You are plotting the noise spectral density. You are supposed to integrate the noise power by squaring the noise spectral density values. You then take the square root of that integration result. The equation on the board shows that you should be integrating the square of the noise spectral density.
But what about the 0.1 Hz to 10 Hz noise value on the datasheet? (Which is often quite large.) Do we not need to know this and add this on to the calculation above? For example: For OPA314: - Noise is 14 nV / sqrt(Hz) at 1 kHz (rising to 40 nV / sqrt(Hz) at only 10 Hz). - But 0.1-10 Hz noise is already 5 uVpp. So, for example, for the ECG (electrocardiogram) range of 0-150 Hz: - With your technique I get only 171 nVrms noise (≈ 1 uVpp ) - Even if I use the high 10 Hz noise value I get 490 nVrms noise (≈ 2.9 uVpp ) (I'm multiplying by 6 to get peak-to-peak noise, for 99.7% of values, as used in your next video.) But according to the datasheet, the noise for even just the 0.1 - 10 Hz range alone is 5 uVpp. Both of the values above using your method are much lower than the actual noise! Even for a larger range of 0 - 1 kHz, the 0.1 - 10 Hz noise is still important. Also: Is the seemingly always undocumented range of 0-0.1 Hz ever of any significance?
I can't get the result of 6,3Vrms that you did, what am I doing wrong? last time I did this: (40*10^-9)*(sqrt(10000*1,57) which = 5,011985634E-6 which is about 5µVrms, what am I missing?
Hey David, You're exactly right. That is a mistake in the video. When we uploaded the video we put a note in the description about this, but that note is very easy to miss. We've now annotated the screen when I'm discussing it so that it's clear.
Suppose that I combine four op-amps in parallel, resulting in 1/2 of the noise density of a single op-amp. Next suppose that the op-amps are generating some excess or non-Gaussian noise (popcorn, telegraph, etc). A single excess noise event in a single op-amp of the quad-array would be attenuated by 1/4 instead of 1/2. . Therefore isn't it true that the quad op-amp array has a noise advantage, even greater than the Gaussian noise attenuation of 1/2 ?
Hi Matt, you mentioned about determining the frequency of the system, what exactly you meant by that, say I am feeding a 1MHz sine to an opampof 10MHz bandwidth? Will the filter cut off frequencies be the last factor to determine this?
It's the bandwidth of the system. So if your system is an amplifier stage with 10 MHz, that would be it. The frequency of the signal you are putting in doesn't matter.
Hi Matt, this was a good video. However, is there a simple way to estimate this noise spectral density plot from noise measurements taken from a new DUT? I am trying to ensure that a new device that I have does not have noise greater than the opamp noise.
I am assuming when you say "noise measurements from the DUT" you mean you have measurements that give you the rms or peak to peak noise? If you pretend your DUT has no 1/f noise, you can do this by manipulating the equation in the video: rms noise / sqrt(bandwidth) = spectral noise. A key thing to know is the bandwidth of your DUT.
Thanks for the quick reply. I am trying to work on a front end for a completely new sensor which has not been characterized. However, I have the equipment to measure the sensor's instantaneous noise voltage (mVrms). I took all those points and did an FFT in Matlab which gave me a plot. The FFT should give you the noise voltage in mV. So, should I just perform the calculation mVrms/sqrt(frequency on the X-axis for that voltage)?
If you have one rms number that represents the noise you are getting, yes, you can use the formula. If you have an FFT with vrms value at various frequency bins, I think you will need to scale it based on your window and maybe your bin size? (it's been a while since I've done this and unfortunately I don't remember.)
I'm not so sure about this. If you want to estimate the area in frequency domain with a brick, the x axis should be linear but your plot is logarithmic. This is weird to me. Can somebody tell me about this? Thank you in advance
Hi, in my opinion that shouldn't matter. The x-axes could be linear or logarithmic. The only important value is the maximum frequency for the integration. Another way to look at it is that you are getting the area of a rectangle which is height times length where the length is the frequency in this case.
You are plotting the noise spectral density. You are supposed to integrate the noise power by squaring the noise spectral density values. You then take the square root of that integration result. The equation on the board shows that you should be integrating the square of the noise spectral density.
But what about the 0.1 Hz to 10 Hz noise value on the datasheet? (Which is often quite large.) Do we not need to know this and add this on to the calculation above?
