A typical doorbell transformer is AC to 24VAC. So, reasonably, any 24VAC transformer would work. The doorbell switch just acts as an interrupter, keeping the circuit disconnected until the button is pressed.
So connecting the SAGE in place of the chimes should work just fine.
Illiustrates typical wiring for the doorbell. I should think you'd just substitute your wall wart for the transformer, and the Sage for the chime. Based on the way you wrote things, it sounds like you have wiring from the doorbell button to the basement. If that's true, it seems to me that you could connect the positive output wire of the wall wart to one side of the doorbell button, then connect that to the "F" or "R" wires on the SAGE, and connect the negative/common wire to the SAGE.
Not familiar with Sage but doorbells typically use AC not DC. Most of today's doorbell transformers output 24V AC while the older ones were 16V AC. If your device is meant to be powered from the doorbell circuit, connecting DC power likely won't work.
You'll likely still need the transformer if the device is meant to be powered from the doorbell circuit but you can replace having to have a chime with a resistor instead. I would have to do some research on the resistor size but this would work.
Edit: Did a quick search and likely a 25 to 30 ohm resistor will work to take the place of the chime. This shouldn't cost more than $3-6 or possibly cheaper. Make sure it has at least a 20 watt or higher power rating. In all you'd need the transformer and the resistor assuming you already have a doorbell button to make it work like I think you want.
Initially, this setup appeared to work as desired. However, I noticed during testing that the SAGE device would stop responding after ~20 button pushes performed during a several minute period.
Since I moved on to other options, I did not try inserting resistors as some of the other posts below have suggested.
My initial experiment:
24VAC 750mA wall wart transformer from an irrigation controller.
Connected doorbell button wire 1 to green/front door lead on the SAGE device.
Connected doorbell button wire 2 to neutral wire of the transformer.
Connected positive wire from transformer to white wire on the SAGE device.
Looking at the HE logs, the events seems to occur very quickly.
In the following diagram, per @scottgu3 recommendation, I replaced the bell with the SAGE device.
Just an opinion from this old electronics tech but if you take something out of a circuit that is current limiting (the chime), you generally need to put something back in place of it. In this case, the resistor would be for current limiting so you don't burn something up eventually. It may work now and might work for awhile but eventually without the current limiting device, it's very possible it could burn out the input to the controller or worse yet, start a fire when it does.
I seem to remember (maybe it was on the ST Forums) a discussion about mounting a contact sensor in the bell housing - when a magnetic field is generated the switch trips or something like that - was a while ago. The other solution is just get an Aeotec Ring Doorbell 6 and see if you can't hardwire the doorbell button.
Ahh sorry skipped over that part!! Then maybe the Aeon/Aeotec doorbell then.. I use the Ring doorbell + Virtual Switch and Alexa to trigger an older Aeon/Aeotec Doorbell chime.
It shows the Sage connected directly across the chime terminals. This means you do not need a load resistor. You can wire:
the transformer to the button -- the button to the Sage Green wire -- The Sage white wire to the other terminal of the transformer.
I also found a troubleshooting manual It says the Sage will work on any doorbell voltage from 10 to 24 VAC.
So all you need is a 12VAC wall adapter and your are good to go.
Note:
I realize the Sage is designed for use with AC systems, however it is unlikely the Sage actually requires AC to sense the door bell. However since its not possible to test the Sage with DC, AC is a safer direction.
It is possible this device has built in current limiting judging by the video @JohnRob linked. If that is the case, then no you would not need the resistor.
Its kinda like that but its not really current limiting. Think of the Sage as a voltmeter. It is connected right across the chime input power..........hmmm good you said that...
Thinking more about the Sage input. You might have to put a small resistor across the Sage inputs. Would think a small 1k to 5k resistor. My thought is, originally the chime input insures the Sage inputs are at 0V when the doorbell button is not pushed.
Now when the button is not pushed, the Sage inputs see an OPEN circuit which it may or may not sense correctly or immediately.
A voltmeter has a high internal resistance specifically to limit current, but in that case it's to keep from loading the circuit. You are running AC through a coil. That is going to create a voltage drop across that coil equal to the transformer voltage when the button is pressed, then it could be floating when it's not. So I think you are correct in wanting to use a resistor to ensure the Sage inputs do correctly go to zero when the button is released.
I think I just really said the same thing in different words.
Yes, something funky is going on with the SAGE device when no resistors are included. For example, I can get the SAGE device to record ~20 button press events before it stops processing button pushes.
Removing the battery, reinserting the battery, waiting a few minutes and the device still doesn't respond to events. I left it over night and then it started responding.
I'm done with the $5 SAGE experiment.
Plan B: Modify Visonic MCT-340 E Zigbee - ~$20 USD
This route looks interesting based on community members' successes:
The two downsides are:
Since there are no built-in screw-in internal contacts, you have to solder two wires to the board.
Battery only power. No mains supported.
Plan C: EcoTech DWZWAVE2.5 Z-Wave - ~$30 USD
If the Visonic device doesn't work out, I'll make use of the internal contacts on EcoTech DWZWAVE2.5 device. Based on other community members' experiences, it looks like this device will work for my needs with a minimum of fuss.
If the DWZWAVE2.5 doesn't work to my satisfaction, I'll go with the Aeotec Doorbell 6 device. I don't really need the chime function part of it, but at least I'll likely get a reliable doorbell button, a mains powered device, and supported integration with HE.
I would disable the chime part of it for doorbell use and consider using the siren feature for other use cases.
The only downside with this approach will be Z-Wave vs Zigbee, but if the response time is fast enough, the radio tech doesn't matter to me.