The Current Ripple Ratio 'r'
In Figure 2-2 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 2-2. 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 2-5. In this so-called boundary (or "critical") conduction mode, I AC = I DC by definition. Note that readers can refer back to Chapter 1 , in which CCM, DCM, and BCM were all...