Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Magn comp. relucta

Magnetic complex reluctance (SI Unit: H−1) is a measurement of a passive magnetic circuit (or element within that circuit) dependent on sinusoidal magnetomotive force (SI Unit: At·Wb−1) and sinusoidal magnetic flux (SI Unit: T·m2), and this is determined by deriving the ratio of their complex effective amplitudes.[Ref. 1-3]

Z_mu = frac{dot N}{dot Phi} = frac{dot {N}_m}{dot {Phi}_m} = z_mu e^{jphi}

As seen above, magnetic complex reluctance is a phasor represented as uppercase Z mu where:

dot N and dot {N}_m represent the magnetomotive force (complex effective amplitude)
dot Phi and dot {Phi}_m represent the magnetic flux (complex effective amplitude)
z_mu, lowercase z mu, is the real part of magnetic complex reluctance

The "lossless" magnetic reluctance, lowercase z mu, is equal to the absolute value (modulus) of the magnetic complex reluctance. The argument distinguishing the "lossy" magnetic complex reluctance from the "lossless" magnetic reluctance is equal to the natural number e raised to a power equal to:

jphi = jleft(eta - alpha
ight)

Where:

  • j is the imaginary number
  • eta is the phase of the magnetomotive force
  • alpha is the phase of the magnetic flux
  • phi is the phase difference

The "lossy" magnetic complex reluctance represents a magnetic circuit element's resistance to not only magnetic flux but also to changes in magnetic flux. When applied to harmonic regimes, this formality is similar to Ohm's Law in ideal AC circuits. In magnetic circuits, magnetic complex reluctance is equal to:

Z_mu = frac{1}{dot {mu} mu_0}frac{l}{S}

Where:

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