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Amplify Voltage Change and Shift Voltage

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Hello. I'm trying to modify a motion detector so that I get the first derivative of the heat energy.

In the attached image, the top line has input voltage of 5V and the bottom line is ground. Point 2 out of the PIR (passive infrared sensor) has a fixed voltage of about 0.5V when nothing producing heat is in front of the PIR. When I keep my hand in front of it, the voltage is fixed at about 0.55V. I'll call 0.5V the resting voltage.

The output of the first opamp, IC1A, is proportional to the derivative of the heat energy from my hand. When I move my hand in front of the PIR and keep it there, voltage jumps from 0.5V to about 1V, then drops to 0.5V. When I remove my hand, voltage drops from 0.5V to 0V, then comes back up to 0.5V. Ideally, I would like to amplify: (output voltage of the first opamp - 0.5V). I would also like to shift the resting voltage of 0.5V to the halfway point of my power source (2.5V) because I need to use opamps or comparators to see when the derivative of the heat intensity strays out of a range.

The second opamp, IC1B, shifts the resting voltage from 0.5V to 2.5V, but the output of IC1B is the second derivative of the heat signal because of capacitor C5, which is between the output of IC1A and the negative input of IC1B.

Can you recommend how I can amplify the first derivative of the heat signal and shift the resting voltage? Thank you for your help.
 

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