000001 - 129 + small signal
10000000 - 128 zero
01111111 - 127 - small signal
01111110 - 126
01111101 - 125
01111100 - 124
..
00000000 - 000 - limit
So even very low signals have the MSB bits changing all the time, that why TI/BB have their sign-magnitude architecture using two 23 bit DAC's.
Making a great 24 bit R2R discrete DAC is actually not that complicated as you only really need to concentrate on the MSB's, and when doing a discrete DAC I would suggest trimming the MSB with a small potentionmeter, you only need to trim very little if using t.ex. 0.01% parts, that way you should be able to get maybe 0.003% THD at -1 dB, and maybe 0.03% at -60 dB. And you could do with using only the really expensive precision resistors on t.ex. the 8 MSB bits, using less precise and less expensive parts for the rest of the bits....
When selecting resistors the temperature drift is actually more important than precision, you want to keep the performance when the box is heating up a little.... Precision resistors have also been getting cheaper, looking at Digikey you can t.ex. get these precision smd resistors:
Susumi URG 0.01% 2ppm/C $1.79 each
Susumi RG 0.02% 5ppm/C $1.08 each
Susumi RG 0.05% 10ppm/C $0.40 each
You really need to purchase whole reels, luckily the precision parts comes on smaller qty 1K reels....
S/N is a question about source impedance and signal levels, a good compromise for a R2R voltage mode DAC is 5K and 10K resistors, that will result in 5K impedance with a thermal noise of 1.3 uV, driving with 3.3V p-p (1.2V RMS) from a FPGA gives 119 dB S/N ratio. Do a balanced version and you get 122 dB S/N plus some suppression of power supply and/or reference noise....
Ooh, by the way I'm working on hardware based on the above, haven't yet decided to offer DIY versions....
Best Regards,
Soren
First, Dynamic Range, S/N Ratio and S/N+THD, and THD are often mixed together. It's impossible to get 144 dB S/N ratio no matter how many bits as thermal noise will set a lower limit, but you can get easily 144 dB Dynamic Range.... I still believe 24 bit is needed, but to archieve good audio performance at low levels, t.ex. always look at the -60 dB measurements. I also believe that those ultra low levels of THD at -1 dB doesn't really matter, again, look at the -60 dB THD....
The critical thing with many bit R2R DACs is the zero crossing. Digital Audio is usually in binary 2s complement format, in a R2R DAC you just invert the MSB bit. Lets take an 8 bit example:
11111111 - 255 +limit
..
10000011 - 131
10000010 - 130
10000001 - 129 + small signal
10000000 - 128 zero
01111111 - 127 - small signal
01111110 - 126
01111101 - 125
01111100 - 124
..
00000000 - 000 - limit
So even very low signals have the MSB bits changing all the time, that why TI/BB have their sign-magnitude architecture using two 23 bit DAC's.
Making a great 24 bit R2R discrete DAC is actually not that complicated as you only really need to concentrate on the MSB's, and when doing a discrete DAC I would suggest trimming the MSB with a small potentionmeter, you only need to trim very little if using t.ex. 0.01% parts, that way you should be able to get maybe 0.003% THD at -1 dB, and maybe 0.03% at -60 dB. And you could do with using only the really expensive precision resistors on t.ex. the 8 MSB bits, using less precise and less expensive parts for the rest of the bits....
When selecting resistors the temperature drift is actually more important than precision, you want to keep the performance when the box is heating up a little.... Precision resistors have also been getting cheaper, looking at Digikey you can t.ex. get these precision smd resistors:
Susumi URG 0.01% 2ppm/C $1.79 each
Susumi RG 0.02% 5ppm/C $1.08 each
Susumi RG 0.05% 10ppm/C $0.40 each
You really need to purchase whole reels, luckily the precision parts comes on smaller qty 1K reels....
S/N is a question about source impedance and signal levels, a good compromise for a R2R voltage mode DAC is 5K and 10K resistors, that will result in 5K impedance with a thermal noise of 1.3 uV, driving with 3.3V p-p (1.2V RMS) from a FPGA gives 119 dB S/N ratio. Do a balanced version and you get 122 dB S/N plus some suppression of power supply and/or reference noise....
Ooh, by the way I'm working on hardware based on the above, haven't yet decided to offer DIY versions....
Best Regards,
Soren
There are some very low priced low noise foil based non magnetic surface mount resistors out there,and pairs of them could be matched up. It would take a lot of binning of units, then matching them up to get to a precice resitance. But it is doable.
it is the long way home, labor wise, but cost wise, as final results go, it is probably the best production plan (making actual units for resale).
The other possibility is pairing with a vishay foil adjustable unit. The adjustable foil units have very low nose, directly comparable to the set foil units. One adjustable, one permanent, adjust across the pair.
However, the set foil unit pairing, or even tripling, is probably the best way to go. As a matter of fact, with tripling, the possibility of hitting exact numbers go up. Thermal noise probably changes in your favor, as does a drop in other sources of jitter. We're talking about three resistors of identical value, that would enable the best results.
Make the pads three wide, with the resistors touching one another, single solder junction on each end.
Thus, with parts testing and binning, go to the low budget triple resistor/single-pad trick,and you've got your low noise, low jitter, exact resistance. Probably for about 1/3rd or less than the cost of the Vishay foils. Possibly even a tenth the cost, if well thought out.
it is the long way home, labor wise, but cost wise, as final results go, it is probably the best production plan (making actual units for resale).
The other possibility is pairing with a vishay foil adjustable unit. The adjustable foil units have very low nose, directly comparable to the set foil units. One adjustable, one permanent, adjust across the pair.
However, the set foil unit pairing, or even tripling, is probably the best way to go. As a matter of fact, with tripling, the possibility of hitting exact numbers go up. Thermal noise probably changes in your favor, as does a drop in other sources of jitter. We're talking about three resistors of identical value, that would enable the best results.
Make the pads three wide, with the resistors touching one another, single solder junction on each end.
Thus, with parts testing and binning, go to the low budget triple resistor/single-pad trick,and you've got your low noise, low jitter, exact resistance. Probably for about 1/3rd or less than the cost of the Vishay foils. Possibly even a tenth the cost, if well thought out.
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Is there a way to increase the output of the FPGA, something like 1-bit DACs, amplifiers or similar... ?
That could provide even greater dynamic range, and allow the use of a lower gain amplifier.
This is probably for another topic, but as I am also contemplating it in terms of R2R DIY build:
if we use a DSP crossover before the DAC, that would relax the bandwidth requirement. How can we exploit the new situation?
I still have to dig up my signal and information theory books and calculate the information content of the signal after the crossover.
Until then, I'd like to share the following questions here:
What would you say, are the "benefits" in this case?
What is the required bit-depth to describe a signal of certain bandwidth?
How does dynamic range behave?
This article covers many aspects which can be applied to the DAC as well...
BiAmp (Bi-Amplification - Not Quite Magic, But Close) - Part 1
That could provide even greater dynamic range, and allow the use of a lower gain amplifier.
This is probably for another topic, but as I am also contemplating it in terms of R2R DIY build:
if we use a DSP crossover before the DAC, that would relax the bandwidth requirement. How can we exploit the new situation?
I still have to dig up my signal and information theory books and calculate the information content of the signal after the crossover.
Until then, I'd like to share the following questions here:
What would you say, are the "benefits" in this case?
What is the required bit-depth to describe a signal of certain bandwidth?
How does dynamic range behave?
This article covers many aspects which can be applied to the DAC as well...
BiAmp (Bi-Amplification - Not Quite Magic, But Close) - Part 1
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