Figure $4$: Active Filter Circuit Diagram

Consider the first order circuit illustrated in $4.$ Use whatever computer resource you prefer for the following tasks.

a$.)$ Longrightarrow Calculate the voltage transfer function for this circuit in terms of $R_1,R_2,$ and $C.$ What type of filter is this?

b$.)$ Let $R_1=470,R_2=1k,$ and $C=1F.$Longrightarrow Compute the DC gain $($i$.$e$.,$ gain when $=0)$ and the cut$-$off frequency $f_c$ in Hz $.$

c$.)$ Longrightarrow Over a frequency range from $1$ Hz to $10$ kHz plot the magnitude bode plot $($using dB$)$ and, of course, a $lo{g}_{10}$ axis for frequency. Label the half$-$power frequency on your plot.

d$.)$ Longrightarrow How can you tell this is a first order filter from your bode plot?

e$.)$ Longrightarrow Over a frequency range from $1$ Hz to $10$ kHz plot the phase bode plot $($using degrees$)$ and, of course, a $lo{g}_{10}$ axis for frequency. Comment on the phase in the passband.