Is my method of finding maximum peak-to-peak noise voltage valid?

[jonlg_uk]

Hello can somebody tell me if what I am doing is valid.

Ok I have a DVM measuring a AC noise voltage every 0.08 seconds (12.5 Hz)

This data is spat out in an excel sheet and looks like this:

Elapsed seconds noise voltage value
0 -2.88748E-07
0.079999998 -2.98099E-07
0.159999996 -2.22171E-07
0.239999995 -3.01465E-07
0.319999993 -2.21423E-07
0.399999991 -1.62701E-07
0.479999989 -2.6294E-07
0.559999987 -2.96602E-07
0.639999986 -1.57465E-07
0.719999984 -2.08332E-07
0.799999982 -2.88E-07
0.87999998 -1.98608E-07
0.959999979 -2.00852E-07
1.039999977 -2.16561E-07
1.119999975 -2.50971E-07
1.199999973 -2.71917E-07
1.279999971 -2.04592E-07
1.35999997 -2.89122E-07
1.439999968 -2.16187E-07
1.519999966 -2.3414E-07
1.599999964 -2.43865E-07
1.679999962 -2.85756E-07
1.759999961 -1.95615E-07
1.839999959 -3.31387E-07
1.919999957 -3.00717E-07
1.999999955 -2.93984E-07
2.079999954 -3.33257E-07
2.159999952 -2.88374E-07
2.23999995 -3.27647E-07
2.319999948 -3.12312E-07
2.399999946 -3.76644E-07
2.479999945 -3.71034E-07
2.559999943 -3.04457E-07
2.639999941 -3.03335E-07
2.719999939 -2.5733E-07
2.799999937 -2.73039E-07
2.879999936 -2.95106E-07
2.959999934 -3.50462E-07
3.039999932 -4.11428E-07
3.11999993 -3.94971E-07
3.199999928 -3.65797E-07
3.279999927 -3.59813E-07
3.359999925 -2.96228E-07
3.439999923 -3.04457E-07
3.519999921 -3.30639E-07
3.59999992 -3.34379E-07
3.679999918 -4.52571E-07
3.759999916 -4.26015E-07
3.839999914 -3.38119E-07
3.919999912 -4.21153E-07
3.999999911 -4.34244E-07
4.079999909 -3.83376E-07
4.159999907 -3.87117E-07
4.239999905 -4.27886E-07
4.319999903 -4.18535E-07
4.399999902 -4.86234E-07
4.4799999 -4.26389E-07
4.559999898 -5.13163E-07
4.639999896 -4.29008E-07
4.719999894 -4.39854E-07
4.799999893 -4.78753E-07
4.879999891 -4.85485E-07
4.959999889 -4.34244E-07
5.039999887 -5.59543E-07


So I want to find the maximum peak-to-peak noise voltage at 10Hz. To do this I subtract the voltage value at time=0 from the voltage value at time=0.1, or in this case 0.1599 seconds (as close to 0.1 seconds as I can get). I do this for each value, so next will be the voltage value at t=0.0799 seconds subtracted from the voltage value 0.2399 seconds and so on...I then search all the values to find the maximum peak-to-peak voltage with the time interval of 0.1599 seconds between them.

By doing this am I finding the maximum noise voltage at 10Hz?? Is this a valid method?

I have also done this for 0.5Hz (2 second time intervals) e.g I subtract the voltage value at t=0 second from the voltage value at t=1.999 seconds. However I noticed that when I do it for 0.5Hz the maximum peak-to-peak voltage now with a time interval of 2 seconds is lower than that of when I subsampled at 10Hz. I know why this is, its because of the longer time interval...but I have now started to question what the hell I am doing.


Please help...

I thank you all in advance.

J

 

[jonlg_uk]

I think I may have solved this...

before I was only subtracting the first and last voltage values, at the beginning and end of the time intervals, this is assuming that the peak voltage is at the beginning of the time interval and the minimum voltage is at the end of the time interval.

Instead I have now have ABS(MAX(C1:C3)-MIN(C1:C3)), where as before i had just =ABS(C1-C3) when subsampling at ~0.1Hz

 

[jonlg_uk]

However I would still really appreciate someone verifying that this is a valid method of sub sampling.


PLEASE HELP

 

[vk6kro]

No, the sampling rate is not related to the noise frequency.

