Troubleshooting an AC/DC power supply
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Plug the power supply into a wall socket and measure its DC output, noting if the output is steady or fluctuates. If the output is close to the rated value, but fluctuates, the transformer and rectifier are likely okay. If there is no DC output, skip ahead to Step 4.
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Unplug the power supply. Unsolder the connection from the rectifier to the filter and use the DMM to measure each filter capacitor, checking for a shorted, open or leaky capacitor. If there are no bad capacitors, go to the next step. Remove the bad capacitor, being sure to suck or wick the bad capacitor's attachment points before soldering the replacement back in. Test again as in Step 1.
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Use the DMM to measure the filter's smoothing resistor's value or verify continuity if smoothing is done with an inductor. Replace bad component if resistor value is off or the inductor is completely shorted. Repeat test from Step 1.
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Use the DMM to read the AC voltage across the step down transformer's secondary (not the AC input) winding. This should read an AC voltage a bit over twice the expected DC voltage output.
In a 12VDC power supply, the secondary winding should read around 30 VAC. Most likely, a failed transformer will have little or no reading on the secondary winding. Replace transformer if bad, then test the new one as in Step 1.
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Switch the DMM to read DC voltage and measure the output of the rectifier stage. This should show a value near the expected DC output but will have a lot of fluctuation in the reading as it is a series of half-waves.
At this point for the 12 VDC power supply, the rectifier reading will be around 13 VDC with a lot of fluctuation.