The op-amp circuit shown below is commonly used as a filter in control systems

In the class handout we showed that the output of the standard inverting amplifier is

(a) Extend the argument in the handout to show that for any impedance elements Zf and Zin the output may be written

(b) Find the transfer function Vout(s)/Vin(s) for the circuit above. (c) Find the differential equation relating vout(t) to vin(t).

(d) If R2 = 22 k (22,000 ), R1 = 6.8 k, and C = 0.47 F (these are common values), find (i) The time-constant, and (ii) the steady-state output voltage vout when the input is 2.5 v.

Problem 7: The op-amp circuit shown below is commonly used as a "filter" in control systems In the class handout we showed that the output of the standard inverting amplifier is vout=RinRfvin (a) Extend the argument in the handout to show that for any impedance elements Zf and Zin the output may be written Vout(s)=ZinZfVin(s) (b) Find the transfer function Vour(s)/Vin(s) for the circuit above. (c) Find the differential equation relating vour(t) to vin(t). (d) If R2=22k(22,000),R1=6.8k, and C=0.47F (these are common values), find (i) The time-constant, and (ii) the steady-state output voltage vout when the input is 2.5v