Linear power supply units are relatively simple and common for low power applications. They fundamentally work by stepping down the AC voltage of the utility power grid, rectify it to DC voltage and finally filtering it by using a capacitor.
In order to step the voltage from the 90-250V (depending on your location on the planet) utility grid voltage down to a low voltage usable by the equipment, linear power supplies use a transformer. The transformer steps down the supplied AC voltage to a lower value, down to 14 VAC for example, but the original waveform remains unchanged. Then a rectifier is used to transform the sine wave AC voltage into a fully rectified pulse voltage. As this rectified voltage is far too unstable, it cannot be yet used by the equipment. The rectified pulse voltage requires filtering through a capacitor to be transformed into near-DC. Then a voltage regulation stage is necessary to adjust this near-DC voltage to true DC voltage and sustain it regardless of any load current changes. In very small and simple applications that can be done by simply using a Zener diode but most of the time a full voltage regulation circuit using a power transistor operating in its linear region is necessary. This power transistor has the ability to act as a variable resistor in series with the load, regulating the output current and voltage accordingly. It is controlled from a circuit sensing the output voltage and modifies the transistor bias to maintain a set voltage output despite of any load current changes.
Linear power supplies have many desirable characteristics. They are very easy and cheap to manufacture because of the few and common components, which also makes them very reliable when correctly designed. Some early units which were released 25 to 30 years ago are still operational. Their performance is excellent as well, with exceptional output voltage regulation and next to non-existent ripple. Finally even the lowest quality products show very little electromagnetic interference (EMI) and exceptionally fast response times.
Linear PSU Schematic