Switching Regulators in Series

Answers to 1 and 2 should come mostly from the datasheet of whatever switching power supply chip you plan to use. First you have to make sure the chip is intended for your input voltage, output voltage, and maximum current. After that you need to follow the directions, carefully.

These kinds of chips are designed assuming a certain range of parts external to them. The datasheet will tell you what is acceptable and it may even give you some guidance what values to use over a range of parameters. For example, the datasheet might recommend a larger inductor for the upper half of the input voltage range. However, you'll probably pick a chip because it's max characteristics exceed your requirements by some reasonable margin. In that case, you follow the recommendations for the max case, since that's effectively what you will be using. Some datasheets assume this and only give you one set of recommended values. Just follow them.

As for question 3, yes, switching power supplies can cause more EMI. The main trick is to keep all the local loop currents localized to the power supply sub-circuit, and to keep these loops physically small. This means starting with a good layout, then carefully routing the key nets. Make a separate local ground net for the switcher, then tie that to the main ground in only one place, probably right at the ground side of the output capacitor. This keeps the loop current thru the diode, inductor, and output cap localized and off your main ground plane. Only the net delivered current should flow thru the power and ground feed points from the power supply sub-section.

This is a great example of why you need to do the math and nost just blindly build something. It should have been obvious from the start your regulators would get hot just from the basic physics.

You say you have about 18 V in and that each regulator is producing 12 V at 1 A. That means (18 V - 12 V) * 1 A = 6 W is being dissipated by each regulator. That is way more than a TO-220 case can handle in free air.

There are two obvious options:

1. Put a heatsink on each regulator. Make sure it can handle the 6 W of power and still keep the part cool enough at whatever your ambient temperature is. This time do the math up front. Make sure to take into account not just the thermal resistance of the heat sink but also the thermal resistance of the die to the case. The total must be low enough so that 6 W into the die won't exceed its operating temperature.

   For example, let's say you need to keep the die at 125°C or below (I just made that up, it's your job to look at the datasheet and find the real number) and that your ambient won't exceed 25°C. That means you can afford up to 100°C rise in the die above ambient. Since 6 W of power is being dissipated, that means your combined die to case and case to ambient thermal resistance needs to be 100°C / 6 W = 16.6°C/W.

2. Use a swithing regulator. At these voltages, you should be able to find something that can do 2 A out. The single switcher will replace the two linear regulators. It will also be smaller and cheaper since it won't have to deal with getting rid of 18 W of heat.