How does a pull up resistor change a voltage divider calculation?

Question

I am using this proximity sensor with a raspberry pi. the sensor outputs a 24V signal when triggered, which I need to step down to 3.3V using a voltage divider so as to not blow out the pi. The datasheet shows that I need a pull-up resistor between the output signal and the 24V power, but I'm wondering how this would change the calculations for figuring out the right resistor values to use.

Not considering the pull up resistor, I'd pick 100ohm for R15 and 680ohm for R14 but I'm not sure how to factor in the pull up resistor (would it change the values or R14 and R15?) or how to find the right value for it.

Answer 1

The proximity switch has an NPN open-collector output.

It's to be wired as show below.

The Raspberry Pi input will normally be high and go low when the proximity switch senses.

Answer 2

So you are using the NPN output version.

You don't have to pull up the output to 24V.

So if the output is really just an NPN open collector output then you don't even need any resistors at all, just enable internal pull-up in software.

EDIT: It seems there are internal pull-ups or the sensor is not NPN type. It is also unclear how much current the device can sink or source. But according to your measurements it might have PNP output.

As the datasheet does not say how it works and how much current it can sink or source, to be on the safe side, the current should be kept below 1mA.

Just calculate a simple divider that divides 24V to 3.3V when 1mA flows through the divider. 1mA at 3.3V is obviously 3.3kohms and 1mA at 20.7V can be rounded to a resistor of 21k or 22k.