Most of documents about this article show two basic formula –

For PWM off time – Vphase = 3/2*e

For PWM on time – Vphase = 3/2*e + Vdc/2

And show us beautiful voltage waveforms with PWMed BEMF, where ON and OFF time parallel. But i have another situation with mine 8kW hub-motor. Look at this:

Typical examle, where off-time BEMF differs from on-time on Vdc/2. Here’s mine:

Second PWM cycle inverted. Green area- affected by diode, integration starts in red area, after zero crossing. Closer view:

At the beginning of the cycle is seen resonant oscillations, for my motor they lasts about 10uS, ADC samples in center of ON time and OFF time, what give us clear data, without interference.

What is source of this mis-alignment? For proper BEMF integration i should take phase voltage, subtract neutral point, and integrate the resulting value. For off-time it is right, if we take neutral point as zero, coz other two phases on the ground, resultant step-switch very accurate with installed hall sensors. But if i take raw value from on-time, subtract Vdc/2, voltage is incorrect, step-switch comes too early. This means neutral point moves with BEMF, actually it is always moves, coz of third harmonic, but this is seen only when two other phases is powered.

UPD1: Finally i’ve got this:

I had to make current spike detector, you can see on BEMF graph filtered and real value BEMFs. Only this way high inductance motors run fine under load.

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Hi vasilisks,

Did you ever find why there is a difference between ontime and offtime slope ?

Hi, i have read a lot of IEEE documents about BEMF, most of them have conflicting states with each other. Some of them are far from real world, and using mathematical magic have wrong conclusion. I come to this –

ON time bemf = Vop – (Vdd+Vop)/3

Off time bemf = Vop OR Vop-Vdd if measured from top.

Vop – voltage on open phase

Vdd – supply voltage

“(Vdd+Vop)/3” – virtual middle point, (Va+Vb+Vc)/3, so we have one phase on top(Vdd) and one on bottom(zero), one is open phase(Vop)

Hi Vasiliy,

I also use (Va+Vb+Vc)/3 as midpoint reference during ontime which seems to give the best result. The bemf looking at ontime is nice and symmetrical if I used ontime measurement. But if you look at that time also to the offtime voltage is not symmetrical. I think this is because of the different slopes of ontime and offtime.

Im aslo see a little difference in slope ON vs OFF for some motors (not all) even using this formula (Va+Vb+Vc)/3, i’m not sure what influences this