Stepping Down DC Voltage

The 7812 is known as a linear voltage regulator. As you've noticed, using a linear regulator to halve the source voltage means that the regulator circuit must dissipate the same amount of power as your load. This cannot be avoided with a linear regulator. However, a trick that can minimize the heat dissipated by the semiconductor so that a smaller heatsink will be needed for the chip will be to put a power resistor in series with the input to the regulator. Now the power resistor and the voltage regulator will dissipate this wasted 18 watts (12V*1.5A=18W) of power. But as you will quickly find out, this will narrow the usable regulated current range (minimum load vs maximum load) and somebody will likely still get very hot.

What you will probably prefer though is a traditional buck converter switching design. This will be a much more efficient design. While many companies make very good controllers with design application notes, fabricating a whole circuit that does not interfere with other circuits can get much more difficult than one might originally think.

Fast-switching transistor and 50% duty cycle, 50 kHz, with capacitor for smoothing.

The key word in the post is 'simple'.
There are IC's which will convert DC to DC (buck converter etc as someone has posted) These generally require a few extra components, inductors and the like...
It depends on your definition of 'Simple'
There are dirty ways to cheat to avoid dissipating too much heat.... but don't tell any 'purist', they may wince.
Don't use a bridge rectifier or much smoothing, put this 'lumpy' half wave regulated supply into say a 15 volt regulator, or an adjustable regulator set above 12v.
This will give you a voltage of say 15v with chunks missing out of it...
Now smooth it and put it through the 12v regulator.
You will have to experiment to make sure you don't drop out at full load....
Of course it won't be taking power fom both halves of the mains cycle so you may lose out on power from the transformer, and you will be loading the mains supply asymetrically.

The real way is to get the right transformer in the first place.

Oddly I have had a similar problem at work.
A supply which runs a 24v DC pump, but needs 5v for the micro...
I've used a 0-12v 0-12v transformer, to effectively produce two 12v DC supplies, one is regulated to give 5v, the second 12v supply is then put 'on top' of the first to give 24v.
Ok this is a horrible arrangement, but it gives me the versatility to run 'em in parallel for 12v if I need.
Simple powersupplies can be surprisingly interesting.
Del
_{(Feel free to abuse my weird circuit ideas guys...I'm tough I can take it)}

Weird? I thought that kinda stuff was normal! Sounds like you and I thought of some of the same ways to "do with what you have."

I strongly agree with tcmtech. It is more convenient and cheap to buy from the market where they are ready made devices that do that conversion with high efficiency and power

It just not economical to designing and building a circuit with 7812. You need to add in capacitor, resistor, some heat sink to dissipate the heat and finally you need a casing to house all the parts to it. At the end you project may cost higher and more expensive than you but a good unit from an electronic shop.

If you need an off-line switcher (120-250Vac down to 12-24Vdc) then definitely buy one. These can be difficult to build yourself and lethal voltages are involved.

If all you need is DC-DC voltage conversion under 50V and 100W, then do a little research first. In general, these are EASY to build yourself. I have built well over 100 small switching supplies in this category (boost,buck,flyback,Cuk*,<50v,<100w) with most of them under $10 (US) in parts.

If you find one already made for that price, buy it!

*Cuk converters are a little more difficult to design and build than the others.

Good info...thanks again guy.