Design and Implementation of On-board Electrical Power ... - OUFTI-1

V outV in= D. (5.1)Since D ≤ 1, this formula confirms the fact that a buck converter can only lower ormaintan equal the input voltage. This is actually reflected by the name of the converterwhich is related to the verb “to buck”.This formula is true assuming that all components are ideal. In practice, the switch iscomposed of semiconductor devices, i.e. a transistor and a diode, which implies switchinglosses. Furthermore, the inductor and the capacitor have a series resistance. To take lossesinto account, a coefficient is introduced in the formula. This coefficient is the efficiency η ofthe converter,Inductor designV outV in= ηD. (5.2)The three main criteria to choose the inductor are:• The current ripple in the inductor is inversely proportional to the inductance. A goodpractical rule is to keep the ripple below 20% of the maximum inductor DC current.• The saturation current of the inductor must be higher than the inductor peak currentI max .• The equivalent series resistance of the inductor must be low, to avoid power losses.The voltage across the inductor, v L (t), is equal to V s (t) − V out (t). The inductance andthe capacitor form a second-order low-pass filter. This filter attenuates the high frequenciescomponents of V s . If the filter is well designed, the variation of V out can be neglected. Wehave v L (t) = V in − V out when the switch is in position 1, and v L (t) = −V out when it is inposition 2.isThe relation between v L and i L is v L (t) = L di L(t)dt. Thus, the slope of the inductor currentdi L (t)dtdi L (t)dt= V in − V outL= −V outLduring phase 1. (5.3)during phase 2. (5.4)The inductor current is illustrated in Fig. 5.3 (third curve).The maximum current in the inductor, I max is equal to I av , the average current in L plushalf the current ripple ∆i L (peak to peak). The average current I av is equal to the currentI out flowing in the load. We can thus write50