Where does the 4.44 factor in the EMF equation for sinusoidal excitation originate?

Where does the 4.44 factor in the EMF equation for sinusoidal excitation originate?

• A. 2 multiplied by 2.22.
• B. Pi times 1.11.
• C. 4 multiplied by 1.11.
• D. 4 times the square root of two.

Answer: (C)

The 4.44 factor comes from turning a sinusoid’s peak flux into its RMS emf per turn. If the flux linked by a turn varies as φ(t) = Φ_max sin(ωt), the instantaneous emf is e = dφ/dt = Φ_max ω cos(ωt). The RMS value of this sinusoid is e_rms = Φ_max ω / √2. Since ω = 2πf, you get e_rms = Φ_max (2πf)/√2 = Φ_max f (2π/√2) = Φ_max f (√2π) ≈ 4.44288 f Φ_max. For T turns per phase, the phase EMF is E_rms = 4.44 f Φ T. That constant 4.44 can be written as 4 × 1.11, because 4.44 ≈ 4 × (π/(2√2)) ≈ 4 × 1.1107. The 1.11 is the sine-wave form factor (RMS divided by average value of a sine), and the 4 comes from combining the angular frequency with the RMS conversion. So the 4.44 factor originates from the RMS value of a sinusoid and can be expressed as 4 times 1.11.

The 4.44 factor comes from turning a sinusoid’s peak flux into its RMS emf per turn. If the flux linked by a turn varies as φ(t) = Φ_max sin(ωt), the instantaneous emf is e = dφ/dt = Φ_max ω cos(ωt). The RMS value of this sinusoid is e_rms = Φ_max ω / √2. Since ω = 2πf, you get e_rms = Φ_max (2πf)/√2 = Φ_max f (2π/√2) = Φ_max f (√2π) ≈ 4.44288 f Φ_max. For T turns per phase, the phase EMF is E_rms = 4.44 f Φ T.

That constant 4.44 can be written as 4 × 1.11, because 4.44 ≈ 4 × (π/(2√2)) ≈ 4 × 1.1107. The 1.11 is the sine-wave form factor (RMS divided by average value of a sine), and the 4 comes from combining the angular frequency with the RMS conversion. So the 4.44 factor originates from the RMS value of a sinusoid and can be expressed as 4 times 1.11.