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Maintaining phase accuracy for kHz power measurements
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KaneTW:
I need to measure a 40kHz-100kHz amplifier output for phase and power measurements.

I'm planning to simultaneously sample the voltage and current waveform at up to 3MSPS and then perform most of the filtering and phase correction in software.

My output is a class D filtered sine wave with no harmonics up to roughly the 11th, and then some minor harmonics (don't have a FFT on hand but I'd guess around -20dBm).

Since my output is relatively clean, I'm not too concerned about a steep analog filter. However, component tolerance gives a pretty wide phase delay variance and the current transformer I'm using has a noticeable phase offset.

The question is: how do I calibrate out the phase offset over my band of operation? I could just measure it at the two main fundamentals I'll be using (40k and 100k), but that seems inelegant. I'm thinking a FIR that's calibrated with a low reactance resistive load, but no clue how to approach that.

Right now my signal path is roughly

voltage -> filter and ADC buffer opamp (probably ADA4891) with 100:1 attenuation ->  12-bit SAR ADC on a C2000 micro
current transformer -> filter/ADC buffer with 2-4 V/V gain -> ADC

A multiple feedback filter somewhere between Butterworth and Bessel seems ideal according to my simulations, but I'm not particularly married to it.
ogden:

--- Quote from: KaneTW on January 05, 2020, 02:51:37 pm ---The question is: how do I calibrate out the phase offset over my band of operation? I could just measure it at the two main fundamentals I'll be using (40k and 100k), but that seems inelegant.

--- End quote ---
Inelegant? Not at all. Even more elegant would be to calibrate at more points. Internet is full with information on "how to calculate phase difference/offset/angle". In short: you cross-correlate sampled waveform with 0-degree shifted sine and 90-degree shifted sine (thus cosine), then do simple trigonometry math to calculate phase angle.

[edit] https://www.electronics-tutorials.ws/accircuits/phase-difference.html
splin:

--- Quote from: KaneTW on January 05, 2020, 02:51:37 pm ---The question is: how do I calibrate out the phase offset over my band of operation? I could just measure it at the two main fundamentals I'll be using (40k and 100k), but that seems inelegant.

--- End quote ---

Measuring the current at 100kHz with low phase shift accurately isn't trivial - depending on your phase accuracy requirements and the currents involved of course. If you use a current shunt it has to have very low inductance - eg. a 10milliohm shunt with 1nH of inductance will cause a phase shift of 3.6 degrees at 100kHz if I've calculated it correctly. Phase errors introduced by shunts are even a concern in 50Hz energy meters, especially when the power factor is low.

You can get (or make) low inductance shunts using a coaxial configuration, or at least a bifilar arrangement. This paper covers some of the issues:

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=31690

Alternatively you could try to directly measure the phase shift of the shunt but I'm not sure what a good way to go about it might be. Or you could measure its inductance with an LCR meter and rely on calculating the phase shift.

Another way would be to use a high bandwidth (10MHz+) Rogowski coil sensor with low phase shift at 100kHz such as:

http://www.pemuk.com/products/cwt-current-probe/cwt.aspx.

Read the technical notes here for relevant phase performance information:

http://www.pemuk.com/Userfiles/CWT/CWT%20-%20Technical%20notes%20-%20001.PDF

They aren't especially cheap however - probably getting on for $1k (it's possible they might be somewhat less than that - I'm not certain). You might be able to get something cheap on Ebay as I doubt there is a big demand on the second hand market. There are other manufacturers of course but many are low bandwidth types designed for 50/60Hz measurments. Also note that the high bandwith types are relatively insensitive and thus not suitable for low currents.

Once you have the means to measure your calibration current accurately, I'd have thought that two calibration frequencies would be enough as I would expect only one pole in the frequency response to be significant within the CT's accurate bandwidth. Don't quote me on that however!  >:D
ogden:

--- Quote from: splin on January 10, 2020, 01:20:40 am ---Measuring the current at 100kHz with low phase shift accurately isn't trivial - depending on your phase accuracy requirements and the currents involved of course.  If you use a current shunt it has to have very low inductance - eg. a 10milliohm shunt with 1nH of inductance will cause a phase shift of 3.6 degrees at 100kHz if I've calculated it correctly. Phase errors introduced by shunts are even a concern in 50Hz energy meters, especially when the power factor is low.

--- End quote ---
Much better idea is to implement phase error calibration same way as LCR meters do.
KaneTW:
Some inherent phase shift is unavoidable, but as long as I can calibrate it out in software it's fine.

How does phase error calibration in LCR meters work?
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