$($Problem $6)$

The circuit shown in Figure P$6\mathrm{.}63$ can be used as a low$-$pass filter.

a$.$ Derive the frequency response $\frac{V_0}{V_{in}}$ of the circuit.

b$.$ If $R_1=R_2=100k$ and $C=0\mathrm{.}1F,$ compute the attenuation in decibels at $=1,000ra\frac{d}{s}.$

c$.$ Compute the amplitude and phase of $V_o{V}_{in}$ at $=25ra\frac{d}{s}.$

d$.$ Find the range of frequencies over which the attenuation of $V_{\text{@}}{V}_{in}$ is less than $1$ decibel.

Bode Diagram