Permanent Magnet Flux Linkage
Estimate rotor flux linkage from the back-EMF constant and pole pair count.
Convention matters
Back-EMF can be phase-to-neutral or line-to-line, peak or RMS, and referenced to mechanical or electrical speed. This calculator always shows every representation explicitly and assumes a balanced, wye (star) connected, sinusoidally-wound PMSM — a delta connection changes the line-to-line relationship.
The one relation this calculator uses
Back-EMF
Epeak,phase-neutral = ωe · λm
- Epeak,phase-neutral
- Peak, phase-to-neutral back-EMF at this speed [V]
- ωe
- Electrical angular speed = P · ωm [rad/s]
- λm
- Peak permanent-magnet flux linkage [Wb]
Standard result for a sinusoidal PMSM. Phase RMS = peak ÷ √2. Line-to-line RMS = phase RMS × √3, assuming a balanced, wye (star) connected machine — a delta connection changes this relationship.
Phase vs. line-line, peak vs. RMS, mechanical vs. electrical
Phase-to-neutral voltage is measured between one motor lead and the (usually inaccessible) star point. Line-to-line voltage is measured between two motor leads — what an oscilloscope probe across two phases actually reads — and for a balanced wye connection is √3 times larger.
Peak voltage is the sinusoid's amplitude; RMS is what a true-RMS multimeter displays, √2 smaller. Mixing these up is one of the most common sources of a back-EMF constant being off by a clean-looking but wrong factor.
Mechanical angular speed (ωm) is the physical shaft rotation rate. Electrical angular speed (ωe) is ωm × pole pairs — the rate the stator winding actually sees, and the one that belongs in E = ωe · λm. Using ωm in that formula silently under-computes back-EMF by a factor of the pole pair count.
Worked example
λm = 0.012 Wb, 4 pole pairs, spinning at 3000 RPM:
- ωm = 3000 × 2π / 60 ≈ 314.2 rad/s
- ωe = 314.2 × 4 ≈ 1256.6 rad/s
- Phase peak = 1256.6 × 0.012 ≈ 15.08 V
- Phase RMS = 15.08 / √2 ≈ 10.66 V
- Line-to-line RMS = 10.66 × √3 ≈ 18.47 V
Related calculators
Ke / Kt Constant Converter
Convert between the back-EMF constant (Ke) and torque constant (Kt) of a PMSM or BLDC motor.
Motor Constant Converter
Convert Ke, Kt and flux linkage across RMS/peak, phase/line-line and speed-basis datasheet conventions, with every assumption stated explicitly.
Electrical Speed Calculator
Convert mechanical speed to electrical speed and frequency using the motor's pole pair count.