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Zero-ripple current phenomenon: theory AN3180
6/39 Doc ID 17273 Rev 1
2 Zero-ripple current phenomenon: theory
Zero-ripple current in one of a two-winding coupled inductor, having self-inductances L1 and
L2, can be achieved if the coupling coefficient k, given by:
Equation 1
(M is their mutual inductance), and the effective turns ratio n
e
defined as:
Equation 2
is such that either k n
e
= 1 or k = n
e
, provided the windings are fed by the same voltage.
To confirm this, it is convenient to consider the a = k n
e
coupled-inductor model (refer to
Appendix A) with the terminals excited by proportional voltages v(t) and αv(t) having the
same frequency and phase, shown in Figure 4. This is the only condition to be imposed on
the terminal voltages, their actual waveform is irrelevant.
Figure 4. Coupled inductor a = k n
e
model under zero-ripple current conditions
Figure 4 shows that, in order for the secondary ripple current (i.e. di
2
(t)/dt) to be zero, the
voltage across the inductance L
2
(1-k
2
) must be zero, that is, the voltage on either side of it
must be the same. Thereby:
Equation 3
21
LL
M
k =
1
2
L
L
=
e
n
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L
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D
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α
=
⇒
α
=
ee
nvvn k)t()t(k