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When to share ground reference

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Hello Gents,

Let's say we have a three wire discreet sensor to wire to a controller's PNP inputs and let's assume they have different power source, I understand it to be necessary in this case to connect both grounds together so that they have the same reference point

Assuming the above is correct, what about those two different scenarios:

1- NPN sensor, NPN controller inputs and different power source. Do both ground need to be shared?

2-NPN sensor connected to a PNP controller inputs with a pull-up resistor and two different power sources. Do both grounds need to shared?

Is there a situation where positive is shared?


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