A new current measurement methodology: It’s all about counting the electrons going by!

One thing near and dear to us here at the Power and Energy Division is making accurate current measurements. What exactly is current? It’s basically the flow of electric charge per unit of time. In a conductor it’s the flow of electrons through it per unit of time. 

The ampere is the fundamental unit of current in coulombs per second, which equates to 6.241x10¹⁸ electrons per second. Accurate current measurement is one of the core values of virtually all of our products. Some of the precision SMU products can measure down to femtoamp (fA) levels (10^-15 amps). This is where we tend to muse that we’re getting down to the levels where we’re virtually counting the individual electrons going by.

While there are a few different ways of measuring current, by far the most common is to measure the voltage drop across a resistive shunt. With careful design this provides the most accurate means of current measurement. There are a lot of non-obvious factors that can introduce unexpected errors that many are not aware of, leading them to believe they have better accuracy than what it really is. A good discussion of what it takes to truly make accurate current measurements was covered in a previous posting “How to make more accurate current measurements”(click here to review). We go through great pains in addressing these things in our products in order to provide accurate and repeatable measurements.

Unlike the volt and the ohm, which have quantum standards for their electrical units, the ampere instead relies on the standards for the volt and ohm for measurement, as a quantum standard for the ampere that directly relates it back to charge is still lacking. However, that may change in the not too distant future. A group of scientists were awarded the Helmholtz Prize in metrology for realization of the measurement of the ampere based on fundamental constants. Basically they’ve created an electron charge pump that moves a small, fixed quantity of electrons under control by a clock. You can say they’re literally “counting the electrons as they go by”. This could become the new SI standard reference for current measurement. To me this is very fascinating to find out about. More can be learned on this from the following link to the press release “Helmholtz Prize for the “new” ampere”(click here to review).  I am curious to see how this all plays out in the long run. Maybe it will lead to yet another, and better, way to make more accurate current measurements in products we all use today in our work in electronics!

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.