!THE REFUSAL TO STOP CREATES THE SPIKE
To step a voltage down, you chop it and smooth it. To step a voltage up, you must weaponize inertia.
A boost converter closes a switch, shorting the input through an inductor to ground. Current rushes in, and the inductor stores this energy by building a magnetic field.
Then, the switch is violently opened. The path to ground is gone.
An inductor's fundamental property is its refusal to let current stop instantly. As the magnetic field collapses, the inductor acts as a pump, violently spiking its voltage as high as necessary to force the current to keep moving. This massive spike of voltage, added to the original input, is shoved through a one-way diode into a capacitor, trapping it at a higher pressure than the source.
The voltage is stepped up not by gentle accumulation, but by the violent refusal of the magnetic field to stop.