In that graph, for f > 10 Hz, the noise spectrum is flat or "white", which means the noise voltage in a given bandwidth is proportional to the square root of the bandwidth.
Below 10 Hz, you are in "pink" or "1/f" part of the spectrum, where the "excess noise" found in all semiconductor and similar devices increases with decreasing frequency, so that the total noise over bands that include the low frequency region increases over the "white" voltage.
The "corner frequency", below which pink noise rears its ugly head over white noise, depends on the details of the active devices used in the circuit and requires that the circuit be powered externally.
I know but 5nV/Sqrt (Hz) should already described the noise voltage. In the last 2 images in my original message. The noise voltage at 100Hz vs 1000Hz bandwidth should have similar nV/Sqrt(Hz) but it varies from 100nV/Sqrt (Hz) to 1uV/Sqrt (Hz), why? what components can make the noise density change?
Watchfuleye, what software is the RTA in your last message?
If it's the REW RTA.. how did you run it without the hardware? Did you use the 1000 Hz noise file?
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the above was the RTA setting I used. Why can't you use FFT length of 4M instead of your 64k? or Averages of Exponential 0.97 instead of Forever?
You mean it's possible the E1DA has read them wrong reporting the 100nV/Sqrt (Hz) at 100Hz and 1uV/Sqrt (Hz) at 1000Hz? that was why you couldn't figure how they were derived? My original message was also about whether the E1DA can read noise floor accurate. It can't?
Edit: Or did you mean I must change the 1V rms to 1.7V rms in the RTA and the output will be accurate? Or must it be 5V peak to peak (changed to rms)?
Watchfuleye, what software is the RTA in your last message?
If it's the REW RTA.. how did you run it without the hardware? Did you use the 1000 Hz noise file?
(Attachment Link)It's the same software - REW. I just used my audio interface hardware.Quotethe above was the RTA setting I used. Why can't you use FFT length of 4M instead of your 64k? or Averages of Exponential 0.97 instead of Forever?
Longer FFT gives more frequency resolution but takes longer - You don't need the frequency resolution or low frequencies.
Because noise is noisy, you need good amplitude resolution to see the patterns. This needs a lot of averages. The default exponential moving average in the REW software is not enough.QuoteYou mean it's possible the E1DA has read them wrong reporting the 100nV/Sqrt (Hz) at 100Hz and 1uV/Sqrt (Hz) at 1000Hz? that was why you couldn't figure how they were derived? My original message was also about whether the E1DA can read noise floor accurate. It can't?
Edit: Or did you mean I must change the 1V rms to 1.7V rms in the RTA and the output will be accurate? Or must it be 5V peak to peak (changed to rms)?If you set the software scale to 1.7 V rms, I am confident that you will be getting accurate readings of output referred noise. You will need to divide by amplifier gain to get the input referred noise.
It will just be more useful if you have a clean plot - and this is obtained most quickly with short FFTs and lots of averages.
Are you supposed to look at the peak or black lines? What do they mean? In the 1000Hz bandwidth case, the peak is 3.91uV/Sqrt (Hz), divided it by 10X gain is 0.391uV/Sqrt (Hz) or 391nV/Sqrt (Hz). Is this noise only for 1000Hz? But then is it not you multiply 391nV/Sqrt (Hz) x Sqrt (Bandwidth) to get noise Vrms. So 391nV/Sqrt (Hz) x Sqrt (1000) = 391nv x 31.62 = 12364nV ??
In the case of the 100Hz bandwidth, the peak is 469.7nV/Sqrt (Hz) / 10 gain = 46.97nV/Sqrt (Hz) Should you multiply this by Sqrt (100Hz bandwidth) to get nV rms?
Are you supposed to look at the peak or black lines? What do they mean? In the 1000Hz bandwidth case, the peak is 3.91uV/Sqrt (Hz), divided it by 10X gain is 0.391uV/Sqrt (Hz) or 391nV/Sqrt (Hz). Is this noise only for 1000Hz? But then is it not you multiply 391nV/Sqrt (Hz) x Sqrt (Bandwidth) to get noise Vrms. So 391nV/Sqrt (Hz) x Sqrt (1000) = 391nv x 31.62 = 12364nV ??
Ignore the peak line. Only the black "mean" line is relevant. The black line is the output-referred noise density, it tells you the amount of noise contained with a portion of the frequency spectrum.
If you have a frequency range of interest, then to compute the rms noise, requires integration. Where the noise density is constant (white noise) over the frequency band of interest, this can be simplified to N * Sqrt (BW) where BW is the bandwidth, and N is the representative noise density within the band. If the noise density is not constant, then numerical integration is required.QuoteIn the case of the 100Hz bandwidth, the peak is 469.7nV/Sqrt (Hz) / 10 gain = 46.97nV/Sqrt (Hz) Should you multiply this by Sqrt (100Hz bandwidth) to get nV rms?
The peak measure is not relevant. Also, the 469.7 nV/Sqrt(Hz) measure appears to have been taken at 1000 Hz, which is outside of the band you are interested in and not representative of the band you are interested in, so this measure is irrelevant.
If all you are interested in is noise rms, then you don't need the noise density. You just need to filter your signal, and measure the amplitude rms directly. You already have an amplifier with built in filters. Conveniently, the REW software will measure and display rms voltage at the top right of the display.
