What makes an R-2R DAC nonmonotonic? - Page 2 - diyAudio
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Old 18th July 2013, 04:07 AM   #11
bcarso is offline bcarso  United States
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Quote:
Originally Posted by abraxalito View Post
I'm unclear how nonmonotonicity would relate to such a measurement.
So far as I can tell, I don't know that anyone does. Which to me is somewhat astonishing.

But I'm sure all of this is somewhere, at the least in some obscure thesis or conference proceedings.
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Old 18th July 2013, 09:38 AM   #12
DF96 is offline DF96  England
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Quote:
Originally Posted by bcarso
Others, noting the large amounts of spurious high frequency energy in the DAC outputs prescribe various passive filter networks ahead of the opamp inverting input(s). But consideration of the above numbers suggests that this may spoil things very easily.
A diplexer might work OK. LF current sent to the opamp virtual ground. HF current sent to a low value resistor. Given that low impedance is a requirement, the finite Q of any inductor may need to be taken into account in the design.

Also, the virtual ground is not a short circuit or even resistive itself but looks rather like a lossy inductor due to the dominant pole in the opamp forward path. This doesn't often seem to get mentioned.
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Old 18th July 2013, 02:20 PM   #13
bcarso is offline bcarso  United States
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Originally Posted by DF96 View Post
A diplexer might work OK. LF current sent to the opamp virtual ground. HF current sent to a low value resistor. Given that low impedance is a requirement, the finite Q of any inductor may need to be taken into account in the design.

Also, the virtual ground is not a short circuit or even resistive itself but looks rather like a lossy inductor due to the dominant pole in the opamp forward path. This doesn't often seem to get mentioned.
Yes, the input Z is inductive for resistive FB in the opamp circuits most employ, although with a feedback capacitor can be resistive for a portion.

What would be interesting: the actual spectrum of the out-of-band energies for various noise-shaped DACs. CMOS is fast but not unlimited. And depending on the DAC topology, the transitions are not swinging the maximum amount all the time, although I guess some DSD schemes approach it.

The approach that's under development starts with something inherently low-Z and fast, and then applies feedback around that input (not necessarily global feedback as in a current-feedback amp) to further reduce the impedance. Of course there are other errors in the conversion besides those arising from the input impedance, but it's nice to have the input Z low. Pushing things, one can acquire a high sensitivity to capacitance at that node as well, and some DACs also have significant variation in that C with code, also rarely specified.

The BF862, or paralleled 862s for higher currents, seem fairly promising, and should accommodate some rather high-frequency energy without significant errors and without additional filtering in series with the DAC.
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Old 18th July 2013, 03:37 PM   #14
DF96 is offline DF96  England
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Quote:
Originally Posted by bcarso
Pushing things, one can acquire a high sensitivity to capacitance at that node as well, and some DACs also have significant variation in that C with code, also rarely specified.
Good point. I hadn't thought of that.

Just to put some numbers on the virtual ground, assume an opamp with GBW of 20MHz, DC gain of 10^6, and a feedback resistor of 1k. This gives a virtual ground equivalent to 8uH in series with 1mR.

Put a 3nF cap across the 1k to get about 50kHz rolloff and this adds a 2.5R resistor in parallel with the inductor. An alternative way to get a 50kHz rolloff would be to omit the cap and instead just put a real 2.5R resistor in parallel with the opamp input. The advantage of this is that the resistor shunts HF current away from the opamp. The snag with this is that the actual rolloff freq then depends on the GBW of the opamp, which will suffer from sample variation so you could get inter-channel differences. Maybe use a smaller cap and larger parallel resistor?
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Old 18th July 2013, 05:36 PM   #15
bcarso is offline bcarso  United States
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Originally Posted by DF96 View Post
Good point. I hadn't thought of that.

Just to put some numbers on the virtual ground, assume an opamp with GBW of 20MHz, DC gain of 10^6, and a feedback resistor of 1k. This gives a virtual ground equivalent to 8uH in series with 1mR.

Put a 3nF cap across the 1k to get about 50kHz rolloff and this adds a 2.5R resistor in parallel with the inductor. An alternative way to get a 50kHz rolloff would be to omit the cap and instead just put a real 2.5R resistor in parallel with the opamp input. The advantage of this is that the resistor shunts HF current away from the opamp. The snag with this is that the actual rolloff freq then depends on the GBW of the opamp, which will suffer from sample variation so you could get inter-channel differences. Maybe use a smaller cap and larger parallel resistor?
The main problem with a small physical parallel resistor is its high parallel noise (or "current" noise), and the very high noise gain for the opamp's e sub n. So for example a 2.5 ohm resistor at 300K has about 81.4pA/sq rt Hz, which with the 1k feedback R amounts to an output voltage noise density of 81.4nV/sq rt Hz. If the opamp is even as low as 1nV/sq rt Hz, this is multiplied by 1k/2.5 + 1, to give us 401nV/sq rt Hz at the output. Well at least this swamps the 2.5R current noise ; the two noise sources thus amounting to 409.2nV/sq rt Hz.

If the two noise sources are flat this amounts to an output rms noise of about 114.7uV with a single-pole 50kHz rolloff, and about 57.9uV rms with a brickwall 20kHz. So for a, say, 8mA peak DAC output, we have 5.657mA rms hence 5.657V rms at the opamp out. we'd manage at best a 99.8dB signal-to-noise ratio, if I haven't blundered here. Not the end of the world and for some apps even respectable, but probably well below most DACs' performances. And that is a pretty good opamp too.

With A-weighting things would get a little better, and I notice most DAC vendors throw that in.
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Old 18th July 2013, 05:46 PM   #16
jcx is offline jcx  United States
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"noise gain compensation" puts a C in series with the input shunt R - you can tailor the noise gain frrequency rise to start at the top of the audio band for little S/N impact
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Old 18th July 2013, 06:11 PM   #17
DF96 is offline DF96  England
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2.2nF feedback cap plus 7.5R across virtual ground? That would increase SNR by about 10dB, but still shunt some HF away from the opamp.
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