The operational amplifier (hereafter OP-AMP)is developed in the 1940s primarily for use in analog computers, made cheaply and readily available in the late 1960s through integrated-circuit technology. The actual construction of a modern OP-AMP is indeed very complex, involving many transistors, diodes, resistors and capacitors

The voltage follower is a circuit in which the output is identical to the input

A current-carrying conductor produced a magnetic field (1800). A changing magnetic field could induce a voltage in a neighboring circuit(1820)

Two circuits are dual if the mesh equations that characterize one of them have the same mathematical form as nodal equations that characterize the other

4-5 Simple capacitor-OP-AMP-circuits Integrator op-amp circuit (Integrator):

Let us assume a solution i(t=Ae, where a and S, are constant to be determined

The complete response of any RC circuit may also be obtained as the sum of the natural and the forced response

A1, A,----two arbitrary constants S S2----real numbers or conjugate complex Since the s,t and s,t must be dimensionless, S,, S2----(1/s)

The complete response is written as the sum of the forced and the natural response, and the initial conditions are then determined and applied to the complete response to find the values of the constants

The forced response The steady state responseThe(t) has been switched into the circuit at some remote U.=V. cos ot time in the past, and the natural response has died-out completely. The forced response(steady state response)must satisfy the differential equation