(Solved): Circuit: Show that the transfer function for integral or I control action is R3R4R1 ...

Circuit:

Show that the transfer function for integral or $$I$$ control action is $$\frac{R_4}{R_3}\frac{1}{R_1{C}_{2}s}$$ for circuit 2 in the op amp table handout. Hint: Find the transfer function for the first amplifier with $${\mathrm{R}}_1$$ and $${\mathrm{C}}_2$$. Then find the transfer function for the second amplifier with $${\mathrm{R}}_3$$ and $${\mathrm{R}}_4$$. Multiply the two transfer functions to get the overall $${\mathrm{E}}_0(\mathrm{s})/{\mathrm{E}}_{\mathrm{i}}(\mathrm{s})$$. Amplifiers in series like this are called cascaded amplifiers. $$\frac{R_4}{R_3}\frac{1}{R_1{C}_{2}s}$$