I have an accelerator pedal which outputs .75 to 4 V and I need to convert this to a 0-5 V output for my controller.I found a circuit that fits(shown below),which uses an opamp in non-inverting configuration with feedback,but I'm not sure how it works so I am not able to adjust the resistor values on my own to get the desired output.Can someone explain how I should calculate the resistor values?
from eyeballing the circuit, it should be this: R1 and R2 sets the 0 level of the output so set R1 and R2 so that their junction is 0.75V. This makes 0.75V input correspond to 0V output.
Now set R3 and R4 so that your gain is what you want, which is (5V - 0V) / (4V - 0.75V) = 1.538. Gain = 1 + R4/R3. That should do it.
Ideally, the gain equation would include R1 and R2 but if you make R3 and R4 way big compared to R1 and R2 (like 30x) then you can ignore the extra terms keep the gain equation simple and it will be 'close enough'.
Hope that helps, -Vince
Graphical solution
Figure 1. \$ V_{IN} \$ and \$ V_{OUT} \$ represented graphically. The reference voltage for the non-inverting amplifier can be estimated by the height of the intersection of the green lines.
The first thing to calculate is the gain of the circuit. Your input range is from 0.75 to 4 V, a span of 3.25 V. The output span is 5 V so the gain, \$ G = \frac {5}{3.25} = 1.54 \$.
We can measure Vref from our graph where the green lines intersect. This appears to be about +2.1 V.
We can also calculate it using a little trignometry using the relationship between the portions of the blue arrows above the orange \$ V_{REF} \$ line:
$$ (4 - V_{REF}) G = 5 - V_{REF} $$
$$ (4 - V_{REF}) 1.54 = 5 - V_{REF} $$
$$ 6.16 - 5 = 1.54 V_{REF} - V_{REF} $$
$$ 0.54 V_{REF} = 1.16 $$
$$ V_{REF} = \frac {1.16}{0.54} = 2.15~V $$
This isn't far off our graphical estimate.
Practical circuit
simulate this circuit – Schematic created using CircuitLab
Figure 2. The familiar inverting mode opamp circuit but with the less familiar Ri connected to a reference voltage other than ground.
The gain of the non-inverting amplifier is given by \$ G = 1 + \frac {R_f}{R_i} \$. Setting \$ R_i = 100k \$ we can calculate \$ R_f = (G-1)R_i \$ \$ = (1.54 - 1)100k = 54k \$.
You now need to generate a 2.15 V reference for R1. This can be achieved with the potential divider shown in the original question. Calculation of the values is left as an exercise for the reader. Choose values of < 1/10 times \$ R_i \$ so the voltage remains stable across the full output range of the opamp.
[OP comments:] Only problem is that the minimum output that the opamp gives is 0.03 instead of a 0. ... I'm using LM324-N from Texas Instruments.
Figure 2. Note that the output stage will have a very weak pull-down when it gets close to 0 V.
You may have trouble with your circuit depending on the load you are driving. If for example, you are trying to sink current from a pull-up resistor you may need to refer to Figure 11 of the LM324 datasheet reproduced below.
Figure 3. Note that the 0.03 V output voltage you achieved is only capable of sinking 20 μA.