You would have to filter the noise so you got only the 10 Hz spectrum of the source and then measure the voltage of that.


Also, there is no point in subtracting previous voltages. The voltage reading you get is the one you need to use.

Looks like a very nice DVM. Have you tried shorting out the terminals of the meter to see if it has internal noise?

 

[jonlg_uk]

Thanks for the reply.

No, the sampling rate is not related to the noise frequency.

I know. My post must of been unclear. However the maximum signal frequency that can be measured with the DVM with the NPLC set to 4 is 12.5 Hz frequencies above this are attenuated by the integration process.

You would have to filter the noise so you got only the 10 Hz spectrum of the source and then measure the voltage of that.

I am not sure what you mean. Why is this the case? Why can't you just sample at the DVM highest sampling frequency in this case it would be 12.5hz, limited by the NPLC setting.

Also, there is no point in subtracting previous voltages. The voltage reading you get is the one you need to use.

Can you explain in more detail please?

Looks like a very nice DVM. Have you tried shorting out the terminals of the meter to see if it has internal noise?

This is basically what I am doing. The values in listed above are a "sample" of voltage values taken with the input terminals shorted with copper wire. I am basically trying to find the internal noise floor of the meter. In order to find the theoretical limit of measurement with the DVM set to NPLC 4. Sorry if I wasn't clear. BTW it is a very expensive 8.5 digit meter.

thanks again.

 

[vk6kro]

You would just be taking a series of noise voltage readings, so each reading would not affect the next one. So you don't need to subtract them.

I think you need to see the actual waveform you are measuring.
I don't suppose you have an oscilloscope that let's you view half a microvolt do you? I don't, but if you have a multimeter like that, maybe you do.
Maybe it is just random noise or maybe it is hum pickup from nearby power sources.

It seems very variable which suggests it might be samples of different parts of a hum waveform.

 

[jonlg_uk]

You would just be taking a series of noise voltage readings, so each reading would not affect the next one. So you don't need to subtract them.

I don't understand?

I think you need to see the actual waveform you are measuring.

Why?

I don't suppose you have an oscilloscope that let's you view half a microvolt do you? I don't, but if you have a multimeter like that, maybe you do.
Maybe it is just random noise or maybe it is hum pickup from nearby power sources.

It seems very variable which suggests it might be samples of different parts of a hum waveform.

A osscilloscope is not sensitive enough to measure microvolts.




I just want to measure the noise that the DVM measures when its input terminals are shorted (with copper wire). I am not really bothered about where the noise is coming from at the moment I am just assuming that all the noise I am seeing is due to the noise floor of the meter. Afterall the input terminals are shorted and meter is inside a Faraday cage, and there is a good filter on the power supply.

All I want to know is how to measure the peak-to-peak voltage noise at 10Hz and 0.5Hz. At the moment to do this for 10Hz I use excel to search for the maxium amplitude signal in a 0.1sec time interval, I then search for the minium amplitude signal and subtract them from each other. I move to the next 0.1sec time interval in the data and do the same thing, I then move to the next time interval and repeat over all the voltage data values. Doing this is giving me my peak-to-peak voltages at 10Hz or 0.1 second . I do the same for 0.5Hz but in this instance the time interval is 2 seconds.

The figure below shows what a typical plot of DVM sampled data looks like:

I would of thought that a rough estimate of the 10Hz noise would be the equivalent "thickness of the line" on the top graph?

 

[jonlg_uk]

I guess my main question is why I can't sub-sample as I am doing? Why is it not a valid method. I need this explained to me in laymans terms.

 

[vk6kro]

The problem is that you can't tell if you are sampling a waveform at the same place on the waveform each time you sample.

If you sample at a low point each time, you could get an abnormally low reading, for example.

What are you going to measure eventually?
What would the signal level be?

 

[jonlg_uk]

The problem is that you can't tell if you are sampling a waveform at the same place on the waveform each time you sample.

No I won’t be sampling the waveform at the same place each time I sample, but my purpose is to find the peak-to-peak noise voltage at a given frequency of a random noise signal. To do this I first look for the maximum noise voltage and then the minimum noise voltage in a given time interval and subtracting these values from each other. So for 0.5Hz, I look at a 2 second time interval in the data, find the maximum voltage in that interval, then the minimum and subtract the values from each other to derive the peak-to-peak voltage for that frequency. Please see my excel screenshot below, hopefully this should explain what I am doing:

If you sample at a low point each time, you could get an abnormally low reading, for example.