So, by way of example, looking at your 1000 Hz filtered recording analysis. The overall noise amplitude at amplifier output is 74.5 uV, giving an input referred noise of 7.45 uV rms.
You mentioned in another thread, that a test signal you want to measure has an amplitude of 3.4 uV rms (10 uV p-p sine wave). As you can, see the expected signal to noise ratio is less than 0.5, meaning that your signal is unlikely to be recovered in a useful manner.
Your amplifier and recording setup will likely have much better performance with the amplifier set to higher gain. You should try repeating the measurements with the amplifier configured more appropriately for measuring signals of such a low amplitude (try a gain of 10k).
noise Vrms = 2.123V / 50k = 0.00004246 or 42.46uV rms... does it make sense? remember for my previous 10uV 50Hz signal you analyzed; the sine wave could still be resolved. Here the noise is much larger than it.
Should the noise density be about 45nV/Sqrt (Hz)? (5nV/Sqrt (Hz) for AMP01, 25nV/Sqrt (Hz) for LF412, 15nV/Sqrt (Hz) for other components like resistors in the circuit) Why 5.61nV/Sqrt(Hz)?
noise Vrms = 2.123V / 50k = 0.00004246 or 42.46uV rms... does it make sense? remember for my previous 10uV 50Hz signal you analyzed; the sine wave could still be resolved. Here the noise is much larger than it.
Something is wrong at 50k gain. The ADC is clipping, leading to severe signal distortion (You can see the "max sample 0 db" which indicates that the ADC has clipped). There is probably a DC offset somewhere. When doing these noise measurements, you are shorting the amplifier inputs to each other and to common, aren't you? If the inputs are properly shorted, you will need to adjust the DC offset on the amplifier to bring it back into range.
At these high gains, you may need to adjust the DC offset from time to time.QuoteShould the noise density be about 45nV/Sqrt (Hz)? (5nV/Sqrt (Hz) for AMP01, 25nV/Sqrt (Hz) for LF412, 15nV/Sqrt (Hz) for other components like resistors in the circuit) Why 5.61nV/Sqrt(Hz)?
That sounds about right - there are 2x LF412, 2x 5k resistors, and the rest of the amp. So, from datasheet figures that adds up to somewhere in the region of 40 nV/Sqrt Hz at 1 kHz.
noise Vrms = 2.123V / 50k = 0.00004246 or 42.46uV rms... does it make sense? remember for my previous 10uV 50Hz signal you analyzed; the sine wave could still be resolved. Here the noise is much larger than it.
Something is wrong at 50k gain. The ADC is clipping, leading to severe signal distortion (You can see the "max sample 0 db" which indicates that the ADC has clipped). There is probably a DC offset somewhere. When doing these noise measurements, you are shorting the amplifier inputs to each other and to common, aren't you? If the inputs are properly shorted, you will need to adjust the DC offset on the amplifier to bring it back into range.
At these high gains, you may need to adjust the DC offset from time to time.QuoteShould the noise density be about 45nV/Sqrt (Hz)? (5nV/Sqrt (Hz) for AMP01, 25nV/Sqrt (Hz) for LF412, 15nV/Sqrt (Hz) for other components like resistors in the circuit) Why 5.61nV/Sqrt(Hz)?
That sounds about right - there are 2x LF412, 2x 5k resistors, and the rest of the amp. So, from datasheet figures that adds up to somewhere in the region of 40 nV/Sqrt Hz at 1 kHz.
The inputs were not shorted but all floating. you mean I should short the +in, -in and ground together?
For the 10k gain. is the 46nV/Sqrt(Hz) (from 459.3uV/sqrt (Hz) /10000 gain) only for the 1kHz bandwidth selected or is it the formula for all bandwidth? I mean you multiply it by Sqrt (Hz bandwidth) to get the Vrms. but if the noise density is different for each bandwidth. how can you multiply each by Sqrt ( Hz bandwidth)? do you get what im saying here? I asked this several times pls elaborate on this. Many tnx.
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In the above I used 20Hz to 1000Hz in the distortion setting but the noise density didn't change, so it still integrates from 20Hz to 20kHz. How do you make it integrate over 20Hz to 1000Hz only? Also using the 200Hz flat response portion, the noise density is 1.323mV/Sqrt (Hz) / 50000 = 26.4nV/Sqrt (Hz). Still too low considering AMP01 has 5nV/rtHz and LF412 has 25nv/rtHz noise. It's not possible for the LF412 to become half noise only. That will be beyond milspec for them.
Can you manually try to integrate power density over frequency in the range above? using the V^2/Hz instead of V/Sqrt (Hz)? Would the result come close to 45nV/Sqrt (Hz)? Please compute.
Also I wonder if the gain of 50000 is really accurate. How do you test it? For example. For the 1.7Vrms in the E1DA. What voltage must appear in the 1 to -1 of Audacity. Is it 1.7Vrms? Maybe I can check whether 50000 gain is accurate by amplifying say 10uV x 50000 times to come up with 0.5V and see if it would tally with the 1.7Vrms setting? I can use peak to peak or rms in the 10uV no problem since I'm not sure if the 10uV in the Netech signal generator is peak-to-peak or rms.