rectangles in figure 5 are the same. This yields: So the value of δ is: The output current delivered to the load () is constant, as we consider that the output capacitor is large enough to maintain a constant voltage across its terminals during a commutation cycle. This implies that the current flowing through the capacitor has a zero average value. Therefore, we have : Where is the average value of the inductor current. As can be seen in figure 5, the inductor current waveform has a triangular shape. Therefore, the average value of IL can be sorted out geometrically as follows: The inductor current is zero at the beginning and rises during ton up to ILmax. That means that ILmax is equal to: Substituting the value of ILmax in the previous equation leads to: And substituting δ by the expression given above yields: This expression can be rewritten as: It can be seen that the output voltage of a buck converter operating in discontinuous mode is much more complicated than its counterpart of the continuous mode. Furthermore, the output voltage is now a function not only of the input voltage (Vi) and the duty cycle D, but also of the inductor value (L), the commutation period (T) and the output current (Io). From discontinuous to continuous mode (and vice versa) The converter operates in discontinuous mode when low current is drawn by the load, and in continuous mode at higher load current levels. The limit between discontinuous and continuous modes is reached when the inductor current falls to zero exactly at the end of the commutation cycle. Using the notations of figure 5, this corresponds to : Therefore, the output current (equal to the average inductor current) at the limit between discontinuous and continuous modes is (see above): Substituting ILmax by its value: On the limit between the two modes, the output voltage obeys both the expressions given respectively in the continuous and the discontinuous sections. In particular, the former is So Iolim can be written as: Let's now introduce two more notations: the normalized voltage, defined by . It is zero when , and 1 when ; the normalized current, defined by . The term is equal to the maximum increase of the inductor current during a cycle; i.e., the increase of the inductor current with a duty cycle D=1. So, in steady state operation of the converter,