I am sampling at the “highest point” and the “lowest point” in a given time interval. So if I wanted to subsample at 0.5Hz I subtract the highest point in that time interval by the lowest point.

What are you going to measure eventually?
What would the signal level be?

First I need to characterize the noise floor of the DVM, then I will be using the DVM to measure the noise produced by a HV power supply, using a resistive divider to step it down to 10V output. I will be looking to measure a 1ppm/10uV in 10V.


Thanks


J

 

[jonlg_uk]

sorry to bump this again, but bump.

 

[sophiecentaur]

If you want the right answer, you need a Nyquist (low pass, anti-aliassing) filter before your sampling circuit or you don't know what frequency of noise in your system is being interpreted as any particular frequency in your data.
If you are interested in noise at other frequencies, you can still sub-sample but you will need the appropriate band pass filters to restrict the input frequency range to within a bandwidth less than half the sampling frequency.
PS The noise floor that your DVM will show you can be due to noise over a whole band of internally generated frequencies and you can do nothing about that except to do some very long term averaging of data with no input and with input.
If you are really fussy, you would need to measure your internal noise with the input terminated with a resistor of the same value as your source signal.

 

[jonlg_uk]

If you want the right answer, you need a Nyquist (low pass, anti-aliassing) filter before your sampling circuit or you don't know what frequency of noise in your system is being interpreted as any particular frequency in your data.
If you are interested in noise at other frequencies, you can still sub-sample but you will need the appropriate band pass filters to restrict the input frequency range to within a bandwidth less than half the sampling frequency.

Hi sophiecentaur, it seems like you always come to my rescue lol.

I can't get my head around why I need a filter before my sampling circuit.

My DVM has a cut off frequency of 12.5Hz (it samples every 0.08 seconds).

I don't think Nyquist principles apply here because my excel equation (refer to pic ) is "searching" for the maximum and minimum voltage in a specific time interval* and subtracting these values from each other to derive a peak-to-peak voltage at a subsampled frequency** of 0.5Hz and 10Hz (the pic only shows it for 0.5Hz). What I am effectively trying to do is to calculate the peak-to-peak voltage of a random noise at a sub-sampled frequency.

* In theory I should be able to subsample all the way upto 12.5Hz, the sampling frequency on the DVM (shouldn't I?)

**The time interval interval i.e. the C51:C76 part, DICTATES the sub-sample frequency. The MAX bit finds the maximum voltage and the MIN finds the minimum voltage. These are subtracted from each other to find the peak-to-peak voltage at a specific subsampled frequency.

Look at the pic of my excel sheet do you understand what I am doing??


Thanks a bunch

J

 

[sophiecentaur]

I'm using my phone and can't look at big stuff but your DVM samples will not distinguish between in band and out of band signals. No post processing can solve that prob. Sub sampling can be sorted for input signals with filtering, though. To find the internal noise level I think you should find the RMS of all your samples with a zero volts input.

 

[jonlg_uk]

I'm using my phone and can't look at big stuff

I will leave it until you get some time to cast your eye on my excel pic that I posted, hopefully it will clear things up.

but your DVM samples will not distinguish between in band and out of band signals. No post processing can solve that prob.

I have a specification that I must adhere to. That is my measurement system (resistive divider) must be quiet enough to enable sub-ppm measurements of a HV power supply for frequencies between of 0.5Hz and below. Thus the time interval that I am defining in my excel sheet allows is 2 seconds, I search the first 2 seconds (and subsequent 2 sec intervals after that) of the output voltage measurement for the maximum voltage and I search it for the minimum voltage and subtract these values from each other to find the peak-to-peak voltage at 0.5Hz...

Sub sampling can be sorted for input signals with filtering, though.

I don't understand why I need filtering to do this.

To find the internal noise level I think you should find the RMS of all your samples with a zero volts input.

I have zero volts input at the moment, I have a short across the input terminals of the DVM. I think you mean post process the data to get rid of any DC offset? This is kind of difficult as its varying positive and negative, but its doable. Thanks again. J

 

[vk6kro]

A digital voltmeter takes an instantaneous sample-and-hold "snapshot" of the incoming waveform and then goes through an integration process to work out what the voltage is.

