110212-1009 EST
big john:
How many switches do you have in the series loop?
What are the characteristics of the time delay relay?
I calculate 240 ohms for its resistance from 24 V and 100 MA.
Is this a linear resistance? Is this an electronic time delay relay with an electro-mechanical output relay? This might have a changing resistance between relay energized and de-energized. Tell us more about the TD relay.
What is the minimum voltage where the TD relay starts to time? Is this an on delay relay? If this was a thermal time delay relay, Amprite, then any moderate residual current thru the relay would alter its time delay time.
After all the switches are closed is the timer started, and then at the end of the time delay does the TD output relay change state?
Assume the TD relay looks like a constant 240 ohms, then a 200 ohm resistor across a switch will produce 240/(200+240) = 0.545 times the source voltage across the TD relay when the TD relay is supposed to be NOT timing.
You have not specified the input resistance of your solid-state relay, and it is not linear. Nor is it a constant load current vs voltage. A P&B ODC5 is energized by 3 V at least. Its V-I characteristic on a sample of one is
03 V 06.9 MA = 435 ohms
04 V 10.0 MA = 400 ohms
10 V 32.0 MA = 312 ohms
The on threshold point of a solid-state relay will not be constant with temperature, life, and from device to device. In other words you can not depend upon a constant known on threshold point, and it is somewhat soft. Soft meaning a not sharp threshold.
Let's ball park 435 ohms in parallel with 240 ohms. This is 155 ohms. 12 200 ohm resistors in series = 2400 ohms. With all switches open the voltage across the relay pair is about 24*155/(155+2400) = 24*0.061 = 1.5 V. Not sufficient to guarantee that any solid-state relay of the model you choose will be energized.
At the other extreme condition to consider is with only one switch is open. Now the load relays look like something somewhat less than 312 and 240 in parallel, or about 135 ohms. The voltage across the relays is about 24*135/(135+200) = 24*0.4 = 9.7 V. How does the TD relay respond with 9.7 V applied to it?
Now consider zbang's diode approach. Use a 17 V AC source. Peak is about 24 V. At 10 MA and room temperature the voltage drop is 0.62 V on a sample of 1 of a 1N5060 diode. 12 of these would be 7.5 V. However the drop will be somewhat higher used to produce 10 MA from a half wave capacitor input filter. But also I do not need 10 MA input to make a successful optical coupling, the input to a solid-state relay.
Assume we have 12 V at 10 MA for our input, then the resistance in series with the optical coupler is about 1200 ohms, use somewhat less because of the diode drop in the coupler. The monitoring circuit has between 12 and 0 diodes in series for the switch section of the circuit. The monitoring portion has two diodes, a series resistor of about 1000 ohms, and a 30 mfd capacitor. One diode is in the coupler, and the other diode is for the rectifier and current routing. This circuit has lots of latitude for variations.
The TD relay will have one routing diode, oppositely phase to the monitoring diode, and possibly a 100 mfd filter capacitor. No problem from the shunting devices, diodes across the switches, because their reverse leakage is very small. Thus, the monitoring circuit contributes virtually nothing to residual voltage across the TD relay when one or more switches are open. Again very good margins.
I do not have time to check what I wrote, and have to leave now. But the essence of the method is here.
.