Relay Chattering: Causes & Prevention

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What causes relay chattering and what can be done to prevent it?
 
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What are your thoughts? What specific circuit are you working with? Is this homework?
 
I've dealt with a relay chattering on an A/C unit due to the pressure fluctuations of the reciprocating compressor on the pressure switch that pulled-in the relay...

...so this is very situation specific.
 
How is 'chattering' defined? I mean, as in frequency and/or mechanical vibration. If it's really fast, like a buzzer, I'm wondering about a bad connection that causes the primary circuit to fail when the armature moves...?
 
Two common reasons:
1. When the relay 'makes' the new system load causes a step current drop in the relay drive coil due to an insufficiently sourced system power supply. This causes the relay to 'break', the open load allows the coil current to recover closing the relay again an so on. Decouple the coil drive from the relay load to correct: more head room on your system power supply, separate power for coil and load (usually is anyway for a relay - that's the point) or better local AC coupling caps (careful - can be complicated as you can just create more problems in a tank circuit w/ the coil and caps)
2. A simple oscillation of some kind on the coil (signal side) independent of the load.