Most of DC-DC switching circuit analysis uses linear approximation of an inductor voltage and current according to graphs below.
If we use basic formula for the inductor,
v = L di/dt
It is clear that linear changes in current produces constant voltage so from mathematical point of view it is clear.
However, I have trouble to fit this concept into the physical picture of the inductor, knowing that the transient changes on a inductor are described with an i(t) = I(1-e(-t/Tau)) and i(t) = Ie(-t/Tau).
What troubles me is the constant voltage of the inductor given in a approximation.
When the inductor is connected on DC power supply it will build magnetic field, which induces voltage that opposes to the source voltage, which than produces current that opposes the original current. So the original current through the inductor cannot raise nor decline instantly. Induced voltage will be "temporary" present and will tend to reach almost 0 after magnetic field is completely formed and reaches saturation. So approximation of the constant voltage is not quite clear to me from a physical point of view. How can this approximation be physically interpreted?