I'm using an adjustable power supply (0-18V and 0-3A) to power my EZ-B v4. But it seems that every time I'm moving some servo's a bit too fast, the controller loses connection to my wifi. As long as I make sure the movements are very slow it usually doesn't happen. Could it be that my power supply can't deliver enough amps? Would using a 2 cell Lipo fix the problem? The only Lipo's I've got lying around right now are 3s, so I'm not able to test it right now.
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It is just as you suspected and as Josh has confirmed, your power adapter just can't handle the in-rush current requirements of the servos and drops the voltage (browns out) as a result.
We definitely recommend using 2S (7.4V) 25C LiPo batteries, that's what we use for our robot kits.