Computation of flux switching in magnetic circuits

A number of physical and semiempirical flux-switching models that have appeared in the literature are reviewed briefly and classified. A thin ferrite core is switched by essentially a step mmf (with short rise time T
r
). Three components of the total
\dot{\phi}(t)
are distinguished and semiempirical models are proposed for each : 1) an initial elastic
\dot{\phi}
spike during the rise time of
F, \dot{\phi}_{\epsilon} = \epsilon\dot{F}
, where ε is constant in time; 2) a decaying inelastic
\dot{\phi}
starting at
t \cong T_{r}
,
\dot{\phi}_{rho i} = \rho_{i}(F - F_{d}^{min}) \exp [-(t - T_{r})(F - F_{d}^{min})/C_{i}]
, where ρ
i
and C
i
are constants in time and
F_{d}^{min}
is the static mmf threshold; and 3) the bell-shaped, main inelastic
\dot{\phi}, \dot{\phi} = \dot{\phi}_{p}{1 - [(2\phi + \phi_{s} - \phi_{d})/(\phi_{s} + \phi_{d})]^{2}}
, where, for given
F , \phi_{p}
is the peak of
\dot{\phi}, \phi_{d}
is the φ value on the static
\phi(F)
curve, and φ
s
is saturation flux. Expressions involving switching parameters are given for
\epsilon, \dot{\phi}_{p}
, and φ
d
. The agreement between these models and
\phi(t)
of a thin core is satisfactory. The main-
\dot{\phi}
model is applied in a numerical analysis of three magnetic circuits: an unloaded core, a core loaded by
R, L, C
, and a diode, and a core-diode shift register. The agreement between computed and experimental results is satisfactory, especially if different parameters are used for computing step-
F
and ramp-
F
switching.