[lucas]

Horizontal is at 5msec/div.

I'll try to explain, English is not my maternal language and choice of words can cause misinterpretation.

This is the waveform at the current sense resistor for a single phase, not a series resistor.

on the screen shot for your driver it appears to me that we may be looking at multiple sweeps (perhaps four?) with a bit of triggering jitter, and not one sweep (whereas the shot of the Chinese driver looks like a double sweep). Otherwise I'm not sure that I understand the vertical overlap with offset of adjacent 'square' portions of the trace on the shot from your driver.

There are indeed multiple sweeps overlapping each other, that's due to the automatic shutter timing of the camera in combination with the poor triggering of the scope, I also adjusted the intensity on the scope and that must have changed the shutter timing. They look better in real maybe a movie iso of picture would have been better.

>>Only the positive part is relevant, the negative part of the waves are a result of the decay mode.

I'm a bit confused at that, because I would have thought that the negative part of the waveforms would have represented the bipolar nature of the driving. But then I have not previously looked at waveforms from a chopping bipolar microstepping drive. I'd appreciate any clarification of that point.

The waveform is taken from the current sense resistors, if you have a detailed look at the current paths in the datasheet then the forward and reverse current through the motor both produce a positve half sinewave over these resistors and the decay currents generate the negative one.

Edit: you can also see some spots at zero current.
The TB6600 uses mixed decay, fast creates a negative current through the resistor and there's no current for slow decay.

My assumption is that the width of each 'square' part of the trace is the duration between one step pulse arriving and the next as it holds a certain position and current level until it is advanced to the next microstep, and there is chopping (and decay) going on at each current level as it awaits the next step pulse which is represented by the height of eqch 'square' of the trace, and that if we were also simultaneously looking at the other winding's current we would see it out of phase with the first trace in order to handle the microstepping.

That's entirely correct, if both windings would be visible there would be a sine/cosine waveform with a 90° phase shift.

The important thing here is that the chinese drive never reaches full current, you can see the "hairy" pulses after each step trying to get to full current.
But they don't due to the inductance of the coils.