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Average Current Model

A simplified model that assumes the inductor current is well-approximated by its average value over the switching period. This is often used for initial control design and analysis of high-frequency converters.
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The statement of the theorem

The inductor current iL(t)i_L(t) is approximated by its average value iˉL\bar{i}_L. The state dynamics are simplified by assuming diˉLdt≈0\frac{d\bar{i}_L}{dt} \approx 0 over the switching period TsT_s. The resulting averaged model relates the average current iˉL\bar{i}_L to the average voltage drop ⟨vL⟩\langle v_L \rangle: diˉLdt=1L⟨vL⟩≈1L(Vin−Vout)DTs\frac{d\bar{i}_L}{dt} = \frac{1}{L} \langle v_L \rangle \approx \frac{1}{L} (V_{in} - V_{out}) \frac{D}{T_s}