For example: For OPA314:
- Noise is 14 nV / sqrt(Hz) at 1 kHz (rising to 40 nV / sqrt(Hz) at only 10 Hz).
- But 0.1-10 Hz noise is already 5 uVpp.
So, for example, for the ECG (electrocardiogram) range of 0-150 Hz:
- With your technique I get only 171 nVrms noise (≈ 1 uVpp
)
- Even if I use the high 10 Hz noise value I get 490 nVrms noise (≈ 2.9 uVpp
)
(I'm multiplying by 6 to get peak-to-peak noise, for 99.7% of values, as used in your next video.)
But according to the datasheet, the noise for even just the 0.1 - 10 Hz range alone is 5 uVpp. Both of the values above using your method are much lower than the actual noise!
Even for a larger range of 0 - 1 kHz, the 0.1 - 10 Hz noise is still important.
Also: Is the seemingly always undocumented range of 0-0.1 Hz ever of any significance?
I can't get the result of 6,3Vrms that you did, what am I doing wrong? last time I did this: (40*10^-9)*(sqrt(10000*1,57) which = 5,011985634E-6 which is about 5µVrms, what am I missing?
Hey David, You're exactly right. That is a mistake in the video. When we uploaded the video we put a note in the description about this, but that note is very easy to miss. We've now annotated the screen when I'm discussing it so that it's clear.
A year late, but you are taking the root of the product of 10 000 and 1.57 and should be taking the sqr root of 10 000 and multiplying that by 1.57.
You can insert a quote directly in the video. Check 'edit video' in your channel
Suppose that I combine four op-amps in parallel, resulting in 1/2 of the noise density of a single op-amp. Next suppose that the op-amps are generating some excess or non-Gaussian noise (popcorn, telegraph, etc). A single excess noise event in a single op-amp of the quad-array would be attenuated by 1/4 instead of 1/2.
.
Therefore isn't it true that the quad op-amp array has a noise advantage, even greater than the Gaussian noise attenuation of 1/2 ?
Great video. Thank you.
Hi Matt, you mentioned about determining the frequency of the system, what exactly you meant by that, say I am feeding a 1MHz sine to an opampof 10MHz bandwidth?
Will the filter cut off frequencies be the last factor to determine this?
It's the bandwidth of the system. So if your system is an amplifier stage with 10 MHz, that would be it. The frequency of the signal you are putting in doesn't matter.
Hi Matt, this was a good video. However, is there a simple way to estimate this noise spectral density plot from noise measurements taken from a new DUT? I am trying to ensure that a new device that I have does not have noise greater than the opamp noise.
I am assuming when you say "noise measurements from the DUT" you mean you have measurements that give you the rms or peak to peak noise? If you pretend your DUT has no 1/f noise, you can do this by manipulating the equation in the video: rms noise / sqrt(bandwidth) = spectral noise. A key thing to know is the bandwidth of your DUT.
Thanks for the quick reply. I am trying to work on a front end for a completely new sensor which has not been characterized. However, I have the equipment to measure the sensor's instantaneous noise voltage (mVrms). I took all those points and did an FFT in Matlab which gave me a plot. The FFT should give you the noise voltage in mV. So, should I just perform the calculation mVrms/sqrt(frequency on the X-axis for that voltage)?
If you have one rms number that represents the noise you are getting, yes, you can use the formula. If you have an FFT with vrms value at various frequency bins, I think you will need to scale it based on your window and maybe your bin size? (it's been a while since I've done this and unfortunately I don't remember.)
Thanks for the reply, that helps. I think I should read up more. Do you suggest a book with a good explanation on this?
Can I know what is the full name expression of SDf meaning, plz?
Spectral density at the frequency f
I'm not so sure about this. If you want to estimate the area in frequency domain with a brick, the x axis should be linear but your plot is logarithmic. This is weird to me. Can somebody tell me about this? Thank you in advance
Hi, in my opinion that shouldn't matter. The x-axes could be linear or logarithmic. The only important value is the maximum frequency for the integration. Another way to look at it is that you are getting the area of a rectangle which is height times length where the length is the frequency in this case.
Wait... How is this? What is this? Where did i stumble to?
GREAT !!!!
I need get voltage from spectral noise density figure, your video cheats and pulls it from a datasheet
Thanks a lot
sweet......
wow
Got lost... you start with a signal...then end up with a filter
GREAT !!!!