It's important to check any power supply before using, especially flea market/garage sales etc. You can't rely on the stated output which will not be correct if the power supply isn't regulated or switching. A non-regulated supply will ALWAYS output higher voltage until the load equals the rated amperage. If the load exceeds the rated amperage, the voltage will drop below the stated number. For the most part, it's best to use regulated or switching power supplies.I am using a 9V wall wart for my arduino micro. I made sure it was not supplying over 10V though. Some that I picked up at the flea market / goodwill were putting out as much as 18V when they were supposed to be either 9 or 12 V supplies.
I doubt it's a filtering issue. I assume your relay board is 5V? Are you powering the relay board from the Arduino? If so, that could be the issue, the Arduino voltage regulator is likely cutting out from the load. Try powering the relay board with a separate power supply and see if the problem goes away. When using 2 power supplies, you may need to connect a common GND between the relay board and the Arduino.I'm using a Uno. Wall wort is 9v/1A, measures 9.4v with no load. Feed in through the jack. When I use the USB to power, all is well and it's very stable. I've tried a 12v wall wort and it goes crazy...so I'm thinking its the power supplies...probably not filtered. What wall wort brand and output have folks had good luck with? BTW, I'm powering an 8-relay module.