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Chapter 3

3.6 The Current Ripple Ratio r

In Figure 3.2 we ﬁ rst introduced the most basic yet far-reaching design parameter of the

power supply itself—its current ripple ratio r . This is a geometrical ratio that compares

and connects the AC value of the inductor current to its associated DC value. So

r

I

I

I

I

L

AC

DC

2

(3-10)

Here we have used I 2 I

AC

, as deﬁ ned earlier in Figure 3.2 . Once r is set by the

designer (at maximum load current and worst-case input), almost everything else is

pre-ordained — like the currents in the input and output capacitors, the RMS (root mean

square) current in the switch, and so on. Therefore, the choice of r affects component

selection and cost, and it must be understood clearly, and picked carefully.

Note that the ratio r is deﬁ ned for CCM ( continuous conduction mode ) operation only.

Its valid range is from 0 to 2. When r is 0, I must be 0, and the inductor equation then

implies a very large (inﬁ nite) inductance. Clearly, r 0 is not a practical value! If r

equals 2, the converter is operating at the boundary of continuous and discontinuous

conduction modes (boundary conduction mode or BCM). See Figure 3.5 . In this so-called

boundary (or “ critical ” ) conduction mode, I

AC

I

DC

by deﬁ nition.

I

DC

I

AC

I

AC

I

AC

r = 2 ×= 2

I

DC

I

DC

I

DC

I

AC

r = 2 ×≥ 2

Boundary conduction mode

Forced continuous conduction mode

I

AC

is greater than I

DC

I

AC

is equal to I

DC

negative current,

negative slope

negative current,

positive slope

Figure 3.5 : BCM and forced CCM operating modes

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