First, note the application we are working with here. It's a current sensor to be used with a uC chip ADC unit. The uC may then display the current, or it may use it to adjust some process or even just store readings for later review by a human being.
On a construction of a cathedral you can see a long chain of people carrying stones. One of them was asked what he was doing and he said: "I'm carrying a stone". When another man was asked the same questions, he said: "I'm earning my living". A third man replied: "I'm building the cathedral".
I don't think the goal here to build a current management circuit. The goal here is to use this example to help PG to learn how to design circuits. There are many steps, and none of them should be skipped.
Here's how I would see the process:
The first thing is to set a goal. Say +-3A needs to be measured. We're given a sensor which does 185mV/A with assumed accuracy of 1%.
How much do we need to magnify that? Look at the op-amp output range - 0.25 to 4.75 (datasheet), perhaps little tighter. Gives us 4.5V. We need to map 6A into 4.5V. It gives us 0.75V/A. The device produces 0.185V/A. Need to magnify 4 times.
How do we do that? (Vout - 2.5) = -I*0.185*R3/R1. Looking at this, the amount of amplifications is directly proportional to R3/R1 ratio. We have only standard resistors. What level? Do we try to save power with bigger resistors or increase speed and precision? Sensor is at best 1% accurate, don't need to worry about precision, speed is not important - go power save - 10K for R1, (33K + 6.8K) for R3. Can short 6.8K later if need be.
Check the op-amp. We don't need much but it's good to check anyway. Input offset must be within 1mV. Noise? Other criteria? Are they met?
How do we measure that? ADC. Sensor is 1% accurate, we need 7bit, add one bit for rounding 8bit. We have 10bit ADC - fine 10 times more resolution. Checking ADC linearity, gain, offset errors (datasheet). Combined error is 3 counts. Good.
Now to the program. Get ADC count A. V = A*5/1024 (or perhaps V = A*5/1023? Doesn't matter. The last digit is well below sensor accuracy, it's bogus anway).
I = (2.5 - V)/(0.185*R3/R1).
o.185*R3/R1 is a constant = 0.185*(33+6.8)/10 = 0.763.
Other part: 2.5 - V = 2.5 - A*5/1024 = (512 - A)*5/1024 = (512 - A)* 0.00488
Combine: I = (512 - A)*0.00488/0.763 = (512-A)*0.00640. Go to mA: I = (512 - A)*6.4
Coding (in C). Processor is slow, do integer arithmetics in mA. Average some number of ADC samples. OP wants 30. Calculate the sum
C:
int16_t sum = 0;
sum += adc_count_received_from_adc; // repeat 30 times
30 samples will go up to 30*1024 = 30720. Will fit into int16.
Now, need to do averaging and scaling.
I = (512*30 - Sum)*6.4/30 = 15360 - Sum*0.2133.
Rewrite this in a form suitable for the computer: I = 15360 - Sum*13979/65536.
Go back, check all the numbers, make sure they're right. People do make mistake (at least me - I never get correct numbers in the first pass).
Convert to C:
C:
int16_t current;
sum = 15360 - sum;
current = (sum*13979L)>>16;
Write more to get it out to LCD or UART.
Testing. Produce different currents, measure with DMM and compare. Are they within 1% of ours. Good, we're done.
Not within 1%. Collect more data, do least squares. Check linearity. No linearity - big problem. Get a scope, go through the circuit, see where linearity is lost.
Linearity is good. Recalculate coefficents. Adjust 15360 and 13979 constants. Does it put us within 1%. Not within 1%? Can we leave with the error? No? Too bad, back to the drawing board, so what are we going to measure?