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## DC Transfer Functions

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.

Table 2-1: Derivation of dc transfer functions of the three topologies

Applying Voltseconds Law and D = t ON/(t ON + t OFF)

Steps

Therefore,

(duty cycle equation...

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##### Topics of Interest

The DC Level and the "Swing" of the Inductor Current Waveform From V = LdI/dt, we get ?I = V ?t/L. So the " swinging" component of the inductor current " ?I" is completely determined by the applied...

3.1 DC Transfer Functions 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 =...

3.2 The DC Level and the "Swing" of the Inductor Current Waveform From V = L dI/dt we get ? I = V ?t/L. So the "swinging" component of the inductor current "? I" is completely determined by the...

How Inductance and Inductor Size Depend on Frequency The following discussion applies to all the topologies. If keeping everything else fixed (including D) we double the frequency, the voltseconds...

3.10 How Inductance and Inductor Size Depend on Frequency The following discussion applies to all the topologies. If keeping everything else fixed (including D) we double the frequency, the...

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