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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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