Boost topology duty cycle

As seen in Section 4.1, the major types of losses are the conduction and switching losses. Conduction losses are addressed by selecting a better power switch or rectifier with a lower conduction voltage. The synchronous rectifier can be used to reduce the conduction loss of a rectifier, but it can only be used for forward-mode topologies, and excludes the discontinuous boost-mode converters. The synchronous rectifier will improve the efficiency of a power supply about one to six percent depending upon the average operating duty cycle of the supply. For further improvements, other techniques must be pursued. 

In the buck, Idc and Io are equal. But in the boost and buck-boost, Idc depends also on the duty cycle. That makes the design/selection of magnetics for these two topologies rather different from a buck. For example, if the duty cycle is 0.5, their average inductor current is twice the load current. Therefore, using a 5 A inductor for a 5 A load current may be a recipe for disaster. 

Another thing we can conclude with certainty is that in all the topologies, the dc level of the inductor current is proportional to the load current. So doubling the load current for example (keeping everything else the same), doubles the dc level of the inductor current (whatever it was to start with). So in a boost with a duty cycle of 0.5 for example, if we have a 5 A load, then the Idc is 10 A. And if Io is increased to 10 A, Idc will become 20 A. 

The first thing we have to remember is that for this topology (as for the buck-boost), the worst-case is the lowest end of the input range, since that corresponds to the highest duty cycle and thus the highest average current II = Iq/(1 — D). So for all practical purposes,... 

Answer In a buck, the average inductor current ( II ) is equal to the load current ( Io )> that is, II = Io- But in a boost and a buck-boost, this average current is equal to Io/(l - D). Therefore, in the latter two topologies, the inductor current is a function ofD (duty cycle) — and therefore indirectly a function of the input voltage too (for a given output). 

So the point here is as follows if we have a composite topology in which the duty cycle of a buck in CCM is used to drive a buck-boost in DCM, we can get the dependency on Vin above to cancel out completely as follows ... 

We can also use the fact that the output voltage of a discontinuous mode converter at a given duty cycle depends on its inductance. So we can tune the slave buck-boost to have the required output level (at its expected maximum load current) by a careful choice of inductance. Within a valid range, this technique provides completely adjustable auxiliary output voltages, something we cannot normally expect from composite topologies based only on continuous conduction modes. 

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