I am using Traco Power TEN 5-1223 which has +12V input and +-15V output.
I am trying to connect 4 +12V DC/DC converters in series.
How can this be done? What are the connections to be made and to what pins?
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Yes, in this case what (it appears) you want to do will work. To be specific, you connect the inputs of the four DC-DC converters in parallel to the same power supply, and their outputs in series. However, this is a very klunky and expensive way to get what you want.
The reason it works in this case is because these converters are isolated. The datasheet says the output can float up to 1.5 kV from the input.
Stacking the output of multiple converters in series would not work if the outputs of each was referenced back to the input (non-isolated). For example, the input and output ground might be tied together. This would be what you get, for example, if you were to make a simple boost or buck converter with a single inductor.