Six-step at 120° and 180° conduction

Six-step commutation can drive the inverter in two ways. In 120° conduction, two phases are driven at a time and the third is left open. That is the mode used so far, because the open phase is where the back-EMF is read for sensorless commutation. In 180° conduction, all three legs are always driven, each one high for half the electrical cycle and low for the other half. On paper 180° gives 15.5% more fundamental voltage from the same bus. This post covers a test of whether that is worth having on our motors. It is not: on the motor tested, 180° cost far more current than it saved in voltage.

The test ran on the F302 board with motor 3 (maxon EC-i 40, 7 pole pairs, R = 1.42 Ω, L = 0.356 mH, ψ = 6.64 mWb) at 18 V. Both patterns were hall-commutated through the same speed loop, with no commutation advance in either mode, so the only difference was the conduction pattern.

The two patterns

	120°	180°
Each leg per electrical revolution	high 120°, open 60°, low 120°, open 60°	high 180°, low 180°
Phases driven at once	two	three
Ideal fundamental phase voltage	√3/π · Vdc = 0.551 Vdc	2/π · Vdc = 0.637 Vdc
Voltage harmonics	5th, 7th, 11th, 13th, …, each 1/n of the fundamental	the same
Rotor position from	back-EMF on the open phase (sensorless)	halls or an observer

A 180° state is the union of two consecutive 120° sectors. For example, U+V− followed by U+W− gives U+ V− W−. Its boundaries therefore sit at the centres of the 120° sectors, which is where the 120° open phase crosses zero. The instants that 120° detects are the instants that 180° commutates. A unit test checks that each leg switches at its own back-EMF zero crossing.

The scope shows the practical difference on one phase terminal. In 120° there are two windows per cycle where the bridge lets go and the terminal follows the back-EMF. In 180° the terminal is switching all the time.

Where the extra current comes from

Both patterns have the same voltage harmonics. What differs is whether those harmonics can drive current. Motor 3 has a sinusoidal back-EMF, so there is no 5th or 7th harmonic in the back-EMF to oppose the 5th and 7th in the applied voltage. In 180° every phase is driven, so the harmonic voltage drives current through the winding impedance:

I_n = (V1 / n) / |R + j·n·ω·L|,   with V1 ≈ ψ·ω

once n·ω·L ≫ R:   I_n → ψ / (n²·L)

At speed the harmonic current stops depending on speed or load. It is a fixed fraction of the motor’s short-circuit current ψ/L. In 120°, the open phase forces the current to zero for a third of each cycle, so there is no path for those harmonics to circulate.

Motor	ψ/L	5th harmonic, ψ/25L	7th harmonic, ψ/49L
Motor 1 (30 µH)	31 A	1.25 A	0.64 A
Motor 2 (4-pole)	50 A	1.98 A	1.01 A
Motor 3 (EC-i 40, tested)	18.7 A	0.75 A	0.38 A

The 5th and 7th peaks add, so the peak phase current is larger than either one. Against the 1.5 A overcurrent limit on this board, every motor we have runs out of margin at light load.

Folding two seconds of phase current onto one electrical revolution shows the result. At the same speed and nearly the same torque, 120° carries small current blocks and 180° carries a large ripple at six times the electrical frequency.

Projecting the same data onto the hall angle gives the harmonic amplitudes. The measured 5th and 7th in 180° are within about 10% of the R + jnωL prediction from the fitted motor parameters. In 120° both are about 0.02 A.

Speed sweep

Both modes ran the same five speed set-points from 150 to 800 rad/s electrical. The rotor was loaded only by its own friction, so i_q stayed around 0.11–0.12 A in both. Any difference in current or power is current that produces no torque.

Across the sweep, 180° drew 1.5–3.7× the RMS phase current and 1.4–1.7× the input power. Copper loss, 3·I_rms²·R, accounts for nearly all of the difference: input power minus copper loss agrees between the two modes to within 0.1 W at each speed.

The duty needed for a given speed was only 5–7% lower in 180°, against the ideal 13%. The 120° open terminal sits at the back-EMF rather than at zero, so 120° delivers somewhat more than its ideal fundamental.

Top speed

The last test commanded 2000 rad/s with duty capped at 0.85. 120° accelerated until it ran out of duty at about 1350 rad/s and held there. 180° reached 639 rad/s while still accelerating, then tripped the 1.5 A limit.

Limits of the test

• Light load only. The harmonic current does not depend on load, so at rated torque it would be a smaller share of the total, but it would still use up the same trip margin.
• One motor, one direction, no commutation advance in either mode.
• Input power is computed from duty and shunt current, ignoring dead time.
• Telemetry runs at about 1.4 kHz, so only the fundamental, 5th and 7th are resolved at 600 rad/s.

What changed

• 120° stays the default. It is also the only pattern sensorless six-step can use, since 180° has no open phase to read.
• A new parameter, ss_conduction (120 or 180), selects the pattern for hall-commutated six-step. It stays in for experiments. A motor with small ψ/L relative to its rated current would be the place to try it again.
• A sensorless “150°” hybrid, which floats each leg briefly around its expected zero crossing, is not worth building on these motors. It would carry the same harmonic current.
• The extra 15% of voltage is better taken from FOC with space-vector overmodulation, which keeps the current under closed-loop control.

The repository has the code, the unit tests for the 180° table, and the captures behind every chart above.