It's hard to tell from your schematic what the voltages might be. What is the relay pullin voltage?
I imagine your simulation does not take into account the pickup voltage of the relay. For example, most 5V relays will actually pickup at about 3V or less, a 12V relay might pickup at 4-5V.
One potential way to ensure a higher pickup voltage on your C3 charge curve is to use a series Zener to offset the pickup voltage (though it's a kludge).
There are major problems with the schematic you have:
- The output stage has very limited base current drive, and any current drawn by the BJT base will tend to sop the cap charging.
- Even at low current requirements the half wave rectifier results in a large ripple voltage on C1. This may cause relay chatter as it picks up.
- The second RC stage provides very little time extension since it's charging along with the first stage.
I would not attempt to provide a timer in this fashion, but if you are trapped into this type of circuit for some reason, here is one that might work:
simulate this circuit – Schematic created using CircuitLab
- Changing to a full wave bridge reduces the ripple.
- Increasing C1 reduces the ripple.
- M1/M2 act as a long tailed pair, and R3-R4 set the transfer point.
- D1-R6 provide a more rapid discharge for C2 when the power is off.
The waveforms are like this:
Notice there is still considerable ripple IMO, but much less than the half wave circuit.
A more reliable way to implement timing requirements like this is with a comparator (or even a 555 timer) to provide positive switching of the relay. Given the packages available, it would end up no more complicated than the above circuit.