So, your DVM may be taking 1 μS snapshots and then not looking again for 150000 μS.

You have no way of knowing what happens in that other 150000 μS.

There is also no reason to say that this 1 μS snapshot will capture a peak in that time slot. It is just a snapshot and it may or may not be a minimum, an average or a peak value.
It certainly won't somehow affect the next reading.


Resistors become very noisy when you put high voltages on them. You should be using a commercial high voltage probe (with known noise performance) and viewing the noise on an oscilloscope. You can use the AC/DC switch on an oscilloscope to get rid of the DC component and observe just the noise.

 

[sophiecentaur]

Sampling theory has to apply to all sampling processes, surely. If you cannot do anything about pre-filtering of your signal then you need to include a strong caveat in any assessment of results you produce.
However, it may be that your DVM already does this Nyquist filtering for you. You could check by applying a range of LF tones to it and see what it 'thinks' is there. If your sampling is at 12.5 Hz then first see what it thinks of a 3Hz tone, then a 5HZ (both of these are Kosher) then try 9.5HZ and 7.5Hz and 15.5, 17.5 etc. Unless there is some filtering, the results for the higher frequencies will be indistinguishable from the 3 and 5Hz results. Without this assurance, how can you tell that the noise signals that your varying samples contain are, in fact, the in band noise you are looking for? There will always be a degree of filtering, inherent in the sampling process which would ideally be 'instantaneous' but takes a finite time so will have an inherent LP filtering (but only enough to remove relatively high frequencies)

Also, because of the statistics of noise, it is not usual practice to talk of "peak noise" values because this will depend on chance. Noise is usually specified as a Power (alternatively, an RMS value) which avoids this problem*. It would not be difficult to find your noise floor this way by finding the standard deviation of the DVM output with no input and you will have an 'accepted measure' for it. This value for the noise floor can then be used to give a measure of the uncertainty of your results.
*Audio SNR is usually specified in terms of Peak Signal to RMS noise, for instance.

 

[jonlg_uk]

Sampling theory has to apply to all sampling processes, surely. If you cannot do anything about pre-filtering of your signal then you need to include a strong caveat in any assessment of results you produce.

I cannot use any filter the results that I have were collected a while again and I no longer have access to the DVM or the resistive divider

However, it may be that your DVM already does this Nyquist filtering for you. You could check by applying a range of LF tones to it and see what it 'thinks' is there. If your sampling is at 12.5 Hz then first see what it thinks of a 3Hz tone, then a 5HZ (both of these are Kosher) then try 9.5HZ and 7.5Hz and 15.5, 17.5 etc. Unless there is some filtering, the results for the higher frequencies will be indistinguishable from the 3 and 5Hz results.

I have done this before. Unfortunately I cannot find the result but I remember conducting 2 tests; both tests involved connecting a 50Hz signal generator to the 8 1/2 DVM. The NPLC was set to 4, the reason for choosing 4 power line cycles is because we are trying to measure low frequency noise from 10 Hz to 0.5Hz. When the NPLC is set to 4 the DVM will only attenuate the 10Hz signal by a negligible amount, if the NPLC is greater than 4 then the attenuation on a 10Hz signal starts to become noticeable. If you were to change the NPLC setting and keep the frequency constant here is what happens:

A 60 Hz sine waveform 1V p-p 60 Hz ac voltage with 5V dc offset. The results show the voltage measured for each NPLC value across 20 readings.

Without this assurance, how can you tell that the noise signals that your varying samples contain are, in fact, the in band noise you are looking for?

Because I am evaluating the voltage samples in a time interval across the whole 2 seconds (0.5Hz) and because it is random noise (non periodic in nature) the peak-to-peak voltage will occur at different places within that 2 second interval of voltage data. I am saying that if the peak-to-peak voltage, REGARDLESS* of where it takes place in that 2 second time interval, is greater than the sub-ppm resolution that my measurement system is aiming for, then I know that the noise floor of the DVM is too much.

*As the noise data contained in that 2 second interval will be random the max and min will could occur anywhere in that interval. The excel code evaluates all the data points gathered in that 2 second interval to find the max and min. So for a 2 sec interval it will evaluate 25 (2/0.08) samples to find voltage max and mins.

