Is ripple bad for DC relay coil?

Hello,
I`m modifying a relay with DC coil to be triggered with AC.
I want to keep everything in the relay itself, so size does matter.
I added a diode (half wave rectifier) and a 200uF capacitor.
Relay works, but I have 11v ripple 😱 at 12v.
Is this bad for coil? I will need around 2200uF capacitor to smooth this out, but in that case I will have to fit it outside the relay.

So will ripple damage the coil? If yes, how much ripple would be acceptable at 12v?

Thank you
 
Can you use a full wave rectifier? That would reduce size of the capacitor needed.
The relay requires a certain minimum voltage, which constrains the ripple.
That was the original plan, but when I opened the relay, I realised that I can unsolder only one coils wire from the terminal, the other one is unreachable.
 
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Can you post the schematic?

half-wave-rectifier-capacitor-filter.png

This is how I did it
 
It won´t damage the coil because it´s highly inductive and tends to keep current constant, but I am amazed at the huge 11V ripple on a 12V supply.
Coil inductance will integrate that so it´s as if you had around 7V DC applied to it.

I don´t consider that reliable operation.

You were asked if it chatters, for good reason.

Can´t you generate "good" 12V outside, at some convenient place (even quite a few inches away), with a bridge and a larger capacitor, and feed resulting dc to relay through a couple wires? No big deal.