AN3180 Datasheet, PDF (14/39 Pages) STMicroelectronics – A 200 W ripple-free input current

Zero-ripple current phenomenon: practice
AN3180
Figure 9.
Two-section slotted bobbin
suggested for the realization of a
coupled inductor - top view
Figure 10. Two-section slotted bobbin
suggested for the realization of a
coupled inductor - side view
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3. As a result of the aforementioned current splitting action, the same happens to the
magnetic flux: the AC winding is responsible for generating the AC component of the
flux and the DC winding for its DC component, but their sum is the same as in a single
inductor carrying the total current. This means that no core size increase is expected
because of flux density limitations (core saturation) or core loss reasons. Also the core
size selection approach is the same.
To complete the picture, an important property of the “gapped ferrite core plus bobbin”
assembly should be recalled. The reluctance of the leakage flux path is constant for a given
core geometry and is independent of the gap thickness, l_gap: essentially, it is a function of
the physical dimensions of the core and the distance between the windings. This implies
that the leakage inductance of the primary winding, Ll1, depends only on the turn number
N₁ and does not change if l_gap is adjusted. However, the total primary inductance L₁= L_l1+
L_M is strongly affected by the gap thickness, but it is only the magnetizing inductance L_M that
changes. With reference to the zero-ripple current condition in Equation 7:
Equation 13
L_{M n =} L₁ − L_{l1 n = 1}
L_l1 + L_M
L₁
once the ferrite core and the associated bobbin are defined, it is thereby possible to control
LL_l1 and L_M separately, acting on N₁ and l_gap respectively, then the secondary turn number
N₂ is determined so that the ratio n = N₂/N₁ meets the condition in Equation 7.
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