Splitting AC into two DC

Hi I need to connect a digital control that requires 24V and closes a relay when a certain humidity is reached (a dehumidistat). The problem is that I have only two wires between my HVAC (load) and the humidistat (control). I was thinking about the following idea: Create 2 DC sources (+33.6V and -33.6V) from one 24VAC source, by using two half-wave rectifiers. One rectifier would drive the control and the other one would drive the output, but only when the control relay is closed, using a diode to control the direction. Like this: Let's assume that the control and load supports 33Vdc, would this circuit work? Am I missing something? Is there another easy way to achieve what I need? Can I avoid using DC and keeping full-wave AC on the control without driving current through the load? Keep in mind that I need maximum 2 conductors going to the control. The source and the load are away from the control.

I would use this:: https://www.amazon.com/dp/B000LESCI2/ref=cm_sw_r_sms_awd_x_RjKgyb9GPVDXM Relay operates with AC or DC voltage Works within the realm of what your needing. If you already have the power source you don't need rectifiers etcGary Sather

tonanzith wrote: If you already have the power source you don't need rectifiers etc

My power source and the load (a relay) are in the closet. There is only a pair of wires going to the control in the wall (humidistat). So basically, I'm trying to carry 2 signals over the same pair of wires: -A constant 24V input -A switched 24V output Usually, 3 wires are used to achieve this. But I have only two and I can't run a new wire inside the wall. I'm basically missing a common (or neutral) wire. My idea in the circuit above is to use the positive half-wave for the input and the negative half-wave for the switched output. It's a sort of simplified power-stealing circuit that doesn't involve complex electronic and logic.

Update: My circuit works even without the capacitor across the control, a Honeywell H6062 working on 24VAC. It can handle half-wave 24VAC. I can activate the relay remotely using only 1 output wire. I only have to be careful not to plug anything in reverse.