# Automated voltage measurement: Tradeoff between PLC and averages

I am setting up an automated voltage measurement of a precision device. In my case, I am using a Keithley 2000 and controlling it over RS232 from MATLAB.

The voltages I am measuring have to be quite precise (more than 16 bit precision, resolution of tens of $\mu V$ on a $\pm4\ V$ signal). As such, I need to use some method to get low noise in my measurement. At the same time I need the measurement to be fast enough, since I need to repeat this measurement for every one of the boards $2^{16}$ possible outputs.

There are a few ways I can try to lower the measured noise, but I am not sure which is the best. The Keithley 2000, just like most bench multimeters, allows the user to set the measurement time (in number of power-line cycles) and apply filters. I want to work in multiples of a power-line cycle, so all noise from mains hum is canceled out as much as possible. Should I then use as much power-line-cycles as possible and lower number of measurements before averaging, or just 1 power-line cycle and then do a higher number of samples for averageing? For example, 3 measurements at 10 PLC versus 30 measurements at 1 PLC.

• What is the signal bandwidth? and Noise bandwidth besides 60Hz. What is the SNR ? Commented Mar 5, 2018 at 6:59
• Signal bandwidth is very low - this is a DC source. SNR of the measurement is on the order of 110 dB. Commented Mar 5, 2018 at 7:30

I know little about this but I expect that you need to sample at an odd number of mains half-cycles so that the noise cancels out.

Figure 1. The image shows hum superimposed on a steady signal. Each black 'x' is a sampling point and it should be reasonably obvious that sampling at any odd multiple of the half-wave time (every half-wave, every 3, every 5, etc.) will result in samples that alternate above or below or exactly on the signal. Averaging each pair of readings will eliminate the hum.

This approach is commonly used in industrial signal applications such as temperature controllers where a very low voltage signal is being measured and the sensor wires run in close proximity to mains cables.

Keithly themselves have published a book Low Level Measurements - Prcision DC Current, Voltage and Resistance Measurements. I'm looking at the 4th Edition but I haven't studied it. The Sixth Edition is available online.

• I should really get to reading that book... Its been on my computer for months now. I would think you need to measure in even mains half-cycles, since then you have an equal amount of positive and negative hum? EDIT: I now realize what you are saying. The difference here is that the meter (to my knowledge) integrates over the entire cycle - it does not take a single sample and then digitizes only that sample. (in fact, I don't think the DC measurement has a SaH?) Commented Mar 5, 2018 at 7:35
• In addition, it seems like Tektronix has now released the 7th edition of the low level measurements handbook : tek.com/document/handbook/low-level-measurements-handbook Commented Mar 5, 2018 at 9:10

If you have 30 powerline cycles available to do the measurement, how do you choose between asking the meter to do few long measurements, and many short measurements?

You have to read the data sheet very carefully, and back that up with actual measurements. If it's a good quality meter, and the designers have done their stuff, you ought to be able to rely on one long reading to provide the best result. But it's possible that that's not the case.

Do some experiments with a sequence of single readings, to understand what the variation is reading to reading with your measurement setup. Characterise the noise. Then repeat with a sequence of multiple readings. Compare. In the process, you're trying to verify the meter specifications, and I'll wager you will learn something about your test system that you hadn't anticipated. I always do!

It may be interesting to see how long it takes to do a single PLC measurement. Set your system up to take (say) 100 measurements. Does it take 100 PLCs, or 110, or 150, or 200? If 100, it's obviously pipelining measurement and reporting. If 110, it's able to time a single cycle from any phase, and not pipelining the report. If 150, sounds like it's going form zero cross to zero cross, but can use either. If 200, it sounds like it's always waiting for a particular polarity of zero cross to sync to. Each strategy has its costs and benefits.

• In general I think the Keithley 2000 is considered a very good meter. I am now realizing that most of the noise I was seeing was not the system but the environment - the DAC in question is having nanoampere LSB steps (which are then turned into voltages by a TIA), so just looking at it the wrong way will give errors. After covering the test setup in a sealed box, and switching to a coaxial cable for connecting the setup to the meter, the noise dropped significantly. This allowed me to more than half the time it will take to do the measurement! Commented Mar 5, 2018 at 7:33