Also, because of the statistics of noise, it is not usual practice to talk of "peak noise" values because this will depend on chance. Noise is usually specified as a Power (alternatively, an RMS value) which avoids this problem*. It would not be difficult to find your noise floor this way by finding the standard deviation of the DVM output with no input and you will have an 'accepted measure' for it. This value for the noise floor can then be used to give a measure of the uncertainty of your results.
*Audio SNR is usually specified in terms of Peak Signal to RMS noise, for instance.

For this project quoting the noise floor in RMS is not suitable because I am trying to build a resistive divider that has a sub-ppm resolution. Therefore if the DVM or any other component for that matter was to produce say a 10Hz spike, greater than the desired resolution that my project specification is aiming for then it would invalidate my results. The raw voltage data that my DVM is gathering consistently needs to be an order of magnitude below that of the resolution of voltage that I want to measure with this resistive divider - I just want to ensure than this is the case with the DVM.

.

 

[jonlg_uk]

A digital voltmeter takes an instantaneous sample-and-hold "snapshot" of the incoming waveform and then goes through an integration process to work out what the voltage is.

So, your DVM may be taking 1 μS snapshots and then not looking again for 150000 μS.

You have no way of knowing what happens in that other 150000 μS.

There is also no reason to say that this 1 μS snapshot will capture a peak in that time slot. It is just a snapshot and it may or may not be a minimum, an average or a peak value.
It certainly won't somehow affect the next reading.


Resistors become very noisy when you put high voltages on them. You should be using a commercial high voltage probe (with known noise performance) and viewing the noise on an oscilloscope. You can use the AC/DC switch on an oscilloscope to get rid of the DC component and observe just the noise.

Hi vk6kro as I said I no longer have access to this DVM or resistive divider, the results I collected are from a while ago. I understand what you are saying with the integration process, but there is nothing I can do to change that. I had to set the NPLC to 4 in order to get rid of 50 hz (UK) power line interferance. This meant a minimum sampling time of 0.08sec. But you make a good point. This integration process might be obscuring what is ACTUALLY HAPPENING because the real noise is just getting integrating away. Unfortunately there is nothing I can do now, but I will defiantly include that point in my write up.

 

[sophiecentaur]

Quote by sophiecentaur
Without this assurance, how can you tell that the noise signals that your varying samples contain are, in fact, the in band noise you are looking for?

And your reply:
Because I am evaluating the voltage samples in a time interval across the whole 2 seconds (0.5Hz) and because it is random noise the peak-to-peak voltage will occur at different places within that 2 second interval of voltage data. I am saying that if the peak-to-peak voltage, REGARDLESS of where it takes place in that 2 second time interval, is greater than the sub-ppm resolution that my measurement system is aiming for, then I know that the noise floor of the DVM is too much.

I think you have missed my point completely here. Once your subsampling had 'folded down' the original high frequency information it is mixed in with the wanted. in band information and no amount of averaging out will get rid of it. A spike from a 30Hz signal will look the same as the spike from a 5Hz signal to your analysis.

I'm not sure that I see a connection between the measurements you say you did with a simple frequency response measurement which I was suggesting, in effect.

I also have a problem with your use of peak noise. The DVM and the HV power supply can be producing random noise spikes. If you know (or assume) the amplitude distribution of the two forms of noise then cannot the statistics of an occasional DVM noise spike be factored into the appearance of noise from your power supply to arrive at a measure of the significance what you are measuring? It's surely statistics that you are dealing with and if you have enough mass of data, you can find out how significant the power supply contribution is to the data fluctuations, compared with the DVM. Number of 'spikes' with and without an input would be a simple comparison, for instance.

If the power supply is DC, then I am surprised that you didn't AC couple to it to find your noise. You could have been operating way above the DVM noise floor - particularly if you had used a suitable amplifier. But that's water under the bridge, of course.

 

[jonlg_uk]

So when I am evaluating to see if my DVM can permit measurements of my desired resolution at 0.5Hz I need to look over the entire 2 second interval (1/0.5) and say "If a noise signal of 0.5Hz or GREATER occurs in the 2 second interval AND the peak-to-peak voltage is greater than what my system specification calls for, then the DVM is not suitable for not capable of achieving my desired measurement resolution at 0.5Hz and GREATER frequencies (the greatest frequency being 12.5 Hz)"

 

[jonlg_uk]

So when I am evaluating to see if my DVM can permit measurements of my desired resolution at 0.5Hz I need to look over the entire 2 second interval (1/0.5) and say "If a noise signal of 0.5Hz or GREATER occurs in the 2 second interval AND the peak-to-peak voltage is greater than what my system specification calls for, then the DVM is not suitable for not capable of achieving my desired measurement resolution at 0.5Hz and GREATER frequencies (the greatest frequency being 12.5 Hz)"

Sorry I posted this without reading your last comment. But does what I said above^ make sense ? I will try and get my head around what you just said...please bare with my "slowness" in this subject area.

