Here is another alternate circuit. This uses one of my favorite parts, the ULN2003/2004. This is a transistor array chip, with seven darlington transistors. It is intended as a driver for small relays, lights, LED digits, etc. In fact is has a zillion uses. I've often used it as an industrial-strength logic device. It behaves as a sept-inverter, a hex inverter with one extra gate. Each transistor is rated for 50 V, can sink 1/2 amp, and has inductive kick spike suppression built-in. It is a great part for harsh electrical environments, such as automotive. You would not believe what the power system in an ambulance looks like. If I were doing this for myself, this is the circuit I would use. But part of that is because this is an old friend. And I have about 50 of them.
In this circuit I use four of the sections as open-collector inverters. You can see the internal schematic for each stage in the insert below. In very round numbers, each input has a transition level (the voltage at which the output changes state) of around 5 V, and appears sorta-kinda as a 20 K resistor to GND. Because this relatively low input impedance is connected to the timing capacitors, the cap sizes are increased to get the same kinds of time delays as the original circuit. Again, the parts values shown are coarse estimates.
With no input, the U1A input is pulled high by the very low current through the LED, probably not enough to produce visible light. This holds U1A's output low, keeping the capacitor voltage and the U1B input near 0 V. U1B's output is high (open), so R2 holds the voltage across C2 a 0 V (+12 V on both ends). This drives U1C's output low, which forces U1D's output open, and the SSR is off.
When the sensor contacts close, U1A,s output goes open and R1 starts to charge up C1. When the voltage on C1 crosses 5 V, U1B's output goes low. This yanks the input to U1C low, and charges up C2 very rapidly. With the U1C input low, its outut is high, the output of U1D is low, and the SSR comes on.
When the sensor contacts open, its input is pulled high enough to drive its output low. This discharges C1 rapidly and drives the U1B output open. This allows C2 to start discharging into R2, and the input to U1C begins to increase. When it (finally) crosses 5 V, the output goes low, making the U1D output go high (open circuit), turning off the SSR.
That sounds like a lot, but it is very similar to how the original circuit works - the action of one timer affects the action of another timer - the end of one timer initiates the beginning of another timer.
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