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All switching mode power supplies, including of course computer PSUs, use one or more high frequency transformers to transform the high frequency AC input to DC. As we mentioned before the high frequency allows the use of a much smaller transformer which also is considerably cheaper.
Most power supplies have a single large transformer feeding power to each and every output line, except from the +5VSB. However there have been instances of special high output models using more than one primary transformer, such as the Corsair HX1000 which had two. A small transformer, usually found right next to the primary one, is responsible for the +5VSB line. Older units also had a second very small transformer, being used as an isolator for the PWM circuit.
The primary transformer separates the primary from the secondary side of the unit. The primary side is the one under AC voltage (the side where the rectifier bridge and main capacitor are) and the secondary side is the one under DC voltage (the side where the output cables are at).
The primary heatsink holds the number of diodes and transistors which are necessary to convert the incoming high voltage DC to high frequency AC. Other components may be found attached to it, such as several PFC components or even the rectifier bridge.
The secondary heatsink holds the Schottky diodes responsible for converting the DC output of the main transformer(s) to voltages usable by your computer parts. Depending on the power supply configuration Schottky diodes are being used to provide either a) only the +12V output and the lower voltages are being generated by DC to DC circuits, b) the +5V and the 12V output and the +3.3V voltage is generated by adding a voltage regulator to the +5V line, or c) even all three positive voltage outputs found in an ATX power supply and the +3.3V voltage line can be entirely independent or sharing its output with the +5V line. The negative voltages (-5V and -12V) are generated by simple diodes and are slowly being removed from ATX power supplies.
The number and configuration of those components indicate the class (or topology or circuit methods) of the power supply. There are several different topologies currently in use, all with their advantages, disadvantages and operating limits. Manufacturers and engineers choose their product topology by taking into account the manufacturing cost and performance requirements of the product. End users should not be concerned about the topology of their unit because each and every design has its own operating range and its performance depends on the configuration and components used in the entire product. The actual performance and efficiency of a switching power supply depends on the design and quality of the entire product, not on the topology design alone.
On the secondary side of any switching power supply you will also notice induction coils and a large number of smaller capacitors. These are being used for filtering the DC output lines. There are other circuits too, depending on the class and design of the power supply. Some of them are the protection circuits (OVP, OCP, UVP etc), the PWM control, DC to DC conversion circuits and more.
