DC Source Measurement Accuracy and Resolution – With Shorter Measurement Intervals

I had gotten a customer support request a while ago inquiring about what the measurement resolution was on our new family of N6900A and N7900A Advanced Power System (APS) DC sources.  Like many of our newer products they utilize a high-speed digitizing measurement system.

 “I cannot find anything about measurement resolution in the user’s guide, it must have been overlooked!” I was told. Indeed, we have included the measurement resolution in the past on our previous products. We did not include it as a single fixed value this time around, not as an oversight however, but for good reason.

Perhaps the most correct response to the inquiry is “it depends”. Depends on what? The effective measurement resolution depends on the measurement interval that is being used. Why is that? Simply put, there is noise in any measurement system. With older and more basic products that provide low speed measurements and inherently have a long measurement interval that the voltage or current signal is integrated over, measurement system noise is usually not a big factor. However, with the higher speed digitizing measurement systems we now employ in our performance DC sources, factoring in noise based on the measurement interval provides a much more realistic and meaningful answer.

For the N6900A and N7900A APS products we include Table 1 shown below, in our user’s guide to help customers ascertain what the measurement accuracy and resolution is, based on the measurement interval (i.e. measurement integration period) being used is.

  

Table 1: N6900A/N7900A measurement accuracy and resolution vs. Measurement interval

This table is meant to provide an added error term when using shorter measurement intervals. We use 1 power line cycle (1 NPLC) as the reference point at the top of the table, for the measurement accuracy provided in our specifications. This is a result of averaging 3,255 single samples together. By doing this we have effectively spread the measurement system noise over a greater band and filtered it out by the averaging. For voltage measurements the effective resolution is over 20 bits.

Note now at the bottom of the table there is the row for one point averaged. It is for 0.003 NPLCs, which is 5 microseconds, the sampling period of the digitizer in our DC source. For a single sample the effective measurement resolution is now 12.3 bits for voltage. Note also we provide an accuracy error adder term of 0.02%. This is taking into account the measurement repeatability affecting the accuracy.

A convenient expression for converting from number of bits to dB of signal to noise (SNR) for a digitizer is given by:

SNR (dB) = 6.02 x n (# of bits) + 1.76

The 12.3 bits of effective resolution equates to 75.8 dB of SNR, which is very much in line with what to expect from a wide band, high speed digitizing measurement system like what is provided in this product family.

As previously mentioned the effective measurement resolution is over 20 bits for a 1 NPLC measurement interval. This actually happens to be greater than the actual ADC used. While there is less resolution when using shorter measurement intervals, conversely greater resolution can be achieved by using longer measurement intervals, which I expect to talk more about in a future posting here on “Watt’s Up?”!

In the meantime this is just one more example of how we’re trying to do a better job specifying our products to make them more useful and applicable in ascertaining what their true performance will be in one’s end application.

Power Supply Resolution versus Accuracy

One of the questions that we have received on the support team quite a few times and something that confused me when I started at Agilent is the concept of our resolution supplemental characteristic versus our accuracy specification.  I sat down with my colleague Russell and we wanted to do a simple explanation of the differences. 

If you look at our power supply offering, there is always an accuracy specification and a resolution supplemental characteristic for both programming and measurement.  For the purposes of this blog post, we are going to look at the programming accuracy (0.06% + 19 mV) and programming resolution (3.5 mV) of the N6752A High Performance DC Power Module.  Please note that these same explanations apply to the measurement side as well but for the sake of brevity we will be sticking to programming in our example.  

Let’s start by talking about resolution.  Our power supplies use Digital to Analog Converters (DACs) to take the user inputted settings and convert them to analog signals that set a programming voltage that will interact with the control loop of the power supply to set the output.  The resolution supplemental characteristic represents one single count of the DAC.  This is also known as the Least Significant Bit (LSB).  What this means for our end user is that the smallest step they can make between two settings on the unit is the programming resolution number.  In our example, the N6752A can be set to 0.9975 V, 1.001 V, 1.0045 V, etc.  These are all multiples of 3.5 mV and any setting that falls between two DAC counts will be put into the nearest count.  If the user tried to set the N6752A to 1 V, the power supply will actually be set to 1.001 V since that is the nearest count.  This is also known as quantization error. 

The accuracy specification always includes an error term for the quantization error.  This is typically half of the resolution supplemental characteristic.  The accuracy specification also includes many other factors such as DAC accuracy, DAC linearity, offset error of operational amplifiers, gain errors of the feedback loops, and temperature drift of components.   The accuracy will always be worse than the resolution since it includes all of the factors listed above as well as the term for the quantization error.  You can definitely see this in the N6752A where the resolution is 3.5 mV and just the offset of the accuracy specification not including the gain term is 19 mV which is more than 5 times greater than the resolution. 

I hope that this was helpful.   If there are any questions, please leave comments here or on our forum at Agilent Discussion Forums.