Consider the following active low$-$pass filter circuit, constructed from an

ideal op$-$amp:

$($a$)$ Assume the desired filter must have an input impedance of $1$ k and

break$-$point frequency of $500$ Hz $(3$dB $=2$ x$500$ Hz$).$ Moreover, the DC

$()$ voltage gain must be $|$V out$/$V in$|=100.$ Determine the values of R $1,$ R f

and C f that are required.

$($b$)$ With regard to AC signals, what is the transfer function H$()?$ Write

both the general expression and the expression for your particular values of

R$1,$ R f and C f $($from part $($a$)).$