I'm currently in the process of choosing opamps to try in our I/V circuit for an ES9038Q2M in mono mode. My gut tells me that for most of the opamps that are on my list, noise will be of no concern, but let's see if I got my numbers right.
For the following calculations please see attached schematic.
So the noise contribution of the circuit shown are as follows:
- input voltage noise from the opamp
- input current noise from the opamp
- resistor noise
Regarding input voltage and current noise I assume that the noise gain of the I/V converter is 1 - ist that correct? otherwise my calculations will fall apart before they even began...
So let's add things up in an example - I'll use the OPA1611 as it's widely used for that purpose. Let's assume an I/V resistor of 500 ohms and the DAC has an output impedance of 774 ohms
current noise:
The datasheet shows a input current noise density of 2.8pA/sqrt(Hz). That corresponds to 396pA RMS noise current in the range of 20Hz-20kHz. As far as I can see Rdac and Rf are parallel in this case (299ohms) and this will yield a RMS noise voltage of 0.12uV
voltage noise:
Voltage noise densitiy is given as 1.7nV/sqrt(Hz) which calculates to a RMS noise voltage of 0.24uV in the range of 20Hz to 20kHz
resistor noise:
According to Sengpiel's noise calculator a 500 ohms resistor has a RMS noise voltage of 0.4uV in the ususal audio frequency range
Adding these up (taking the square root of the sum of the squared components) gives me 0.48uV RMS noise contributed by the opamp and the resistor, resulting in a 138.4dB SNR for a 4V RMS reference level.
I'd be very thankful if somebody would take the time look over my calculations as I have no formal education in this field and every bit of wisdom used was extracted from the internets
IF all that is correct I deem the noise contribution of a modern opamp to be almost neglible compared to resistor noise and most likely noise from the DAC itself.
For the following calculations please see attached schematic.
So the noise contribution of the circuit shown are as follows:
- input voltage noise from the opamp
- input current noise from the opamp
- resistor noise
Regarding input voltage and current noise I assume that the noise gain of the I/V converter is 1 - ist that correct? otherwise my calculations will fall apart before they even began...
So let's add things up in an example - I'll use the OPA1611 as it's widely used for that purpose. Let's assume an I/V resistor of 500 ohms and the DAC has an output impedance of 774 ohms
current noise:
The datasheet shows a input current noise density of 2.8pA/sqrt(Hz). That corresponds to 396pA RMS noise current in the range of 20Hz-20kHz. As far as I can see Rdac and Rf are parallel in this case (299ohms) and this will yield a RMS noise voltage of 0.12uV
voltage noise:
Voltage noise densitiy is given as 1.7nV/sqrt(Hz) which calculates to a RMS noise voltage of 0.24uV in the range of 20Hz to 20kHz
resistor noise:
According to Sengpiel's noise calculator a 500 ohms resistor has a RMS noise voltage of 0.4uV in the ususal audio frequency range
Adding these up (taking the square root of the sum of the squared components) gives me 0.48uV RMS noise contributed by the opamp and the resistor, resulting in a 138.4dB SNR for a 4V RMS reference level.
I'd be very thankful if somebody would take the time look over my calculations as I have no formal education in this field and every bit of wisdom used was extracted from the internets
IF all that is correct I deem the noise contribution of a modern opamp to be almost neglible compared to resistor noise and most likely noise from the DAC itself.
Attachments
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> assume that the noise gain of the I/V converter is 1 -.... assume an I/V resistor of 500 ohms and the DAC has an output impedance of 774 ohms....
It seems to me the noise voltage gain is 1274/774 or 1.6. Which is not an "arrgh!" difference, but worth noting. (See if anybody agrees with me.)
It seems to me the noise voltage gain is 1274/774 or 1.6. Which is not an "arrgh!" difference, but worth noting. (See if anybody agrees with me.)
If you want to refer everything to the output to compare it to a known output signal, then:
Op-amp voltage noise gets multiplied by Rf/Rdac + 1, like PRR wrote.
Op-amp current noise gets multiplied by Rf (or -Rf, depending on your sign convention, but that doesn't matter in this case). When you draw a little current source between the op-amp inputs, you see it just gets injected into the input of the current to voltage converter circuit, which has a gain -Rf.
Feedback resistor noise ends up 1:1 on the output. Draw a noise voltage source in series with the resistor and you'll see why.
If you also want to calculate A-weighted noise, use a noise bandwidth of about 13 kHz.
Op-amp voltage noise gets multiplied by Rf/Rdac + 1, like PRR wrote.
Op-amp current noise gets multiplied by Rf (or -Rf, depending on your sign convention, but that doesn't matter in this case). When you draw a little current source between the op-amp inputs, you see it just gets injected into the input of the current to voltage converter circuit, which has a gain -Rf.
Feedback resistor noise ends up 1:1 on the output. Draw a noise voltage source in series with the resistor and you'll see why.
If you also want to calculate A-weighted noise, use a noise bandwidth of about 13 kHz.
You normally calculate noise (or noise density) referenced to the input, and then compare to the DAC's noise level - if your circuit is contributing less noise than the DAC, you have a noise figure less than 3dB and are doing well. If you are adding more noise than the DAC, poor choice of opamp for that DAC.
If you want a given output performance you'll need to check the DAC is upto the task in the first place.
Noise engineering is all about finding the worst component and improving it so its no longer the worst, and maybe rinse and repeat. This is often easiest to do when referenced to the input as that's where all the noise sources are.
