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What are the differences between linear and switched-mode power supplies and how do they work?
Linear power supplies have a bulky steel or iron laminated transformer. It provides a safety barrier between for the high voltage AC input and the low voltage DC output. The transformer also reduces and the AC input from typically 115V or 230Vac to a much lower voltage, perhaps around 30Vac. The lower voltage AC is then rectified by two or four diodes and smoothed into low voltage DC by large electrolytic capacitors. That low voltage DC is then regulated into the output voltage by dropping the difference in voltage across a transistor or IC (the shunt regulator).
Switched-mode power supplies are a lot more complicated. The 115V or 230Vac voltage is rectified and smoothed by diodes and capacitors resulting in a high voltage DC. That DC is then converted into a safe, low voltage, high frequency (typically switching at 200 kHz to 500 kHz) voltage using a much smaller ferrite transformer and FETs or transistors. That voltage is then converted into the DC output voltage of choice by another set of diodes, capacitors and inductors. Corrections to the output voltage due to load or input changes are achieved by adjusting the pulse width of the high frequency waveform.