How to Convert CT ADC Readings to Accurate RMS Current Matching DMM Measurements?

Hi All,

We are busy with a project that takes measurements from a Current Transformer (CT) to track current usage in attached appliances. The CT is connected through an amplifier circuit to a micro-controller ADC pin. The AC wave (positive cycle only) is sampled at 100us intervals (there are a few channels to sample) and a snapshot of the positive half of a wave is recorded. From this snapshot we hope to calculate the current usage of the attached load.

We understand that in order to get an accurate power reading of the attached load we need to get an RMS current value from the CT, an RMS voltage value of the supply and the power factor (measure the phase angle difference between the supply voltage and load current).

Step 1 is to convert the ADC reading from the CT to a current value that is consistent with a Digital Multimeter (DMM) or within a small margin of error.

We believe that it should be possible to take snapshots (ADC values) of various types of loads with similar current ratings and the calculation employed should yield values that correspond to DMM readings. ie. If the DMM measures 2 different types of 15W loads and sees a current of 69mA and 58mA respectively (ratio of 1.19), then our calculation using ADC values should yield a similar ratio between the 2 loads.

Here are the values recorded for each load, 15W Incandescent and 15W LED lighting. (See graph)

The various measurement strategies yield the following results and ratios: (see table)

Where we calculate these values using the following formulas:

ADC sum = sum of all values
ADC Ave = average of all values
ADC RMS = peak * 0.707
ADC True RMS = Square root of the average of the sum of the squares

As you can see the sum/ave have a similar ratio but in the opposite direction and the RMS / True RMS calculations are way off.

Is the strategy to get the AC current employed here correct or valid?
What is the DMM using (Doesn't say it's a True RMS meter)?Is the phase angle difference the issue here and do we need it for an accurate current measurement?
What are we missing?

Thank you for any insights.
Mark

Have you thought of using an RMS converter IC? gives you a nice easy to use DC voltage proportional to the RMS value of the input. That';s what they use in RMS DVMs. In your case it would take a load off your software and these ICs usually have pretty good precision.

For more info have a look at

https://www.analog.com/en/product-category/rms-to-dc-converters.html

Nice

Thank you for your reply,

we are going to look full wave rectification to flip the negative side of the wave positive, as well as move the zero point higher away from the adc minimum and noise floor.

We have looked at using a PMIC but there are multiple channels and it does not fit within the product budget.

Mark, some relevant notes.

‘graph’ and ‘table’ seem to be missing from your post.

If the DMM doesn’t say “true rms” then it measures average over some unspecified period. Unless this is an integral number of cycles of the waveform there will be an error, which gets smaller as the number of cycles during the measurement period is increased.

If two different 15W loads give two different readings on the DMM then this is clearly not helpful to measure the power.

Modern scopes can give measurements related to full cycles of waveforms so the rms and half-cycle mean values read correctly. (full cycle mean on a sinewave is zero, and so not of much use).

ADC sum : meaningless unless you take the sum over either a full cycle, a half cycle, or dozens of cycles.
ADC ave : again, what is the measurement period?
ADC rms : peak x 0.707 is based on a sine wave and is no use for non-linear loads like LEDs.

Phase angle is only meaningful for sine waves, not for non-linear loads.

If you get a snapshot of the “positive half” of the waveform (assuming you know where zero is) then you can get a half-cycle average (mean) easily. Likewise you can do your true rms reading on the positive half cycle and get a useful result. This way you can get mean current or rms current correctly.

Multiply rms current and rms voltage and you get VA. This is always greater than or equal to the power being consumed.

Phase angle has nothing to do with current measurement as such. What you intend to do with that current reading is another matter.