Datasheet

Zero-ripple current phenomenon: theory AN3180
8/39 Doc ID 17273 Rev 1
Equation 6
Equation 5
and 6 are noteworthy because of their concision in expressing the conditions for
zero-ripple current phenomenon to occur, but unfortunately its physical nature is not shown.
To provide some physical insight, let us consider the a =
n coupled inductor model (n is the
physical turn ratio N
2
/N
1
) excited by equal terminal voltages v(t), shown in Figure 6.
Figure 6. Coupled inductor a = n model under zero-ripple current conditions
Proceeding with the same technique, in order for the ripple current i
2
(t) to be zero, the
voltage across the secondary leakage L
l
2
must be zero, that is, the voltages on either side of
L
l
2
must be equal to one another. On the other hand, if i2(t)=0 the voltage impressed on the
primary side of the ideal transformer v'(t) is given by the ratio of the inductive divider made
up of the primary leakage inductance L
l
1
and the magnetizing inductance L
M
; the voltage
applied to the left-hand side of L
l
2
is equal to nv'(t). Then, there is zero-ripple current on the
secondary side of the coupled inductor if the following condition is fulfilled:
Equation 7
which is equivalent to Equation 5 and 6, as can be easily shown, considering that L
M
= M/n.
Equation 7 provides the desired physical interpretation of the zero-ripple current condition: it
occurs when the turn ratio exactly compensates for the primary winding leakage flux, so that
the primary winding induces, by transformer effect, a voltage identical to its own excitation
voltage on the secondary winding; and so, if this is externally excited by the same voltage,
no ripple current flows through it.
The extensions of this interpretation to the case of zero-ripple primary current (just reflect
the magnetizing inductance L
M
to the secondary side) and to that of proportional excitation
voltages (α ≠ 1) are obvious.
1
L
M
L
L
kk
11
2
===
e
n
!-V
L

W
L

W
Q
YW YW/
0
/
O

/
O

L
0
W
LGHDO
YWYW
1
L
L
LL
L
(t)(t)
LL
L
1
M
M1
M
M1
M
==
+
⇒=
+
nnvvn
ll