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Hey guys, first post here, so I'm working on my first project and I have a question, also I should note that I'm beginner-status with electronics.

I'm using an infrared temperature sensor to measure the temperature of objects, and I want to measure objects that are just a little bit higher in temperature than the operating range. I'm using an MLX90614, so the max temperature according to literature is about 720 F, and I'd like to be able to measure to around 900 F. The objects that I am measuring range from 200 F to 900 F.

I know that the sensors output is a function of the sensors input minus the electrical resistance generated by the sensor, so do I just need to create my own calibration curves for the temperatures that I want? Or would I need to alter my circuit a bit? For example, I know sometimes you have to put resistors on the output from a sensor and then you must compensate for that in determining the actual output from the sensor.

I'm a chemical engineering student (not electrical) so this is all somewhat new to me. I'm taking a class called 'process controls' and we talk about sensors and creating closed-loop control systems. I understand most the science going on but some aspects of the electronics are new to me. From theory I want to be able to say that I could use resistors to shift the operating range of my IR sensor up a bit, so instead of measuring 0-700F it could measure 300-1000F but I'm not sure if thats possible or not.

So I guess basically my question is "if my sensor's max operating temperature is 700 F and I attempt a measurement of 800 F, what happens?"

Does it go like this?

input = 3.3 v
output = 1.5 v
from the voltage difference, temp is calculated

so at max op temp,
input = 3.3 v
output = 0v ?

Any help would be appreciated :)
Your guess is as good as mine. The best source on that information would always be the manufacturer of the sensor. Operating a device outside of it's stated limits may give results. But challenge those and it may not work for long or well. You'll have to test that out yourself for reliability (something may melt or destabilize beyond those temperature limits), repeat-ability (one day you get this value, the other another at the same temperature due to unknown variables) and resolution (signal response might be limited at the extremes). The datasheet is clear enough on it's maximum operating ranges:

page 4 of the datasheet:
Exceeding the absolute maximum ratings may cause permanent damage. Exposure to absolute-maximumrated conditions for extended periods may affect device reliability.
Since it (MLX90614) really only outputs a digital signal (either SMBus or PWM) it is easy to characterize how it responds in known higher temperatures. Measure! Just make sure you have a different temperature sensor that is known to work correctly to compare it with (thermocouple). And expect it to fail.
You should use the I2C digital output, not the PWM ("analog") output.

The data sheet says the device is calibrated for object temperatures of up to 380 degrees C, so it should continue to function above that, but with larger errors.

The real problem is that the MLX90614 measures the average temperature of everything in its field of view. You must avoid overheating the sensor, and also avoid having large temperature gradients within the sensor, which means that you can't place the sensor very close to objects with very high temperatures. Consequently, it may be difficult to have the entire field of view filled with the object of interest.