## System Accuracy Calculations

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asauter@gmail.com
Newbie
Posts: 0
Joined: Tue Sep 01, 2020 6:47 pm

### System Accuracy Calculations

Background: we want to measure a differential signal (two actually hence we have eliminated PS 4262) from 0 ~ 150V and with a rise time of ~1us and 20 MS/s is desired, the instrument is battery powered but we may make a common reference via the charging port (hence we consider PS 4424).

Can you comment broadly on these figures and the PS 4444 specific questions?

Thank you all!

---Error estimate for PS 4444 with PicoConnect 442 1000V Probes
DC accuracy(to 10 kHz): 1%
Probe accuracy: 2%
Range Used: +/-10V
Actual signal range: 120 (voltage max of signal) / 25 (442 probe 1:25 attenuation)= 4.8V
Effective DC accuracy at 120V is 10V / 4.8 * 1% = 2.1%
System accuracy with sqrt of errors squared: sqrt ((2%)^2 (probe) + (2.1%)^2 (DC accuracy)) = 2.9%

4444 Questions:
1) silly question, can i turn off the bandwidth limit, specsheet says 100kHz and 1MHz, but not explicitly that it can be disabled
2) what accuracy can i expect >10kHz, we do want to characterize rise time with good precision

---Error estimate for PS 4424 with 1:10 Probes
DC accuracy: 1%
Probe accuracy: 1% (estimated)
Range Used: +/-20V
Actual signal range: 150 (voltage max of signal) / 10 (1:10 probe)= 15V
Effective DC accuracy at 120V is 20V / 12V * 1% = 1.7%
...since we are doing a differential/math measurement I 2x these error sources below, although the other side should be ~0V...
System accuracy with sqrt of errors squared: sqrty (2 x (1%)^2 (probe) + 2 x (1.7%)^2 (DC accuracy)) = 2.7%

4424 Questions
1) Is this probe accuracy too conservative? Could we calibrate to increase accuracy? Perhaps we could just use a precision resistor since bandwidth is not very high and we can dial in full-scale usage as well?

Gerry
PICO STAFF Posts: 697
Joined: Mon Aug 11, 2014 11:14 am

### Re: System Accuracy Calculations

Hi asauter@gmail.com,

I'm assuming that, you're considering using 4 channels to perform 2 negative and positive measurements, which you will then sum in a Math channel to give you the differential (which is why you ruled out a 2 channel device). However, that's unnecessary because you only need 2 channels to perform 2 differential measurements, using 2 differential probes (the probes do the summing already, no Math needed). So, if you want to perform a differential measurement, and were concerned enough about precision to consider the PicScope 4262, then you shouldn't rule it out.

Regarding your 1st 4444 question, I will answer that after you reply to my questions (I believe that you CAN turn it off, but I'm working from home without a PicScope 4444, so I'll need to double check when I go to the office at the beginning of next week).

Regarding your 2nd 4444 question, to help you further we need to be clearer on the parameters that are important to you. So, just to clarify some terms used, Precision is NOT the same as Accuracy. Precision is the smallest distance between 2 values that you can reliably measure, while accuracy is how close the measured value is to the actual true value (I''m sure that you don't, but in case you do need further clarification, there is an example below).
So, before commenting on your calculations, to determine where we need to focus in terms of errors, could you tell me the following:
1/ What are you measuring the voltage of?
2/ What is the reason (or goal) for the measurements that you want to make?
3/ What is more important to you, the actual value of a measurement or the difference between measurement values?

Regarding your 4424 questions, yes, you could go down the calibration for accuracy route, and send the scope and probes to a Cal Lab, to get a correction file. You could then use the correction file to create a Custom (higher accuracy) Probe in our software (but your calibrated values would drift out of accuracy much quicker, so you would need to either establish the minimum time period required before re-calibration, or you would need to get them re-calibrated before each set of measurements). But before we go there, let's establish if that's necessary by understanding what you need.
Regarding just using a precision resistor, it's not necessarily a good solution as the input and output impedance will also affect the precision (see here: topic39540.html?&p=140879&hilit=resistor+values#p140879) and the additional noise will reduce your dynamic range.

Precision vs Accuracy example
If we use the example of a digital thermometer with 0.01°C precision, and 2°C accuracy. If you read it and it indicates the temperature is 25°C, then you read it later and it indicates the temperature is 30°C, then you know that the temperature has risen by between 4.99°C and 5.01°C (high precision), but you can only be sure that the actual temperature is somewhere between 27.99°C and 32.01°C (low accuracy).