Another thing to note is the natural noise impedance of the opamp, vn/in, here 1.7n/2.8p ~= 600 ohms. This means the opamp does best for impedances around that value. Try to use the OPA1611 for a 10k circuit and it will be quite noisy, whereas an NE5534A for instance will do much better.
For instance for impedances around 10k very few opamps can beat the NE5534A on noise, and its an ancient design now - it just happens to be optimal around 8k to 10k region and has only 0.4pA/√Hz current noise - very low for a bipolar opamp - it would be quieter than the OPA1611 in standard tone circuits for instance which have impedances around that point.
Or put in short, do the maths to check, which you have...
If you want a given output performance you'll need to check the DAC is upto the task in the first place.
Noise engineering is all about finding the worst component and improving it so its no longer the worst, and maybe rinse and repeat. This is often easiest to do when referenced to the input as that's where all the noise sources are.
Another thing to note is the natural noise impedance of the opamp, vn/in, here 1.7n/2.8p ~= 600 ohms. This means the opamp does best for impedances around that value. Try to use the OPA1611 for a 10k circuit and it will be quite noisy, whereas an NE5534A for instance will do much better.
Depends entirely on the resistor value and the opamp in combination - many "modern opamps" are not even designed for low noise, they might be optimized for bandwidth, low power, low dc-offset, rail-to-rail operation at low voltage, high current/power, etc etc.
For instance for impedances around 10k very few opamps can beat the NE5534A on noise, and its an ancient design now - it just happens to be optimal around 8k to 10k region and has only 0.4pA/√Hz current noise - very low for a bipolar opamp - it would be quieter than the OPA1611 in standard tone circuits for instance which have impedances around that point.
Or put in short, do the maths to check, which you have...
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One more question before I'll post a corrected version of my example calculation:
If the current noise is modeled as a current source between the opamp's input and we assume the noninverting opamp is held at a constant voltage by a low output impedance voltage source, then I see two paths for the current to flow: 1) through Rf and 2) also through Rdac. If so, the current would be split and only a part of it would flow through Rdac. Is this assumption wrong?
Where does that come from? assuming that noise density is the same for the whole audio band and then coming up with a "rule of thumb"?
Often times I think engineering can also go the other way around. For several reasons we already decided on the DAC chip very early on in the project and up to now, several months of research and first experiments later, we didn't find a reason to change that decision.
We also have a list of currently 10 opamps or so which we deem to be fit for the I/V job of an audio DAC. So in our case the question actually was: Can we disregard noise numbers of the opamps in question and use other criteria to determine the best candidates? The final I/V resistance will be determined experimentally by figuring out where the sweet spot for the I/V's output voltage will be regarding THD+N performance. So I used a ballpark value of 500ohms for now.
At least I tried
Yes. None of it flows through Rdac, because the op-amp input behaves as a virtual ground. That is, the feedback loop adjusts the output such that the input voltage remains constant, which results in none of the op-amp's input noise current flowing through Rdac and everything through Rf.
That 13 kHz for A-weighting indeed applies for white noise. When you integrate the squared magnitude of an A-weighting curve to frequency from 0 Hz to infinity, you end up with about 13.5 kHz, when you do it from 20 Hz to 20 kHz, it's about 12.5 kHz. When you search for noise bandwidth or equivalent rectangular bandwidth, you will definitely find an explanation why the squared magnitude has to be integrated to frequency.
If you should measure a much larger impact of the op-amp on in-band noise than calculated, it could also be intermodulation distortion. Sigma-delta DACs have lots of out-of-band quantization noise that can partly be converted to in-band noise when it gets processed non-linearly.
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So, I hope I have this correct now:
As I need two I/V opamps for the positive and negative output of the DAC that will double the noise power which amounts to 0.85uV RMS.
Compared to a signal level of 4V RMS thats a SNR of 133.5dB.
A very amazing number I might add. Big thanks to all the silicon developers out there for providing such marvels of technology to us!
As I need two I/V opamps for the positive and negative output of the DAC that will double the noise power which amounts to 0.85uV RMS.
Compared to a signal level of 4V RMS thats a SNR of 133.5dB.
A very amazing number I might add. Big thanks to all the silicon developers out there for providing such marvels of technology to us!
Attachments
Because I just referred to this thread, one more note: The final SNR number was flawed because a 500 Ohms resistor together with the ES9038Q2M will only give you about 1.37V RMS. Thus the SNR of the I/V is down by 9.3dB resulting in 124.2dB
Hope I don't have an error in the calculation:
Iopp = 0.906 * 3.3V / 774Ohms = 3.86mA (per pos/neg DAC output pin)
Vopp = 3.86mA * 500Ohms = 1.93V (per pos/neg DAC output pin)
Vorms = 1.93V / 1.41 = 1.37V (between both outputs of the two I/V opamps)
Hope I don't have an error in the calculation:
Iopp = 0.906 * 3.3V / 774Ohms = 3.86mA (per pos/neg DAC output pin)
Vopp = 3.86mA * 500Ohms = 1.93V (per pos/neg DAC output pin)
Vorms = 1.93V / 1.41 = 1.37V (between both outputs of the two I/V opamps)
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And if the DAC's quantization noise is -115dB, your psuedo noise figure is about 0dB, ie the circuit is contributing far less noise than the source.
For a theoretical true 24 ENOB DAC -124.2dB is a noise figure of 20dB or so - so it does depend on the DAC.
BTW -127dB is pretty much state of the art for DACs AFAICT, so -124dB is a very good performance level
For a theoretical true 24 ENOB DAC -124.2dB is a noise figure of 20dB or so - so it does depend on the DAC.
BTW -127dB is pretty much state of the art for DACs AFAICT, so -124dB is a very good performance level