High resolution timer on STM32, tricks maybe

Except that it's a Warburg impedance, and rather more cranky.

What's diffusive about an inductor?

You could do second-order delta-sigma yourself in software, diddle the LSB of the PWM register, and get all the bits you want. The price is noise, which you should be able to filter out in the time scale of a battery.

There is a trick used in nuclear spectroscopy: use a DAC to add noise to an ADC input, but then subtract it out of the ADC data. That eliminates ADC linearity errors without a big noise penalty.

Of course, PWM already has perfect linearity, just with quantization.

This dithering is commonly done in radar systems as well, for exactly that reason.

This can also be dithered.

Joe

The diffusion happens in the battery being talked about - the current moves as ions through an electrolyte, and that's a Warburg impedance. Over quite a range of frequencies it presents as 45 degree phase shift, so modelling it as a pure capacitative or inductive element is decidedly unhelpful.

It would be nice to claim that I was taught this as a graduate student in chemistry, but I wasn't - I only found out about in in 2000 when I got stuck with liquid conductivity measurement problem at Haffmanns BV in Venlo in the Netherlands. My boss - who also had a Ph.D. but in different sort of chemistry - didn't seem to know about it either.

It doesn't eliminate them - it just smears them out.

It's covered in the 1988 book "The Art of Digital Audio" by John Watkinson ISBN 0-240-512270-7 and he credits the audio DAC people with inventing the technique.

Sloman A.W. "Comment on 'Noise averaging and measurement resolution" Review of Scientific Instruments, 70 4734 (1999) points something similar out to a spectroscopist, who got a bit peeved about being jeered at for not knowing the European audio literature.

Pulse width modulation only has perfect linearity if you have infinitely fast switches. It does pretty well if the rising and falling waveform edges are symmetrical, but if they aren't it's merely monotonic.

Working through that was tedious when I did it back in 1992.