Glitchy graphics? Random crashes? Shoes shows us why Power Supplies are the most important part of any computer, and how to shop for them.

If underpowered, the components of your system will stress themselves to the point of overheating and often times failure. If powered unstably, the overall stability of your system is drastically reduced, as is the life expectancy of the components themselves. For these reasons, it is my opinion that the Power Supply Unit (PSU) is the single most important part of any computer. Choosing an adequate power supply for their computers is a task that many gaming enthusiasts are not prepared to undertake. This is certainly the result of fallacious product descriptions, and incorrectly placed emphasis on certain specifications. All power supplies have different output levels and different efficiency, but one thing they all have in common is a similar (for the most part) architecture. Although not as important as choosing an appropriate model for your computer, understanding how a power supply supplies power is valuable knowledge for anyone getting ready to put together or upgrade their own custom system.
The Flow:
It all starts at the power plant where potential energy is converted into kinetic energy and exploited through various processes to create an electric potential energy in the form of current. These currents undergo a series of transformations and are sent out in an Alternating Current (AC) through power lines and eventually end up in your humble home, where they are eagerly waiting for you to flip a switch or plug something in. From here it flows through a surge protector (a normal wire that is regulated by MOVs to transfer excess voltages away from whatever you have plugged in), and, ideally, an Uninterruptible Power Supply that will provide constant and conditioned power to your computer even in the event of a brownout. From here it enters your computer, and things start to get complicated.
PC Power Supplies are of the switched-mode type as opposed to the less efficient, less compact, and less quiet linear type. They operate as follows:

Diodes are small semi-conductors that let current flow in only one direction.
Input Rectifier: When the current enters the power supply, it is immediately converted from AC into Direct Current (DC). This is achieved through the use of a circuit with Diodes, semiconductors that conduct current in only one direction. Depending on the manufacturer and relative age of the power supply model, the current might also be smoothed using large capacitors.

MOSFETS switch and regulate current with electrode-gates that inhibit current in patterns.
Frequency Inverter: The current then is converted back into AC at a much higher frequency than the standard 50 or 60 Hz that is present in your wall sockets. This is done with a collection of Metal-Oxide Semiconductor Field Effect Transistors (MOSFETs). MOSFETs are essentially “electrode-gates”, high power transistors that are ideal for switching a lot of current. The inverter MOSFETs basically pulse out the current at a high wave frequency by turning it off and on from 0 to full in a pattern that is recognized by the rest of the PSU as AC.

Transformers manipulate the voltage levels and produce the different rails of a power supply.
Voltage Conversion: Once the current has been manipulated into a high (20+ kHz) frequency, it is ready to be passed through a transformer, which vary in size depending on the input frequency (the higher the frequency, the smaller the transformer). A transformer works by manipulating the magnetic flux that flows through a ferro-magnetic core wrapped with a wire with the input voltage. Secondary coils tap the transformer at the desired voltages. In a computer PSU, these voltage lines (rails) are 5V and 12V (3.3V rails are usually regulated from the 5V rail, though some PSUs have their own 3.3V tap on the transformer).

Capacitors also allow a power supply to provide a short amount of power to your system so it can turn off in the event of a brownout.
Output Regulation: These rough 3.3V, 5V, and 12V rails are then rectified and regulated by another set of MOSFETs that bring them down to their actual specified voltages in the DC current. When the current leaves the MOSFETs, it is in a pulsed form, and is therefore sent through large inductors (often referred to as chokes) and capacitors, which build up charge on one plate before allowing it to discharge to the other plates. This process greatly reduces any ripple in the current by both smoothing the transition from no power to full power through the electromagnetic properties of an inductor, and supplementing each wave in the voltage with charge stored on the positive plate of the capacitor.

Heatsinks with large surface area dissipate energy lost as heat.
Cooling: None of the pieces in a power supply are totally efficient, not even the MOSFETs, and for this reason there are two large heat sinks present in most powers supplies. These heat sinks help transfer the wattage lost as heat from the components out of the power supply in an effort to prevent overheating.
So there it is. Now you are ready to learn what the numbers on a PSU's label mean and how to use those numbers in determining which power supply is ideal for your particular system.
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