STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet

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A system of coupled inductors is a set of coils that share one or more common magnetic 
paths because of their proximity. Because of this, magnetic flux changes in any one coil do 
not only induce a voltage across that coil by self-induction, but also across the others by 
mutual induction.

Accurate descriptions of coupled inductors use the reluctance model approach and its 
derivations, which closely represent the physical structure of the magnetic element. This 
approach is especially useful when dealing with complex magnetic structures, which is not 
the case under consideration. Here a simpler method is used based on the terminal 
equations describing the electrical behavior of the magnetic structure.

From an electrical standpoint, a system of m coupled inductors, is defined by m coefficients 
of self-inductance, relating the voltage across any inductor to the rate of change of current 
through the same inductor, and m·(m-1) coefficients of mutual inductance, equal in two by 
two, relating the voltage induced across any inductor to the rate of change of current in 
every other inductor.

Considering the important practical case of coupled inductors wound on the same core of 
magnetic material, each inductor is commonly termed “winding”. Focusing on the case m=2, 
a system of two coupled inductors, which are designated as the primary and the secondary 
winding, is a linear, time-independent two-port circuit described by the following branch-
constitutive equations:

where L1 and L2 are the self-inductances of the primary and the secondary windings 
respectively, and M is the mutual inductance. Winding resistance is assumed to be 
negligible.

Unlike L1 and L2, which are inherently positive, M can be either positive or negative, 
depending on the voltage polarity of the windings relative to one another: a positive rate of 
change of the current in one winding can induce a voltage either positive or negative in the 
other winding. As shown in 

, this is indicated by dot notation, which follows three 

important rules:

1.

Voltages induced in any winding due to mutual flux changes have the same polarity at 
dotted terminals

2. 

Positive currents flowing into the dotted terminals produce aiding magneto-motive 
forces

3. 

If one winding is open circuited and the current flowing into the dotted terminal of the 
other winding has a positive rate of change, the voltage induced in the open winding is 
positive at the dotted terminal.

Based on rule 1 and on the sign convention of the terminal voltages and currents of two-port 
circuits, it is easy to see that for the coupled inductors in 

 

on the left M>0, while for 

those on the right M<0.

(t)

(t)

dt

d

L

M

M

L

(t)

(t)

2

1

=