3.6 The Current Ripple Ratio r

In Figure 3.2 we first 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

Here we have used ? I =2 I _AC, as defined 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 defined 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 (infinite) 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 definition.

Figure 3.5: BCM and forced CCM operating modes

Note that an exception to the "valid" range of r from 0...