Looks like you know your stuff when it comes to these timer circuits, this one is a little out there but dont believe it is out of your knowledge.
This is a replacement part for an old Bryant furnace 822 relay. What is needed is a circuit that will get a 24VAC supply when the thermostat kicks in, it will have to have a 45 second delay before triggering a relay that powers the 1/3HP blower motor, the motor needs to run for 45 seconds after the voltage is shut off via the thermostat. I'm sure that there is a more efficient circuit other than the 822 relay to do the job, especially when you take cost into the equation.
Once the thermostat kicks in it sends 24VAC thru the limit switch(as long as it's not tripped from an overheat), then thru the pilot lights thermo coupler (providing that the pilot is lit)then applies it to the timer/relay. Once the thermostat kicks out the voltage goes to zero across all components.
Yes, the process would have to repeat each time the thermostat kicks the furnace on.
I was orginaly looking at the 556 timer chip to see if it would be able to serve the dual delay, but looking to you for the best way to get it done.
The circuit shown below will respond exactly as per the requested specs. The entire functioning can be understood with the the following points:
When the thermostat "kicks in", the 24V AC is applied across D1 and ground of the circuit. The 24VAC gets rectified through D1/C1 and passes through R2 to reach the junction of R3 and D3.
Since initially C2 is in a discharged state the supply gets grounded via D3 and C2.
However as C2 starts charging up, after a predetermined time (45 seconds) set by the values of R2/C2, the voltage across C2 reaches about 1.4V which becomes sufficient to trigger T1.
T1 conducts and so does T2, pulling the relay into action.
The blower connected to the relay contacts initiates.
After some specified time the thermostat switches OFF.
When this happens, the voltage at the cathode of D1 becomes zero which makes D2 forward biased. such that The instantaneous voltage at the collector of T2 instantly passes via C3, D2 and retains the conduction of T1.
The above situation inhibits the circuit and the relay from switching OFF even after the thermostat has switched OFF.
However now C3 start charging up, and after some predetermined time (45 seconds) set by the value of C3/R6, it gets fully charged and shuts off the base bias to T1.....the circuit and the relay also shut off....until the thermostat "kicks back" again to repeat the procedure.
Parts List for the proposed timer delay/relay circuit idea
R1 = 100K
R2 = may be replaced with a 1M preset
R3,R4,R5 = 10K
R6 = may be replaced by a 100K preset
D1----D5 = 1N4007
C1,C2 = 100uF/50V
C3 = 220uF/25V
T1 = BC547
T2 = as per the relay coil current