 

[sophiecentaur]

So when I am evaluating to see if my DVM can permit measurements of my desired resolution at 0.5Hz I need to look over the entire 2 second interval (1/0.5) and say "If a noise signal of 0.5Hz or GREATER occurs in the 2 second interval AND the peak-to-peak voltage is greater than what my system specification calls for, then the DVM is not suitable for not capable of achieving my desired measurement resolution at 0.5Hz and GREATER frequencies (the greatest frequency being 12.5 Hz)"

Reading this makes me wonder how you arrived at a 'desired measurement resolution' defined in this way. The nature of noise is that it tends to be random and there is no 'maximum noise pulse amplitude'. (Of course, once amplified, there is always the limit imposed by the system supply volts, but that's not relevant). The reason that noise is usually specified in terms of its RMS value is that it can be measured relatively quickly and reliably (you don't need to wait for a particularly high peak and, even if you did, you wouldn't know that was the highest one likely to occur).
I am wondering how you could best specify the 'noise performance' of your HV supply and how to modify what the DVM tells you, in the light of its own noise performance. It strikes me that you are after something more akin to 'error rate' in a simple digital system, where what is of interest is the statistics of the number of times a 0 becomes a 1 and vice versa. In that case, when the noise is 'well behaved' (e.g. Gaussian) the statistics come straight from the RMS value and, if it's not, you need to look further and do actual error measurements. If, in your case, you can decide on an acceptable level of noise spike, below which the system 'works' and above which it 'fails'. Then the average rate of DVM 'errors' (input just terminated) can be subtracted from the rate you measure when connected to the PSU to give you a good idea of what the PSU is introducing. The advantage of this method is that you have all the data for this and you can easily vary your decision level. The only problem is that you cannot be totally sure about the possible effect of the sub sampling.

Could you say what the effect of PSU noise has on the equipment it's supplying? Presumably we'd be totally in the 'non-sampled world' for that.

 

[jonlg_uk]

Reading this makes me wonder how you arrived at a 'desired measurement resolution' defined in this way. The nature of noise is that it tends to be random and there is no 'maximum noise pulse amplitude'. (Of course, once amplified, there is always the limit imposed by the system supply volts, but that's not relevant). The reason that noise is usually specified in terms of its RMS value is that it can be measured relatively quickly and reliably (you don't need to wait for a particularly high peak and, even if you did, you wouldn't know that was the highest one likely to occur).
I am wondering how you could best specify the 'noise performance' of your HV supply and how to modify what the DVM tells you, in the light of its own noise performance. It strikes me that you are after something more akin to 'error rate' in a simple digital system, where what is of interest is the statistics of the number of times a 0 becomes a 1 and vice versa. In that case, when the noise is 'well behaved' (e.g. Gaussian) the statistics come straight from the RMS value and, if it's not, you need to look further and do actual error measurements. If, in your case, you can decide on an acceptable level of noise spike, below which the system 'works' and above which it 'fails'. Then the average rate of DVM 'errors' (input just terminated) can be subtracted from the rate you measure when connected to the PSU to give you a good idea of what the PSU is introducing. The advantage of this method is that you have all the data for this and you can easily vary your decision level. The only problem is that you cannot be totally sure about the possible effect of the sub sampling.

Could you say what the effect of PSU noise has on the equipment it's supplying? Presumably we'd be totally in the 'non-sampled world' for that.

The equipment is a mass spectrometer (MS) and is considered “supply critical”, that is the quality of the results that it outputs will be directly related to the noise of the power supply. So it is no good me quoting to the customer that the HV power supply has a RMS noise of X Vrms when it is the amplitude of the noise that effects their readings. Quoting the RMS would be obscuring what is really going on. They are interested in the amplitude of low frequency noise and drift signals as this is what MS are most sensitive to.

