The Acme Pole Eliminator Company states in their online cata

The Acme Pole Eliminator Company states in their online catalog that the circuit shown in Figure P10-83 can eliminate any realizable pole. Their catalog states \"Suppose you have a need to eliminate the pole associated with an input, for example, V_S(s) = K/(s + alpha). Selecting 1/R_1 C = alpha will eliminate the pole, while the ratio R_2/R_1 can be used to provide any desired negative gain or attenuation to the output.\" Prove or disprove their claim.

Solution

The output of first opamp is equal to the input voltage as the the opamp is a voltage follower.And the second opamp has its -ve terminal at ground therefore the +ve terminal of second opamp is also at ground due to virtual ground concept.Applying the KCL at +ve terminal of second opamp therefore Vo = -Vin*[R1Cs+1](R2/R1).Given in example that the the input voltage Vin = K/(S+a) has the pole at -a.Therefore secting R1C= 1/a so that the input pole cancels out Vo = -[K/(s+a)]*[s/a + 1](R2/R1) = -K/a(R2/R1).Now, by selecting R2>>>>R1 we get a negative gain and if R1>>>R2 then the same acts as an attenuator