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I'll start by saying that I'm self-taught in electronics, and tend to ask a lot of questions because I don't know NOT to ask them. This is one of those questions.

Consider: I have 120VAC and need 12VDC.

On one hand, I'd get myself a wall-wart transformer that puts out 12VDC and be done with it.

But why a transformer? Why not use a bridge rectifier to get DC, smooth out any ripples with a cap, a throw in a voltage regulator...say a 7812 in this case.

Why is one method preferred over the other? I assume the rectifier/regulator solution would generate a TON of heat and perhaps need a prohibitively large heatsink. Is is engineer's choice? or is there something in the physics that makes one solution is more efficient or cheaper to manufacture than the other? or are there some other crazy unintended safety considerations?

As someone who tinkers and builds stuff, what are some of the considerations in deciding to use a transformer instead of a rectifier/regulator in a project (apart, of course from the why re-invent the wheel when you can buy a wall wart at the corner store argument)?

I'd love to understand this a little better.

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Transformer itself provides a regulation against load changes, Isolation (safety), multiple outputs, didn't change mains frequency, easy step-down and step-up design, easy design of parallel rectifiers (for high-current application), use on 3-phase environment...to count some –  GR Tech Jan 26 at 17:50
    
@GRTech Transformer itself provides a regulation against load changes Usually the transformer output voltage is higher than the rated voltage with no load connected, drops as the output current increase and reaches the rated voltage at the rated current. I'm not sure how that description fits any type of regulation. –  alexan_e Jan 26 at 18:59
    
@alexan_e You are right. But in a well designed transformer this difference is minimum. % Regulation=Vnl – Vfl / Vfl X 100. Vnl:non-lolad voltage, Vfl:full-load voltage. Depends mainly by the equivalent resistance of the transformer, and varying according to the size of the transformer. Typical values starts from 18% for small transformer (~20VA) to 6% for mid one (~450VA) which is very significant. –  GR Tech Jan 26 at 19:59
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5 Answers

But why a transformer? Why not use a bridge rectifier to get DC, smooth out any ripples with a cap, a throw in a voltage regulator...say a 7812 in this case.

Well for one, 120V is above the maximum input voltage specified in the 7812 datasheet.

However, let's say we find or build a linear voltage regulator similar to the 7812, but could handle such an input voltage. Why not that?

It's true of all linear voltage regulators that input current is equal to output current, neglecting some very small current for the operation of the regulator itself. This is because they work by effectively adjusting a resistance to maintain the desired output voltage.

Remember that a resistor with a current through it will also have a voltage across it according to Ohm's law: \$E = IR\$. So for whatever current is required by the load to have the designed output voltage, the voltage regulator effectively adjusts \$R\$ such that \$E\$ is the difference between the input and output voltages.

Thus, for a 120V input, and a 12V output, the voltage across the regulator will be 108V.

Remember also that electrical power is the product of voltage and current: \$P=IE\$. For the voltage regulator, \$E=108\text{V}\$ as above. \$I\$ will be determined by the load.

Let's say we have a pretty small load, and \$I=10\text{mA}\$. The electrical power in the voltage regulator is then \$P=10\text{mA} \cdot 108\text{V} = 1.08\text{W}\$. Not only is this voltage regulator already getting pretty hot, it's horribly inefficient. The power in the load is only \$10\text{mA} \cdot 12\text{V} = 0.12\text{W}\$:

$$ \frac{0.12\text{W}}{1.08\text{W} + 0.12\text{W}} = 10 \text{% efficient} $$

This inefficiency might be acceptable for very low power loads where the heat is more manageable and the cost of the input energy is affordable. However, 10mA isn't even enough to light your typical indicator LED to full rated brightness, so for most things, a linear regulator just isn't feasible.

The solution is to use a transformer, or use a non-linear voltage regulator, such as a buck converter. With these methods it's possible to convert voltages with (given ideal components) 100% efficiency.

Incidentally, the ease of doing this with AC and transformers is why Edison is a jerk and lost the War of Currents.