Regards,

Gerry

UPDATE

Yes, as expected, you can turn off the Bandwidth Limiter
Gerry
Technical Specialist

Gerry
PICO STAFF Posts: 697
Joined: Mon Aug 11, 2014 11:14 am

### Re: System Accuracy Calculations

Hi asauter@gmail.com,

Regarding your PicoScope 444 calculations and remaining question:

Input Range of ±10V = Full-Scale range of 20V, so DC accuracy is 4.2%, and System accuracy is 4.7%

The accuracy you can expect above 10kHz is the Analog Bandwidth, which is within -3dB up to 10MHz, with the 442 probe. So, as the input of our PicoScopes with probes connected can be approximated to a 1st order system, the (10/90) Rise Time would be 35ns (based on Rise Time = 0.35/[10*10^6] ). If the Rise Time measurement, from the DUT, turns out to be 35ns then the accuracy error would be approximately 8%. So, if you want to perform a more accurate measurement of Rise Time then you should use a PicoScope with a faster Rise Time than what is expected from the DUT (the greater the separation between DUT and Scope Rise Times, the greater the accuracy of the measurement) I can't be more specific than this without your response, so you can calculate the accuracy error of your measurement as:
(measured rise time)^2 - (rise time of the scope)^2.

Probe accuracy is 2% (input resistance on the x10 switch setting is 10 MΩ ± 2%), and again Range is 40V, so DC accuracy is 3.4%
If you're doing a Differential Math measurement, using 2 channels, then as you are summing a positive and zero value the error is just the positive value. So system accuracy is √( (2%)^2 + (3.4%)^2 ) = 3.9%
(BTW don't forget to check and compensate, if necessary, the response of the Probe to guarantee the specified accuracy: https://www.picotech.com/library/applic ... ope-probes)

However, if high precision is what you're looking for (and the bandwidth isn't too limiting) then the PicoScope 4262 with TA058 Probes will give you, not only the best accuracy, but by far the best precision (although at a cost).

Regards,

Gerry
Gerry
Technical Specialist

asauter@gmail.com
Newbie
Posts: 0
Joined: Tue Sep 01, 2020 6:47 pm

### Re: System Accuracy Calculations

An interesting suggestion we had not explored your other diff probes! I see that we could use the PS 4262 (\$1,235) with TA041 (also TA331 & PS008, qty 2 ea. For a total probe cost of \$966 ). Noting that it is 10 MS/s which is less than the 20 MS/s we wanted but that is not a hard requirement, can you confirm my error calcs?

PS range: 20V range
TA041 attenuation: 10:1
Actual Signal Range: We have 120V nominal signal (150V is abs max) attenuates to 12V
Effective DC Accuracy: 0.25% absolute accuracy at 40V full scale is 0.8% accuracy at 12V, 40V / 12V x 0.25% = 0.8% (I had confusion about using full scale or half scale for error figure)
System Error:sqrt( 2%^2 (probe error) + 0.8%^2 (DC error)) ~ 2.2%

Seems to be about ~2% accuracy (PS 4262 with probes total cost of ~\$2.2k) vs ~4% accuracy (PS 4424 with probes total cost of ~\$1.5k)

application questions
---
1/ What are you measuring the voltage of?
Battery powered medical device, with H bridge output
2/ What is the reason (or goal) for the measurements that you want to make?
Manufacturing Test Fixture
3/ What is more important to you, the actual value of a measurement or the difference between measurement values?
We require accuracy <10% (want our error budget to be <5% for comfort) due to the therapy and regulation, precision is not specified.

regarding a precision resistor to attenuate
---
1) a calibrated probe may drift (we would just calibrate at DC with a precision DMM, still I think it would help, and doubt significant drift)
2) we cannot easily calibrate out the input impedance to the picoscope presumably because of active circuitry (unless we had a precision source!)
3) using a resistor which would not have good impedance control may introduce error at higher frequency (since we are <3MHz I am hopeful this is not the case)

high frequency error
---
Very good, we are not too near the BW limit, but are approaching the sampling we want to properly characterize the rise-time.

FMI, Can you please provide the equation used to generate the 8% error figure?

Our application information...
Nominal waveform rise time: 350 ns
PS 4262 5MHz rise time equivalent: 70ns

Gerry
PICO STAFF Posts: 697
Joined: Mon Aug 11, 2014 11:14 am

### Re: System Accuracy Calculations

Hi asauter@gmail.com,

Accuracy on ±20V Input Range is ±0.25% of 40V = ±0.1V. For a measured value of 12V, an absolute accuracy of ±0.1V represents a percentage accuracy of ±0.83%. So you're correct.

