Answer 1)
In this case use an adder as the first stage to get rid on 10V offset (we add -10V to the input signal).Then we use an inverting amplifier as the second stage to get a gain of 40X. It also removes the negative sign introduced by the adder stage.
One can take R1 = 1K, therefore 40*R1 = 40K. One can use 39K + 1K to make 40K resistance if one needs to use commercially available resistance values.
Answer 2) In this case we use a differential amplifier of gain 40. It subtracts -10V as well as amplifies the difference by 40X.
Hope this helps.
1. We wish to sample a small signal that is on top of a large DC offset using a DAQ (Digital Acqu...