Your suggested method of finding the rate of DVM 'errors' and subtracting this from the rate I measure when connected to the PSU to give you a good idea of what the PSU is introducing is a good idea, but I don’t think I can do this at this stage. I just need to prove to the customer that the noise produced by the DVM was low enough to permit the reliable sub-ppm measurements.

BTW I made a mistake here:

So when I am evaluating to see if my DVM can permit measurements of my desired resolution at 0.5Hz I need to look over the entire 2 second interval (1/0.5) and say "If a noise signal of 0.5Hz or GREATER occurs in the 2 second interval AND the peak-to-peak voltage is greater than what my system specification calls for, then the DVM is not suitable for not capable of achieving my desired measurement resolution at 0.5Hz and GREATER frequencies (the greatest frequency being 6.25 Hz – its 6.25 Hz because this is the Nyquist frequency of the DVM, before I said it was 12.5Hz but if a signal of 12.5Hz did exist it would get fully integrated by the DVM)"

 

[sophiecentaur]

The more I think this over, the more confused I am becoming.
Your noise level is specified using a combination of frequency domain and time domain and I think that needs care. Are you doing some FT on the data to reveal the frequency components? You seem to be involving the amplitude of a frequency component and referring to the 'peak to peak' voltage. Depending on the phases of the components, the peak to epak voltage could vary (?).
You refer to "sub ppm" measurements when I should have thought that would be normally specified in dB (no?).
However, if they have already given you a required specification for the PSU, all you need to do is to use the same spec for the DVM and hope you have an order of magnitude difference. I should think that, as you are comparing two sources of noise, it would be advisable to use the same criterion for both.

 

[jonlg_uk]

The more I think this over, the more confused I am becoming.
Your noise level is specified using a combination of frequency domain and time domain and I think that needs care. Are you doing some FT on the data to reveal the frequency components? You seem to be involving the amplitude of a frequency component and referring to the 'peak to peak' voltage. Depending on the phases of the components, the peak to epak voltage could vary (?).
You refer to "sub ppm" measurements when I should have thought that would be normally specified in dB (no?).
However, if they have already given you a required specification for the PSU, all you need to do is to use the same spec for the DVM and hope you have an order of magnitude difference. I should think that, as you are comparing two sources of noise, it would be advisable to use the same criterion for both.

The more I think this over, the more confused I am becoming.

Ok I will try and break it down what I want to achieve. I would be grateful if you could verify if this methodology is valid.

Your noise level is specified using a combination of frequency domain and time domain and I think that needs care. Are you doing some FT on the data to reveal the frequency components? You seem to be involving the amplitude of a frequency component and referring to the 'peak to peak' voltage. Depending on the phases of the components, the peak to epak voltage could vary (?).

I thought about FFT'in the data, but the customer requires that the resistive divider measurement system permit measurements of better than 0.2ppm of PS noise. The output voltage of the resistive divider is 10V, the input PS under test voltage is 15kV. Thus and order of magnitude below 0.2 ppm is 0.2uV. In addition the customer is specifically focused on low frequency noise and drift. They really don't want to see the resistive divider or DVM producing low frequency noise, which is defined as frequencies between 0.5Hz and 10Hz or drift, which is defined as 0.5Hz and below. They are not to bothered about high frequency spikes as these effect the mass spectrometer readings less.

N.B The customer is VERY strict, they say that even if the resistive divider or DVM produces one rogue reading that is greater than 0.2uV then the project can not go ahead as they will not be able to distinguish between the noise being generated by the PS or that being generated by the DVM or resistive divider.

The rationale for the way I am processing the data is this.

1. The DVM integrates over a number of power line cycles. In this case I have set the DVM number of power line cycles (NPLC) to 4, thus it is integrated over 0.08 seconds (1/50Hz*4). I have to set the DVM to 4 - assume this cannot be changed. This means that the DVM samples every 0.08 seconds or at 12.5Hz.

2. Now I want to first test the performance of the DVM to ensure that its internal noise is an order of magnitude less than 2ppm, i.e. I want to see if the peak to peak at a given frequency is less than or equal to 0.2uv. To do this I short the input terminals with copper wire. I take a series of measurements with the DVM with the NPLC set to 4 and see that there is noise and drift present from a voltage against time graph. Now I admit I don't know where that noise came from, was I "unlucky", did the DVM sample at the same time a high frequency spike occurred (but the spikes should be "integrated out" anyway by the NPLC setting), or was I "lucky" and the DVM missed all the spikes and only sampled at "quiet" times in the measurement? Either way I have repeated the measurements enough times to be confident that what I see is CONSISTENT i.e there is nothing "odd" on any of the graphs.