Regarding the precision resistor
When calibrating for accuracy, the effective probe would be associated with (and need to be used with) the specific Input Channel of the Scope that was used during the Calibration, to be able to maintain the accuracy through to the measurement (the Cal Lab would typically indicate which Probe was used with which Input Channel). So the drift would relate to both the input channel and Probe. Because the specified accuracy error would be smaller, you would have a smaller range over which the performance can drift before it falls out of the Calibrated range. So, you would have a much shorter period for which the calibration would be valid.
However, you would only benefit from this if the Scope & Probe have significant non-linearity. If you actually use our Probes and PicoScopes, the PicoScopes are corrected in our production Test Process, the Probes are very linear anyway and, based upon your responses, your accuracy requirement is likely to be met by the existing accuracy of our products.

A significant source of error with the resistor would be noise, especially when compared to a differential Probe that is inherently quieter in construction, and has the benefit of Common Mode Rejection of noise. Noise represents the limit of precision, as you can't measure a small signal buried in noise, and precision affects accuracy as you can only measure the accuracy to the precision that you have available.

Regarding the High Frequency error
Sorry I wrote the calculation for the Actual rise time incorrectly. I should (of course) have written:
"...so you can can calculate the actual Rise Time of the DUT as:
( (measured rise time)^2 - (rise time of the scope)^2 ).
"
The scope should incorporate the Probe error, or more explicitly:
Actual DUT Rise Time = √( (measured rise time)^2 - (rise time of the scope)^2 - (rise time of the probe)^2 )

Also, there was a typo, in my last reply, in that my statement for percentage error should have been "If the Rise Time measurement, from the DUT, turns out to be 2.5 x 35ns then the accuracy error would be approximately 8%".

To get the percentage error the following calculations are done:
Measured Rise Time = √( [DUT Rise Time]^2 - [Scope and Probe Rise Time]^2 )
and % Rise Time Error = ( ( [DUT Rise Time] - [Measured Rise Time]) / [DUT Rise Time] ) x 100

So if we use the value that you gave for Nominal Waveform Rise Time (DUT Rise Time), and then calculate what the percentage errors would be in measuring the DUT Rise Time, at different orders of magnitude greater than the Rise Times of the Scope & Probe being used, (i.e. for each factor of [DUT Rise Time = factor x Scope & Probe Rise Time], we get the following results:

At factor of 1.5, Measured Rise Time is √(350^2 - 233.33^2) = 260.87. Percentage error is ( (350 - 260.87) / 350 ) x 100 = 25%
For 2, we have √(350^2 - 175^2) = 303.11 & error is ( (350 -303.11) / 350 ) x 100 = 13%
For 2.5, we have √(350^2 - 140^2) = 320.78 & error is ( (350 -320,78) / 350 ) x 100 = 8%
For 3, we have √(350^2 - 116.67^2) = 329.98 & error is ( (350 -329.98) / 350 ) x 100 = 6%
For 4, we have √(350^2 - 87.5^2) = 338.89 & error is ( (350 -338.89) / 350 ) x 100 = 3%
For 5, we have √(350^2 - 70^2) = 342.93 & error is ( (350 -342.93) / 350 ) x 100 = 2%

Bear in Mind that if the Probe Rise Time is fast enough, the System Rise Time is effectively that of the PS 4262 (which would be the case with the TA041).

The Spec we quote for Rise Time of the PS 4262 is calculated so, as your application would be using the Scope specifically for Rise Time measurements, we need to be clear on a more practical value of Rise Time. I will use a method to measure the approximate value, to give you some idea of what to expect. I used a source that has a Rise Time of 193ns, a method to set the 10/90 levels, and captured 50 data sets for measurement, as shown in the Images and psdata file below.
PS4262 - Measuring 193ns Rise Time.psdata

As you can see by scrolling through the captured values, and from the screen shots of the fastest and slowest measured values, the PS 4262 Rise Time capture measurements vary between 215 and 265 ns, which means that over a statistical sample of 50 the measurement will be 240ns ±9%. So, the Rise time of the Scope, by crude measurement is:
√(240^2 - 193^2) = 143ns ± 9%.
This would put the error of your measurement of a 350ns rise Time at 8%, however, the bigger issue here is that there is a large uncertainty for the value (±9% is for a statistical sample of only 50, so a much larger set of values would be needed for a more realistic indication of the spread of values). This uncertainty along with the accuracy would take the measurement outside your requirement. So, based on the values you gave, you need to consider a different PicoScope.

So, one series that you haven't considered is the 5000 series, which can be set to a resolution of 16-bits. They have much higher bandwidths so they would be ideal for Rise Time measurements. They also have good accuracy, however they also tend to have a higher noise floor than the 4000 series (this may not be such an issue on the Voltage Range you would be using).

So to sum up, I believe your best options are the PS 4224, and PS 5242D (their quoted Rise Times are better and more practical values). Hopefully, you now have a methodology and all of the calculations that you need to perform the analysis (if you need any further help, then let us know).

Best Regards,

Gerry
Gerry
Technical Specialist