Ok, to shed some light on the subject, here’s how the sensor “probably” works. There are two variants, don’t know which one Aeon uses, but essentially, they do the same. However, which they use may impact the complexity of the circuit.
chris2vic is correctly asserting that a relay is a cheap and effective way to go, though you may need to match the relay to your transformer voltage and ensure you are being provided the proper current (AC in this case).
Phobiac is providing an essential piece of information here:
My doorbell is digital
What that means is that his line is most likely using DC (not alternating current) which may explain why his sensor didn’t fry. It never saw a reverse voltage on it’s terminals, plus the impedance of that digital door bell is much higher than that of a coil, meaning a lot less of the total voltage falls on the sensor.
On to the sensor, there are two variants I could think of: pull-up resistor and pull-down resistor.
To explain the parts:
- R1 and R2 are resistors of unknown value.
- U1 is an inverter logical gate, converts the input into a 0/1 value. When the voltage at input is over the threshold, the output will be very close to 0V, when the voltage at input is under the threshold, the output will be very close to Vcc (typically 4.5V - 5V in TTL circuits).
- U2 is a buffer logical gate, does the same as U1 but without inverting. Low voltage in outputs a 0V, higher-than-threshold voltage in outputs a close-to-Vcc voltage.
- BT1 and BT2 are battery holders inside the sensor
- S1 and S2 are single throw single pole switches - your door bell switch
The pull-up resistor variant uses R1 to keep the input voltage high, causing U1 to output a logical 0 (U1 is inverting, so 0 >>> 1 and 1 >>> 0 - also note that these may be reversed, it’s all a matter of personal preference - how they translate 0 = open and 1 = close or the other way around is irrelevant as long as the output of the z-wave controller is understood correctly by the user). When the switch closes, it brings the input voltage to 0V (negative pole of the battery holder), causing U1 to toggle to a logical 1. At this point, the R1 is there to protect the batteries, it should be high enough to limit the current flow between the + and - poles of the battery holder as to avoid a short circuit.
The pull-down resistor variant uses R2 to keep the input voltage low, causing U2 to output a logical 0 (U2 is non-inverting, so 0 >>> 0, 1 >>> 1). Push on the switch and that connects the input to Vcc, causing U2 to output a logical 1.
Now all these work without any external power. The power is provided by the battery holder in the sensor and no external voltage is expected whatsoever.
Due to power constraints, it is very likely that the pull-down resistor variant is being used, to avoid a constant current flowing through the battery due to the pull-up resistor R1 if the pull-up variant was used. But I am only assuming…
We are assuming that the switch is being traversed by AC current from a transformer through a coil in the doorbell.
If the pull-down variant is used, you guys may be lucky. BUT not that lucky. One would have to ensure AC current does not flow into the input of the logic gate and also that the voltage applied does not exceed its capabilities. We can do this by using a rectifying diode to ensure only one way of current passes through. We also need to limit the current and the voltage so we’ll use two resistors to slice that voltage so that the peak won’t reach over the Vcc of the sensor. We can also use a Zener diode to protect the input of the logical gate and a capacitor to slow things down.
Here’s what it looks like:
Note: SPK2 is there to show the doorbell itself, even though the doorbell is most likely mechanical. The coil pulls a bar that hits a bell, causing it to vibrate. Couldn’t find an object for that to put on the schematics, so I used a speaker instead.
Relying on the low impedance of the L2 doorbell coil, we’re closing the circuit through D2, R3 and R4. D2 is there to ensure the top side of R3 always has a higher or equal potential to the bottom side of R4. R3 and R4 effectively act as a potentiometer, splitting the voltage between them. Equal values for R3 and R4 will split the voltage applied to them in 2. C1 is there to slow things down. Or further rectify the current we’re dealing with. Since we’re dealing with AC, half of the time we’ll have current flowing through the diode D2, and half of the time we’ll have nothing (while the current tries to flow backwards). In the US, this happens 60 times per second. When current flows through D2, there will be voltage on the R4, just the same as the C1. The C1 will start charging. When the current flows the other way, D2 will stop it. At this point, C1 will slowly start discharging. The recharge/discharge time is given by the RC product, in our case R4 times C1 (there are other resistors in the circuit we don’t know the value of, like R2 so we need to trial and error here to get our timing right). The goal of the timing is to keep the gate in a stable position while S2 is open. If we don’t do this, we’ll get a lot of 0/1/0/1/…0/1 transitions. The Zener diode is there to ensure the voltage never goes over a certain value. In other words, for protection. May be optional if R3 and R4 are sized appropriately. R3 acts as a current limiting resistor too, so we can’t go too low on it.
Now, assuming the 16V people talked about earlier is peak to peak, it means the voltage swings between -8V and +8V, so on the positive half of the cycle, we’ll have 8V applied to D2-R3-R4. D2 will eat some 0.6V of it, leaving the rest of 7.4V to the resistors. Let’s assume R3 is 4.7kohm and R4 is 10kohm. If voltage on them is 7.4V, we’ll get 2.37V on R3 and 5.03V on R4. C1 will never let the voltage reach 5.03V and will pretty much average it. We only use half the time, and it is safe to apply a square root of 2 factor on the capacitor averaging, so we may see a 5.03 / sqrt(2) / 2 = 1.78V. This is where tinkering starts. make R3 2.2kohm and see if it works, if not, start increasing R4 slightly. C1 needs to be sized according to R4. Start with a 100uF and see how it works. Unfortunately, there are so many unknowns in the sensor that I can’t do the sizing for you. And, at the end of the day, this may not work at all. It all depends on how the sensor is doing its job. Also note that we’ve reversed the way the sensor works. S2 is open, you get a 1 at the digital output. S2 is closed, we get a 0 at the digital output. Reversed.
As for the Zener diode, if your sensor takes 2 AA batteries, use a 3V Zener, if you use 3AA batteries, go for a 4.5V Zener (if available) or a 5V Zener diode.
The pull-up variant is much more complicated to work with.
Also, an opto-coupler should always be used to separate circuits. Makes things more complicated still.
Conclusion:
If you have AC power through the doorbell switch, measure it and use a properly sized relay or a reed sensor attached to the doorbell coil to drive your dry contact sensor. Easier and cleaner than building electronics boards. If your doorbell is digital, you may be lucky enough that you have DC currents flowing through it and that the doorbell itself is actually using a dry contact. In which case hope your dry contact sensor is the same kind (i.e. they are both pull-up or pull-down). And with no knowledge of what’s inside the sensors, It’s a trial and error world we live in 
Good luck,
Adrian
