When the switch turns ON, the current ramps up in the inductor according to the inductor equation V _ON = L ?I _ON/t _ON. The current increment during the on-time is ?I _ON = (V _ON t _ON)/L. When the switch turns OFF, the inductor equation V _OFF = L ?I _ON/t _OFF leads to a current decrement ?I _OFF = (V _OFF t _OFF)/L.

The current increment ?I _ON must be equal to the decrement ?I _OFF, so that the current at the end of the switching cycle returns to the exact value it had at the start of the cycle otherwise we wouldn't be in a repeatable (steady) state. Using this argument, we can derive the input-output (dc) transfer functions of the three topologies, as shown in Table 2-1. It is interesting to note that the reason the transfer functions turn out different in each of the three cases can be traced back to the fact that the expressions for V _ON and V _OFF are different. Other than that, the derivation and its underlying principles remain the same for all topologies.