Six-step commutation

Everything else on this site assumes you want a rotating vector that follows the rotor. There is an older answer, it is still shipping in enormous volume, and it is worth knowing what it does — partly because it explains what field-oriented control is for, and partly because it is better than FOC at one specific thing.

Block commutation energises two phases at a time and steps the applied vector to the next of six fixed directions every 60 electrical degrees. No transforms, no angle beyond which sixth of a revolution the rotor is in, no current regulator worth the name. Three Hall sensors resolve exactly the six sectors it needs, and nothing else is required.

The vector cannot follow the rotor

That is the entire cost, and everything else follows from it.

The current is held in one direction while the rotor keeps turning underneath. So the angle between the current and where it ought to be — a quarter turn ahead of the rotor flux — ramps from +30° at the start of a sector, through zero at the middle, to −30° at the end. Then it jumps and does it again.

Only the component along q makes torque, so torque follows the cosine of that error:

The current Magnitude

Torque over one electrical revolution, at the same current, for both schemes. The field-oriented trace is flat because its vector turns with the rotor. The six-step trace sags between commutations — the dashed verticals are the jumps, and torque is worst either side of each. Both traces scale together with current; the gap between them does not close.

Fourteen percent, and where it comes from

Two constants and nothing else:

\overset{ˉ}{T} = \frac{1}{π /3} \int_{- π /6}^{π /6} cos γ d γ = \frac{3}{π} = 0.9549

T_{min} = cos 30° = 0.8660

which gives a peak-to-peak ripple of

\frac{1 - 0.8660}{0.9549} = 14.0%

of the mean. That is the number quoted for block commutation, and it is worth deriving rather than citing, because it falls out of the sector width alone — it does not depend on the machine, the current, or anything you can tune.

The other consequence of the same integral: field-oriented control produces 4.7% more torque per amp, because $1/0.9549 = 1.047$ . The missing 4.5% is not dissipated anywhere. It is current pointed in a direction that does no work.

On the bench That ripple is at six times the electrical frequency, which is the same signature inverter deadtime leaves. Two quite different causes, one harmonic — so seeing 6× ripple does not tell you which you have.

The distinguishing test is amplitude against load: the commutation ripple is a fixed fraction of torque and scales with current, while the deadtime error is a fixed voltage and matters most when the machine is barely loaded.

What it is better at

Six-step reaches the hexagon’s vertices. Sinusoidal modulation is confined to the inscribed circle, because a rotating request has to fit inside the hexagon at every angle, not just six of them.

On a 48 V link:

Scheme	Peak phase voltage
Sinusoidal PWM	24.0 V
Space-vector PWM	27.7 V
Six-step	32.0 V

Those three sit in a geometric progression, each a factor of $2/ 3 = 1.1547$ apart. So the 15.5% that min-max injection buys over plain SPWM is exactly the same 15.5% again from space-vector modulation up to six-step — and a third more voltage, end to end, than a plain sinusoid.

That is not a coincidence worth admiring so much as a ladder worth knowing, because it says what a field-oriented drive gives up at the top of its speed range. Wanting the last 15.5% means leaving the linear region and overmodulating — and the limit of overmodulation is six-step itself. A drive pushed to its maximum speed is not choosing between the two schemes. It is becoming the other one.

So when would you use it

When the torque ripple does not matter and the simplicity does: fans, pumps, blowers, anything where the load is smooth and inertia filters what is left. Three Hall sensors and six gate signals is a genuinely small amount of hardware and firmware.

And it degrades gracefully in the one place FOC does not: it needs no angle beyond a sector, so there is no observer to lose lock, no transform running on a wrong $θ$ , and nothing to align.

What it cannot do is hold torque steady, run quietly, produce full torque at standstill with any precision, or make use of reluctance — everything, in other words, that the rest of this site is about.

What to take away

Six fixed directions, stepped every 60°. The vector cannot follow the rotor, so the angle error sweeps ±30° across each sector.
Mean torque is $3/ π$ = 95.49% of aligned, and the ripple is 14.0% of the mean. Both follow from the sector width alone.
Field-oriented control therefore gives 4.7% more torque per amp, and the difference is current doing no work rather than heat.
The ripple is at 6× electrical — the same signature as deadtime. Distinguish them by how they scale with load.
Six-step reaches 2V_dc/3, which is 15.5% above the linear limit. SPWM, SVPWM and six-step form a geometric progression of ratio $2/ 3$ .
Overmodulation is the road between the two, and six-step is where it ends.