Convert a 0-200 Microamp Signal for use in PLC?

how much accuracy do you need? What's the compliance voltage?

TTFN (ta ta for now)
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Accuracy isn't too critical. 0.5% - 1.0% or better preferred. The 0-200 microamp signal is just for monitoring, not precise control.

Does the PLC have ADC inputs? Can you run the current into a resistor or transimpedance amplifier/buffer?

TTFN (ta ta for now)
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Parallel the Type K thermocouple with a length Type K wire from the input on the black box into a commercial temperature transmitter which will give you a 4-20mA output that any PLC can handle. Transmitters are typically "2-wire, loop powered", meaning you also have to provide a 24Vdc power supply to power the transmitter, but that power runs over the 2 wires going to the transmitter.

I suggest isolated inputs on temperature transmitters, because many commercial thermocouple junctions are grounded and grounding can produce ground loop problems; an isolated transmitter input avoids that issue.

There are two categories of temperature transmitters - dumb and smart. The dumb transmitter is factory configured for some input range, say, 0-500 Deg F. with a corresponding proportional 4-20mA output.

The smart transmitter's input can be configured zero/span for the 4-20mA output. Problem is, unless you're in an industry where the software/modem or handheld programming communicator is readily available, then you're stuck buying and learning whatever gear is needed to set the range.

A dumb transmitter should be pre-ranged; my recommendation for a smart transmitter one is to find a vendor who will configure the range for you so you don't have deal with the configuration end.

It pays to physically label a field transmitter with its configured input range so the next guy knows what the 4-20mA output signal represents.