this means that equals 0 for no output current, and 1 for the maximum current the converter can deliver. Using these notations, we have: in continuous mode: in discontinuous mode: the current at the limit between continuous and discontinuous mode is: Therefore, the locus of the limit between continuous and discontinuous modes is given by: These expressions have been plotted in figure 6. From this, it can be deduced that in continuous mode, the output voltage does only depend on the duty cycle, whereas it is far more complex in the discontinuous mode. This is important from a control point of view. On the circuit level, the detection of the boundary between CCM and DCM are usually provided by an inductor current sensing, requiring high accuracy and fast detectors as: Real-world factors The analysis above was conducted with the assumptions: The output capacitor has enough capacitance to supply power to the load (a simple resistance) without any noticeable variation in its voltage. The voltage drop across the diode when forward biased is zero No commutation losses in the switch nor in the diode These assumptions can be fairly far from reality, and the imperfections of the real components can have a detrimental effect on the operation of the converter. Output voltage ripple (continuous mode) Output voltage ripple is the name given to the phenomenon where the output voltage rises during the On-state and falls during the Off-state. Several factors contribute to this including, but not limited to, switching frequency, output capacitance, inductor, load and any current limiting features of the control circuitry. At the most basic level the output voltage will rise and fall as a result of the output capacitor charging and discharging: We can best approximate output ripple voltage by shifting the output current versus time waveform (continuous mode) down so that the average output current is along the time axis. When we do this, we see the AC current waveform flowing into and out of the output capacitor (sawtooth waveform). We note that V (where V is the capacitor voltage) occurs at t/2 (just after capacitor has discharged) and V at t/2. By integrating Idt (= dQ ; as I = dQ/dt, C = Q/V so dV = dQ/C) under the output current waveform through writing output ripple voltage as dV = Idt/C we integrate the area above the axis to get the peak-to-peak ripple voltage as: