The Rotating Magnetic Field
Three windings that never move produce a field that rotates — the most elegant result in the subject.
Skip to the animationThree stationary windings spaced 120° apart, fed by currents 120° apart in time, produce a magnetic field of constant magnitude rotating at synchronous speed — which is what lets an induction motor start by itself with nothing connected to its rotor.
The result
Each winding contributes a field along its own axis, proportional to its instantaneous current. The vector sum of the three rotates uniformly — and, less obviously, has constant magnitude, 1.5 times one phase's peak.
Nothing physical moves. The rotation is produced entirely by the time relationship between three currents, which is the most elegant result in the subject. Constant amplitude and constant angular velocity are also why a three-phase machine runs smoothly where a single-phase one pulsates.
One electrical cycle turns the field one revolution in a two-pole machine, giving N_s = 120f/P. At 50 Hz that is 3000 rpm with two poles and 1500 with four — fixed by supply frequency and winding, not by load or voltage.
Why three-phase motors self-start
A three-phase supply produces a rotating field the instant it is applied, so a rotor placed in it experiences torque from standstill.
A single-phase supply produces a pulsating field along one axis, which decomposes into two equal fields rotating in opposite directions — their torques cancel exactly at standstill. Spin the rotor by hand and one wins, which is why every single-phase motor needs a starting winding, a capacitor or a shaded pole.
Reversing
Exchanging any two supply leads reverses the phase sequence and therefore the field's direction. That is the whole of direction control for a three-phase motor.
It is also why phase sequence is verified before commissioning a large machine — connecting it wrongly runs a pump or conveyor backwards on first start, occasionally with expensive consequences.
What it makes possible
Put a conducting rotor in this field and the sweeping flux induces currents in it, with no electrical connection to the rotor at all — which is where the induction machine's name comes from. Those currents interact with the field to produce torque.
And the rotor must lag the field, or there would be no relative motion, no induced current and no torque. That lag is slip, and it is the subject of the next topic.
The numbers you will be asked for
- Synchronous speed
N_s = 120·f / P
rpm, with P the number of poles.
- Resultant magnitude
1.5 × peak of one phase
Constant — which is why it is smooth.
- Field angular velocity
ω_s = 2πf / (P/2)
Electrical radians relate to mechanical by P/2.
- Reversal
swap any two supply leads
Reverses the phase sequence.
Advantages and disadvantages
Advantages
- Produces rotation with no moving parts in the stator.
- Constant magnitude and speed give smooth, ripple-free torque.
- Lets a three-phase motor self-start with no auxiliary circuit.
- Reversal needs only two wires exchanged.
Disadvantages
- Requires a three-phase supply, which domestic premises do not have.
- Synchronous speed is fixed by frequency, so speed control needs a converter.
- Single-phase versions need extra starting hardware.
- Unbalanced supply produces a negative-sequence field that heats the machine.
Watch it work
Check yourself
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