【正文】 s to, but for the moment it is sufficient to assume it charges to a voltage higher than Vin. We will call this voltage Vcap.Since the voltage Vcap is higher than Vin, the voltage across the inductor now has the opposite polarity to before. The inductor discharges according to the equationwhere V is the voltage across the inductor, thusIt is interesting to note that the value of di/dt is determined ONLY by the inductance value and the voltage across the inductor. The controller IC has nothing to do with setting the inductor ramp current.When the MOSFET switches on again the voltage on the drain of the MOSFET Q1 goes from Vcap to 0V. Since the voltage across a capacitor cannot change instantaneously, an equal negative going voltage appears on the anode of diode D so this node transitions from 0V to –Vcap. We now have a negative amplitude square wave voltage (at the right hand node of C1) being applied to an LC filter (L2 and C2). The LC filter averages out this square wave to produce a flat DC voltage whose amplitude is somewhere between 0V and –Vcap. This amplitude is dictated by the duty cycle of the square wave.We are now going to calculate the duty cycle (the ratio of the ON time of the MOSFET Q1 to the total switching period) and the voltage (Vcap) on the coupling capacitor C1. The inductor charge and discharge currents are equal when the circuit is in steady state. Thereforewhere dt1 is the ON time of the MOSFET and dt2 is the OFF time of the MOSFET. Dividing both sides by (dt1+dt2) givesIf the Duty Cycle (DC) can be represented by thensoHere we can see the Drain voltage going from 0V to Vcap (as yet uncalculated) and the ac coupled drain voltage on the anode of the diode. The capacitor has removed the dc offset and the diode has clamped the positive excursions to roughly 0V.Now, when the circuit is regulating there will be a flat negative dc voltage on the output. Thus, when V(diode) is at 0V there will be a positive voltage from V(diode) to V(out) and the inductor current in L2 will ramp in a positive direction. When V(diode) is negative there will be a negative voltage from V(diode) to V(out) so the inductor current will ramp to a more negative value.In steady state, when the MOSFET switches ON V(diode) is at –Vc and the voltage across inductor L2 is (Vout(Vcap)), thus the change in current is represented by When the MOSFET switches OFF, the voltage across L2 is (0(Vout)), so the change in current is represented byEquating the values of di givesDividing both sides by (dt1 + dt2) giveswhere DC is the duty cycle as defined above.ThusFrom before we know that SoSo Vout is the magnitude of the output voltage. This is because in the above derivation, we have ignored the slope of di – it is positive in L1 when negative in L2, so cannot strictly equate the 2 statements for DC without considering this.The result of knowing Vcap is that we now know that the Drain of the MOSFET is exposed to a voltage equal to (Vin + |Vout|) and has to be sized accordingly (as does the capacitor’s working voltage).Knowing thatandWe can work out the Duty Cycle in terms of Vout and Vin. ThusAgain, Vout is the magnitude of the output voltage.The duty cycle is set by the input and output voltages only. The inductor value does not feature in setting the duty cycle, nor does the controller IC.The above is true as long as the current in the inductor does not fall to zero. This is called Continuous Conduction Mode (CCM). If the inductor current falls to zero, the duty cycle equation above does not hold and the controller enters Discontinuous Conduction Mode (DCM).In CCM, if the load current increases, the duty cycle remains unchanged (in steady state). The circuit reacts to the increase in loa