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Quick sanity check please - transformer in power supply

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pete_l

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OK, here's the background. (It does ramble on a bit)
I have built a small SMPS with a MIC4576 to power a low power Peltier cooler. The SMPS outputs about 1.5V at 1.8A and pulls about 4 Watts from my bench supply, over a range of input voltages. OK so far.
Now, I intend to power the SMPS from a mains transformer out of my junk box. The transformer in question has two secondaries rated at 12V, 3VA each. We'll call the connections to these secondaries A B for one secondary and C and D for the other. I can connect B and C together and get a 24V AC output. My first shot at using this transformer to power the SMPS was to connect a diode to each "end" of the secondary - i.e. A and D to provide the positive output to a smoothing cap. and take the B/C "centre tap" to ground. I got about 21V DC into no load from this arrangement.
However, when I used this to power the SMPS, the supply to the SMPS dropped to about 4 Volts and it was unable to drive the Peltier. When I sat back and thought, I reckon this was because only "half" of the secondary winding was working on each half cycle of mains power, so I was unable to get the 3VA + 3VA I was hoping for, from the transformer. I can't just connect the 24V output to a single bridge rectifier and smooth that as the DC Voltage from it would exceed the rating of the MIC4576.

Here's the question.
Plan B is to run each of the secondaries independently, each into a separate bridge rectifier and then parallel up the two positive outputs from the bridges and the two negative outputs, too. That way both secondaries are fully working on each half cycle and I should be able to use the full 6VA capacity of the transformer.
While it looks good on paper, are there any hidden problems with paralleling up the rectified outputs from two secondaries?
 
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You can just parallel the windings into one bridge rectifier.

But you must have the correct polarity. If you don't know the winding polarity, you can test by connecting one wire of each winding together. Measure the AC voltage between the other two wires. If it's close to 0V, then you have the correct connection, If not, then you need to reverse one of the wires.
 
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