Hi,
This is a frequently asked question with many discussions here in this forums.
All information is already available. How to calculate it, what devices to use and schematic.
input: 1.9V ... 2.4V ...3.0V
* 1.9V to 2.4V is 0.5V
* 2.4V to 3.0V is 0.6V
output: 0.0V ... 2.4V ...5.0V
* 2.4V (divided by 0.5V input ==> gain of 4.8)
* 2.6V (divided by 0.6V input ==> gain of 4.33)
There you have an unlinearity. This is difficult to achieve.
--> musa a constant gain.
Hint:
If your supply voltage is 0V / 5V, then you never get 0.000V and never 5.000V output form an amplifier.
Or if 0V to 5V is the input range of an ADC:
--> leave some headroom. I recommend 0.1V at both ends.
My recommendation:
* input range: 1.9V ... 3.0V
* output range: 0.1V ... 4.9V
--> gain = ( 4.9V - 0.1V) / (3.0V -1.9V) = 4.8V / 1.1V = 4.36
complete formula:
U_out = U_in * 4.36 -8.19V (if your offset compensation is output referred)
U_out = (U_in - 1.877) * 4.36 (if your offset compensation is input referred)
Then use a "rail to rail" output OPAMP
Use a differential amplifier circuit.
For even more detailes look at the other discussions.
Klaus