Let's start with a simple model.
Your data sheet lists a maximum control current of 1 mA at 15V, which means the input acts like roughly a 15 kOhm equivalent resistance. What you want is a voltage divider that takes your 24V down to 15V, with a lower resistor of 15 kOhm.
$$
\frac{15 k\Omega}{15 k\Omega+x}= \frac{15V}{24V} \\
x=9 k\Omega
$$
Now, that's your lower limit. Any less series resistance, and the voltage across the input will be over 15V and out of spec.
The data sheet also lists that the controls will pull a minimum current of .2 mA at 4.5V, which is a 22.5 kOhm equivalent resistance. In that case, you get a maximum dropping resistance of 97.5 kOhm. Any more than that and your voltage will be too low and out of spec.
The problem here is that we don't know what happens in between. The control current at 15V will not exceed the 1 mA spec. The data sheet doesn't say it can't be less than 1 mA at 15V, though. So what happens then? Suppose the control current is .5 mA. Now you only get a 4.5V drop across your 9 kOhm resistor, and your voltage is 19.5V, out of spec. The same problem applies to our maximum resistance if the controls draw more current than the specified minimum: your voltage will drop below spec.
Unfortunately we can't make any guarantees based on the information in the data sheet. All we can do is make some reasonable assumptions.
Let's assume the input response is linear between the two points provided. That means it's basically a diode with a resistor in series, which is not unreasonable. Taking the two voltages and currents they provide, you can model the input as a 1.875V constant drop and a 13.125 kOhm resistance. This lets us compute the terminal behavior at any operating point, not just the two provided. Of course, its behavior could be totally different, but it's the best we can do
Now we can ignore the terminal voltage and just worry about keeping the current between .2 mA and 1 mA. So you have a voltage drop of 24V - 1.875V = 22.125V across (13.125 + x) kOhm. We'll target .6 mA, middle of the range. A 23.75 kOhm resistor will hit that target.
I'd use a 22 kOhm. Even 1/16W should be fine.
I will be using momentary switch to control the main power input in my design. Hence to latch the power I need to select a relay. On what basis should I select a relay since I find different types of relay like solid state relay, mechanical relay and on. I dont know the criteria to select a relay. can someone help me in same.
Best Answer
For the mechanical vs. solid state argument, there are certain applications where SSRs are indicated. They have the advantages of:
But they have significant quirks that you will need to design around:
Unless you have a good reason to pick a SSR, a standard electromechanical power relay will be much easier to design into your system.