In the circuit shown in Figure P6.12, if
$$
\begin{array}{ll}
L=190 \mathrm{mH} & R_1=2.3 \mathrm{k} \Omega \\
C=55 \mathrm{nF} & R_2=1.1 \mathrm{k} \Omega
\end{array}
$$
a. Determine how the driving point or input impedance behaves at extremely high or low frequencies.
h. Find an expression for the driving point impedance in the form:
$$
\begin{aligned}
Z(j \omega) & =Z_\theta\left[\frac{1+j f_1[\omega]}{1+j f_2[\omega]}\right] \\
Z_p & =R_1+\frac{L}{R_2 C} \\
f_1(\omega) & =\frac{\omega^2 R_1 L C-R_1-R_2}{\omega\left[R_1 R_2 C+L\right]} \\
f_2(\omega) & =\frac{\omega^2 L C-1}{\omega C R_2}
\end{aligned}
$$
c. Determine the four cutoff frequencies at which $f_1(\omega)=+1$ or -1 and $f_2(\omega)=+1$ or -1 .
d. Determine the resomant frequency of the circuit.
e. Plot the magnitude of the impedance (in dB ) as a function of the $\log$ of the frequency, i.e., a Bode plot.