Linear Regulators Versus Switched Mode Regulators

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Voltage regulators and their efficiency
In this article we will denote the input voltage by Vi and the output voltage by Vo. The input current will be denoted by Ii and the output current by Io.
The voltage regulator can be considered as a blackbox which takes Vi and Ii as inputs and converts to energy to Vo and Io.
The linear voltage regulators usually have a low efficiency because they "decrease" the primary voltage by dissipating the excess energy as heat. The linear regulators are only able to output a voltage lower than the input voltage, and they do this by taking the voltage difference between input and output as a voltage drop on their power element (which is usually a transistor, almost always integrated on chip).
In the case of linear regulators, the output current, Io is approximately equal to the input current Ii, so the power dissipated by the regulator can be approximated by the following relation: Pd = Io * (Vo - Vi).
I will consider a simple example, with Vi = 12 V, Vo = 5 V and Io = 1 A. With those values we get the following dissipated power: Pd = ( 1 2 - 5) * 1 = 7 W. This power, Pd is dissipated as heat and it's basically wasted (unless the purpose of the circuit is to produce heat).
The power sent to the load is P = 5 * 1 = 5 W (the current through the load multiplied by voltage drop on the load). So, in this case the linear regulator wastes more than half of the energy by dissipating it as heat. And you need a big and bulky heatsink to dissipate it.
Now, let's analyze the case of the switched mode voltage regulators. In contrast to the linear regulators, the switched mode voltage regulators use reactive elements (inductors and/or capacitors) for temporary energy storage, so they store the energy instead of wasting it. The reactive elements store the energy in one part of the working cycle, then they give it back to the circuit in another part of the working cycle. In theory, an ideal switching regulator has an efficiency of 100%... but of course that the reality is tough.. and the circuit elements are non-ideal. In practice you can see power converters with an efficiency close to 98%, which is quite good when compared to the efficiency of a linear voltage regulator.
Considering the same numerical example, a converter with 98% efficiency would have a dissipated power of only 0.1 W, and usually you don't even need a heatsink for this power level.
Voltage regulators and their cost
Usually the linear voltage regulators are significantly cheaper than the switched mode voltage regulators. The switched mode voltage regulators are more expensive, require more components, a bigger PCB area and it's good the take special caution when designing the PCB layout (especially due to the electromagnetic interference).
Voltage regulators and the ripple of the output voltage
The linear regulators produce a very stable output voltage with extremely low ripple and they have good transient response. This kind of regulators is suitable if you work with precision analog circuits.
The switched mode voltage regulators produce an output voltage with significant ripple (some times a few hundred of milivolts) and they have a worse transient response when compared to the linear regulators.
Guidelines
If you need an output voltage close to the input voltage (let's say that you need an output voltage which is 80% of the input voltage), then it's a good idea to use a linear voltage regulator. If you work with precision analog circuits, or if you perform some instrumentation, then, again it's a good idea to use a linear voltage regulator.
If you need a very small current, then the efficiency of the regulator is not very important, so again, I recommend a linear regulator.
If you need an output voltage much smaller the input voltage, and a significant current, then the best choice is a switched mode regulator. If have a circuit powered from a battery, then you care about energy efficiency, so again a switched mode regulator is the best choice.
Another strength of the switched mode regulators is that there are also topologies which can output a voltage higher than the input voltage (see the boost topology and the charge pumps), and even a negative voltage. When you need a negative voltage, if you don't need much current, a charge pump is usually a good choice.