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Find the mathematical expression of the relationship between the output and the input of the transfer function of the circuit shown.
The capacitance impedance is 1/jwC= 1/SC.

Ideal inverse proportional amplifier circuit uo/ui =-rf/r1rf = r2+1/sc2r1= r1(1/sc1) = r/kloc-.

Then uo/ui =-[R2+1/sc2]/[r1(1+Sr1c1)] =-[(1+Sr/]

-{[( 1/Sr 1 C2)]+[(r 1c 1+r2c 2)/r 1 C2]+sr2c 1

This is a PID regulator with internal proportional integral differential.

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