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+1 for The Oatmeal. –  Stephen Collings Jan 27 at 1:06
    
It all started with 1mA vs. 10mA ... ;o) –  jippie Jan 27 at 6:35
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But why a transformer? Why not use a bridge rectifier to get DC, smooth out any ripples with a cap, a throw in a voltage regulator...say a 7812 in this case.

As you suspected you will get a ton of heat.
120V AC rectified with a full bridge will result to about 120v *1.414 -1.4v = 168v.
Assuming that you'll design a linear regulator circuit that can accept this DC voltage in order to output 12v (7812 has a max of 35v input) the excess voltage multiplied with the output current would be dissipated as heat.

As an example for 0.5A load current the dissipated power would be

$$ P = V \times I = (168v-12v) \times 0.5A = 78w $$

That is a lot of heat, in addition the efficiency of the power supply would be very bad, the input power is 168v * 0.5A = 84w and the output power 12v * 0.5A = 6W that is about 7% !
A typical transformer has an efficiency of about 98%, this will be reduced depending on the step-down circuit connected to the output of the transformer but the overall efficiency would be at least 10 times better.

An additional disadvantaged of the type of supply you suggest without a transformer, is that it doesn't have mains isolation so it is very dangerous if you get in contact with the output wires, it can be potentially lethal.

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Transformers only transform AC voltages (http://en.wikipedia.org/wiki/Transformer). For instance, a transformer can reduce 120 VAC to 12 VAC. They can not transform AC voltage into DC voltage.

The wall-wart "transformer" that you mention is actually an unregulated, or perhaps a regulated, power supply. The simplest/cheapest one are just a transformer, a diode bridge, and a capacitor. More expensive wall-wart "transformers" might be regulated, but they are typically a more complex switching power supply (http://en.wikipedia.org/wiki/Switching_power_supply).

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"Transformers only transform AC voltages". I've got some that work at DC. ;-) –  Spehro Pefhany Jan 26 at 16:34
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Safety first!

While verybody seems to worry about efficiency first, allow me to worry about your physical safety first.

A transformer brings galvanic separation from the mains (of course when properly connected), a rectifier doesn't. When using a rectififer/regulator and you accidentally touch one of the leads, you'll get zapped/bitten and potentially very hard, even lethal when slightly unlucky.

When for example using the rectifier/regulator method to power a small transistor radio, you have to realize that the housing is often not rated for mains voltages. This mean that when holding this radio in your hands you may receive an electric shock through the housing!

If you still worry about efficiency after worrying about you healt, then do realize that your regulator will dissipate about \$\dfrac{120-12}{12}\cdot 100\% = 900\%\$ more power than the connected appliance.

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I think you'll need a regulation circuit in the case of transformer too.

The transformer by its very nature induces voltage into the secondary which is proportional to that supplied at the primary depending on the turns ratio. But this also means that it does not offer much protection from surges except for the isolation of circuits. What I mean by saying that is, if your device is designed to run at 12 VDC and not at 13 VDC (though that would be a very unfair device) the transformer would induce a voltage proportional to the surge voltage which might be something greater than 13 VDC. This isn't good regulation.

The next stage would again be a bridge rectifier working around 12VDC. This again isn't a regulated output, nor is good DC, since it contains a lot of ripples. To reduce the ripples and hence decreasing the AC component in out output, we use filters (usually a 3 or 4 stage RC or Pi filter). Yet again, the output of this circuit is dependent on the input. If there is a surge, we're still doomed. So, we add voltage regulation which means, I am going to supply a constant voltage of 12 VDC even if the voltage being supplied is more than that (i.e. surge). And most simplistically, it would be a Zener, but it could be a Transistor or an Opamp if power dissipation properties are to be improved and other bells and whistles are to be added.

I hope this answers this part:

Why is one method preferred over the other?

Now:

On one hand, I'd get myself a wall-wart transformer that puts out 12VDC and be done with it.

But why a transformer? Why not use a bridge rectifier to get DC, smooth out any ripples with a cap, a throw in a voltage regulator...say a 7812 in this case.

We don't have Walmarts here, but the cheap DC Adapters that we get here contain a step down transformer, a bridge rectifier and a single stage RC filter, and at best a diode across the output terminals, which could be pretty much what your Walmart adapter looks like?

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