Friday, July 16, 2010

Calculating DMM Accuracy and Resolution

The figure below shows the accuracy specifications for Agilent’s 34410A 6 ½ digit DMM from the data sheet. Let’s assume we are using the 34410A in the 10 V range, it was calibrated within the last 24 hrs, and we are measuring an exact 5 VDC source. We would use the parameters circled in red in the figure and the following formula to calculate the accuracy and useful resolution of our measurement: +/- (% of reading + % of range). For our hypothetical measurement the 34410A would measure: +/- ((5.0 x .000015) + (10.0 x .000004))--> 5.000115 V to 4.999885 V. Since the last digit does not give use any useful information the 34410A provides 6 ½ digits of resolution and the display would read between 5.00012 V and 4.99989 V.

Now that was pretty easy right? One important variable we need to add to the mix is measurement sample time. Sample time is how long the DMM’s internal ADC samples the voltage before integrating the measurement and displaying the result. In the accuracy calculation that we just did, it was assumed we were using the max sample time of 10 PLCs. PLC stands for power line cycle. In the US we use 60 Hz for AC power so 1 PLC is 16.667 ms (1/60). In other parts of the world 50 Hz is sometimes used so 1 PLC would be 20 ms. The DMM’s sample time units are typically based on PLCs. The more PLCs you sample over the better the accuracy you get (To a point). Of course longer sample times equal less throughput so as always there is a tradeoff. Let’s take the same measurement scenario using the 34410A we used above but this time we want to be able to make 10,000 measurements in 1 second. To do this we must set the DMM’s sample rate to 0.006 PLCs. Since our measurement sample time is so much lower we add another uncertainty part to our accuracy calculation. This is due to power line noise and our integration time is smaller so less random noise is being cancelled out. For the 34410A we add the RMS Noise Adder shown in the figure below circled in red.

Accuracy at the 10 V range for a 5 V measurement at 10,000 meas/s: ((5.0 x .000015) + (10.0 x .000004) + (10.0 x .000012))--> 5.00024 V to 4.99976 V. Once again the last digit in this calculation provides no information so there are only 5 digits of useful resolution. The 34410A’s display would read between 5.0002 V and 4.9998 V.
Be careful when purchasing a DMM that is advertised as having high resolution at high measurement speeds. You want to look at its specs and calculate its accuracy at that speed to ensure the advertised resolution is actually “useful” resolution if it isn’t your just paying for extra digits of random noise.
For more information on understanding DMM accuracy and resolution click here

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