3. Ok so each time perform the measurement the data looks similar by eye i.e there is no spurious spikes of ultra quiet readings despite the voltage Vs time graphs randomly varying with the internal noise of the DVM. So I know that there is a good chance that the DVM is producing noise and order or magnitude below that of what the specification demands.

4. Now the customer is particularly concerned with low frequency noise between 0.5Hz and 10Hz and drift below 0.5Hz. Now first let's JUST pick on the noise between 0.5Hz and 10Hz. So I look at my data and say "for each 2 second (1/0.5Hz) interval that occurred did a peak-to-peak voltage occur that was greater than 0.2uV?". Now let's swap the notion of a non-periodic noise signal for a periodic sine wave so it makes this easier to imagine. Let's say the sine wave has a period of 1 second (1Hz) and a peak-to-peak voltage of 0.2uV . The excel sheet comes along and says "for the first 2 seconds worth of data, Sample 1 to Sample 25 (25 samples because 25=2 seconds/0.08seconds), did the peak-to-peak voltage go above 0.2uV?". To answer this question it searches for the maximum voltage value, then the minimum voltage value in samples 1 to 25, and subtracts them from each other. Let's say that the DVM samples the wave when the positive and negative amplitude is only at 0.05uV giving a peak-to peak voltage of ONLY 1uV i.e within spec. 5. Dam it! We have missed the REAL max and mins of the sine wave. However all is not lost, the excel sheet shifts up a block of 25 samples so it now evaluates samples 2 to 26. It might still miss the maximum and minimum voltage. However if it continues this process it will eventually find them! Once it finds them we can say whether or not the specfication that the customer wants is possible with the DVM we have (If the DVM isn't capable of the measurement then its pointless going any further).6. Ok so the Excel sheet has eventually found the REAL/MAXIMUM peak-to-peak amplitude of 0.2uV. But at what frequency did it occur? Can we tell? Well I know that because I sampled and evaluated a time interval of 2 seconds that the frequency of the wave must be between 0.5Hz and 6.25Hz and this happens to be a BW that the customer is particularly interested in. Remember when I said they define low frequency noise as 0.5Hz to 10Hz. (The reason why its 6.25Hz is because this is half the frequency of the sampling frequency 12.5 Hz i.e. the highest frequency that I can subsample, a 12.5Hz signal should get integrated away the fact that the NPLC is set to 4 on the DVM).

7. So I can go back tell the customer that I measured a REAL/MAXIMUM peak-to-peak voltage amplitude of 0.2uV, I know that this signal must be between 0.5Hz and 6.25Hz because I evaluated all the sampled over 2 seconds. and this 2 seconds will include all the data that contains signals from 0.5Hz to 6.25Hz (the limit of the DVM). I know that these are the frequencies that you are most concerned with and I know that if you spot this occurring even once over the measurement it will shake your confidence in the ability to fulfill the specification, thus we can/cannot go any further with this project. I hope you can follow what I am trying to achieve.

Thanks a bunch!

J

 

[sophiecentaur]

My first response is that they haven't asked for a meaningful measure of noise. Noise needs to be specified as RMS in a given bandwidth or some other measure of the statistics. I suggest that they may feel that they are being "strict" but they may not be as well informed as they think they are. You should ask them for clarification, I think.
This all involves exceptionally low frequencies but the same basics of noise and error statistics still apply. (How can it not be so?)
The output of your DVM is only a set of samples of amplitude in a time window of 2s. There is no assurance that, just outside this window, there is not a noise spike that exceeds any sample in your set. There is no assurance, either, that any spikes you see don't correspond to a very sharp spike that has virtually no energy at all in-band but your sampling circuit has happened to pick it up (unless your input signal is specifically band limited.
You really need to read something about the nature of noise and sampled signals before you can proceed further, I'm afraid. The good news is that I don't think your customer knows any more than you do!

Your conclusion point 7, is surely in error. You have a set of time domain samples so you can't say anything about the frequencies involved unless you know about the pre filter. For all you know, the noise waveform you are seeing could all be due to out of band components in the original signal. Please read something about sampling theory and why pre-filtering is essential.