Hi again,
In theory that circuit probably works because the equation works out to the right values. However, for practical reasons it would be better to change R30 to something like 100k instead of 10k. What this does is helps prevent us from having to adjust the pot to a very low value voltage which does not play well with any input offset present in the op amp. A higher 'reference' voltage (at the arm of the pot) is preferable, and that simply requires a higher value for R30. So with R30=100k that means we are looking at a 2v output from the pot arm terminal, or thereabouts. Because that changed though that means we need less gain in the last stage (as you have pictured as the second op amp). To get the new gain we would solve an equation with different input values, and for R30=100k it comes out to a gain of 2.1 which means R34 should be equal to 11k (so that 11/10+1=2.1).
Also, because we need a higher reference voltage now that means R28 has to come down to something like 8k. That will allow us to adjust the pot arm for 2v output with a 12v supply voltage.
In case you want to try some other values, here is the equation for Vout with your new circuit:
Vout=(G*(vref*R31+Vin*A*R30)*R32)/(R31*R32+R30*R32+R30*R31)
where
G is the gain of the first stage (equal to 10),
A is the gain of the last stage (equal to 3 in your circuit or 2.1 with the modified 100k circuit),
vref is the voltage adjusted at the pot arm.
What you would do with this equation is enter in all the known values of R like R31 and R32, enter in the new value of R30 (like 100k) and then simplify. Once simplified, solve for the new gain G and the new reference voltage vref using values of Vin of 0 and 1 and a value of 0 for vref and the known required outputs with the respective Vin values. For example, if vref were equal to zero then Vout must equal 10.000 for Vin equal to 1.000 (that's without an offset).
Note that the reference voltage vref for this example was set to equal around 2 volts. For the higher offset version, you'll have to be able to adjust the pot arm up above 7 volts for a 0.7v offset. That means either a bigger pot value or a smaller value for R28 for that version.
If you wish to check out a particular set of values to see how the pot adjustment affects the output, you can use this equation:
Code:
Vout=(G*R32*(Vs*R2*R31^2*R32+Vin*A*R2*R30*R31*R32+Vs*R2*R30*R31*R32+Vin*A*R1*R30*R31*R32+Vin*A*R2*R30^2*R32+Vin*A*R1*R30^2*R32+Vin*A*R1*R2*R30*R32+Vs*R2*R30*R31^2+Vin*A*R2*R30^2*R31+Vin*A*R1*R30^2*R31+Vin*A*R1*R2*R30*R31))/((R31*R32+R30*R32+R30*R31)*(R2*R31*R32+R1*R31*R32+R2*R30*R32+R1*R30*R32+R1*R2*R32+R2*R30*R31+R1*R30*R31+R1*R2*R31))
where
Vs is the source voltage,
R1 is the upper pot resistance added to the upper pot fixed resistor (R28),
R2 is the lower pot resistance,
A is the first stage gain,
G is the last stage gain
This is a rather large equation but it includes the effects of 'loading' of the pot on the network. It can be used to show that once the gains are set right and the pot is adjusted to the right offset, the output works exactly as required, and that means 0.2v output for 0v input and 10.2v output for 1.00v input and everything in between has the same offset of 0.2 volts.
You could also use this equation to investigate problems due to resistor tolerances.