Figure $5$: Active High Pass Filter Circuit Diagram

$2.$ Consider the first order active highpass circuit illustrated in $5$ with the input voltage taken to be $V_S(t)$ in the figure. 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 $C$ and also the $10k$ resistor.

b$.)$ Longrightarrow Find $R_1,R_2,$ and $C$ to give a passband gain of $5($linear scale$)$ and a cutoff frequency of $1$ kHz $.$

c$.)$ Using your transfer function and computed circuit values calculate the frequency response for this circuit. Longrightarrow Over a frequency range from $10$ Hz to $100$ 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 What is the passband gain in dB$?$ What is the value of the half$-$power gain in dB$?$

e$.)$ Longrightarrow Over a frequency range from $10$ Hz to $100$ 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.