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AN3180

Zero-ripple current phenomenon: theory

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Figure 5.

Coupled inductor a = ne/k model under zero-ripple current conditions

Similarly, considering the model of Figure 5, again excited by proportional voltages v(t) and

αv(t), it is equally apparent that, in order for the primary ripple current to be zero the voltage

across the inductance L1 (1-k

2) must be zero, that is, the voltage on either side of it must be

the same:

Equation 4

If in Equation 3 and 4

α=1, which means that equal voltages are impressed on either side of

the coupled inductor, we find the above mentioned assertion. As

α=1 is the most common

condition found in switching converters, from now on this is the only case that is taken into

consideration, therefore:

●

condition for zero-ripple secondary current

●

condition for zero-ripple primary current

Note that, as k < 1, to obtain a zero-ripple secondary current it must be ne > 1, that is L2 >

L1, while to obtain a zero-ripple primary current it must be ne < 1, that is L1 > L2; and so

ripple current cannot be reduced to zero in both windings simultaneously. In Figure 4 and 5,

note also that the inductance of the winding, where zero-ripple current is achieved, is

irrelevant, since there is no ripple current flowing (only DC current can flow). As a

consequence, the zero-ripple current winding reflects an open circuit to the other one, so

that the inductance seen at the terminals of that winding equals exactly its self-inductance.

The designation of which winding is the primary or the secondary is purely conventional.

Therefore, we consider only one zero-ripple current condition and arbitrarily assume the

condition to be assigned to the secondary winding:

Equation 5

which, consistent with the terminology used for the smoothing transformer of Figure 3, is

termed DC winding, while the primary winding is termed AC or cancellation winding.

Equation 5

, considering Equation 1 and 2 can be written in different equivalent ways:

⇒

)

(

)

(

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