It represents the fraction of the commutation period T during which the switch is On. Therefore, D ranges between 0 (S is never on) and 1 (S is always on). During the Off-state, the switch S is open, so the inductor current flows through the load. If we consider zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of IL is:  formula_14  Therefore, the variation of IL during the Off-period is:  formula_15  As we consider that the converter operates in steady state conditions, the amount of energy stored in each of its components has to be the same at the beginning and at the end of a commutation cycle. In particular, the energy stored in the inductor is given by:  formula_16  So, the inductor current has to be the same at the start and end of the commutation cycle. This means the overall change in the current (the sum of the changes) is zero:  formula_17  Substituting formula_18 and formula_19 by their expressions yields:  formula_20  This can be written as:  formula_21  The above equation shows that the output voltage is always higher than the input voltage (as the duty cycle goes from 0 to 1), and that it increases with D, theoretically to infinity as D approaches 1. This is why this converter is sometimes referred to as a step-"up" converter. Rearranging the equation reveals the duty cycle to be:  formula_22  If the ripple amplitude of the current is too high, the inductor may be completely discharged before the end of a whole commutation cycle. This commonly occurs under light loads. In this case, the current through the inductor falls to zero during part of the period (see waveforms in figure 4). Although the difference is slight, it has a strong effect on the output voltage equation. The voltage gain can be calculated as follows:  As the inductor current at the beginning of the cycle is zero, its maximum value formula_23 (at formula_24) is  formula_25  During the off-period, IL falls to zero after formula_26:  formula_27  Using the two previous equations, δ is:  formula_28  The load current Io is equal to the average diode current (ID). As can be seen on figure 4, the diode current is equal to the inductor current during the off-state.