and 1. Conversely, the decrease in current during the off-state is given by: Assuming that the converter operates in the steady state, the energy stored in each component at the end of a commutation cycle T is equal to that at the beginning of the cycle. That means that the current is the same at and at (figure 4). So, from the above equations it can be written as: The above integrations can be done graphically. In figure 4, is proportional to the area of the yellow surface, and to the area of the orange surface, as these surfaces are defined by the inductor voltage (red lines). As these surfaces are simple rectangles, their areas can be found easily: for the yellow rectangle and for the orange one. For steady state operation, these areas must be equal. As can be seen in figure 4, and . This yields: From this equation, it can be seen that the output voltage of the converter varies linearly with the duty cycle for a given input voltage. As the duty cycle is equal to the ratio between and the period , it cannot be more than 1. Therefore, . This is why this converter is referred to as step-down converter. So, for example, stepping 12 V down to 3 V (output voltage equal to one quarter of the input voltage) would require a duty cycle of 25%, in this theoretically ideal circuit. Discontinuous mode In some cases, the amount of energy required by the load is too small. In this case, the current through the inductor falls to zero during part of the period. The only difference in the principle described above is that the inductor is completely discharged at the end of the commutation cycle (see figure 5). This has, however, some effect on the previous equations. The inductor current falling below zero results in the discharging of the output capacitor during each cycle and therefore higher . A different control technique known as pulse-frequency modulation can be used to minimize these losses. We still consider that the converter operates in steady state. Therefore, the energy in the inductor is the same at the beginning and at the end of the cycle (in the case of discontinuous mode, it is zero). This means that the average value of the inductor voltage (VL) is zero; i.e., that the area of the yellow and orange