Consider the circuit shown in Figure $1$ below, constructed with an ideal opamp. $($NOTE: Verification of your answers with LTSpice, Matlab, etc. is not required for this assignment.$)$

Figure $1.$ Circuit for Problem $1.$

a$)$ The transfer function from input to output for the above circuit in proper Bode approximation form can be shown to be

$H(s)=\frac{V_{\text{o}\text{u}\text{t}}(s)}{V_{in}(s)}=\frac{-(\frac{s}{{}_{ZDC}})}{(1+\frac{s}{{}_{p1}})(1+\frac{s}{{}_{p2}})}$

Derive analytic expressions for the key angular frequencies ${}_{ZDC},{}_{p1},$ and ${}_{p2}$ in terms of the passive components $R_s,L_f,R_f,R_L,$ and$/$or $C_L.$ Box your three expressions so they are easy for me to find. Show your work. DO NOT use the numerical components values given in part $($d$)$ for this part!

b$)$ What is the frequency response magnitude $|\frac{V_{\text{o}\text{u}\text{t}}}{V_{in}}|$ at $DC,$ i$.$e$.,$ at $=0?$ Box your numerical result so that it is easy for me to find. DO NOT use the numerical components values given in part $($d$)$ for this part!

c$)$ What is the frequency response magnitude $|\frac{V_{\text{o}\text{u}\text{t}}}{V_{in}}|$ at very high frequencies, i$.$e$.,$ as $?$ Box your numerical result so that it is easy for me to find. DO NOT use the numerical components values given in part $($d$)$ for this part!

d$)$ Now, for this part, let the passive $c$ ponent values be as follows: $R_s=100,R_f=1k,R_L=1k,L_f=15\mathrm{.}92mH,C_L=1\mathrm{.}59nF($but$,$ again, do not use these numbers for the above parts!$).$

The Bode plot approximation sketch of the circuit of Figure $1$ with the above numerical values is shown in Figure $2$ below.

Figure $2.$ Bode plot approximation for Problem $1,$ part $($d$).$

Referring to Figure $2$ above, determine the numerical values of the following $($note that you are being asked to provide these numerical values which are valid for the Bode plot approximation, not the high$-$accuracy Bode plot from either LTSpice or Matlab; so expect zero credit if you simulate this circuit and grab these values from the simulated plot$)$:

Referring to Figure $2$ above, determine the numerical values of the following $($note that you are being asked to provide these numerical values which are valid for the Bode plot approximation, not the high$-$accuracy Bode plot from either LTSpice or Matlab; so expect zero credit if you simulate this circuit and grab these values from the simulated plot$)$:

$|H{|}_1($with units of dB $)$

slope ${?}_1$ and slope ${?}_2($with units of $d\frac{B}{?}$ decade$)$

slope ${?}_3,$ slope ${?}_4,$ and slope ${?}_5($with units of degrees$/$decade$)$

$\frac{?}{{?}_H{?}_1}\frac{,}{{?}_H{?}_2}\frac{,}{{?}_H{?}_3},$ and $\frac{?}{{?}_H{?}_4}($with units of degrees$)$

$f_1,f_2,f_3,$ and $f_4($with units of Hz $)$

Include units with your numerical answers $($that is why the units are listed$).$ You should first sketch the Bode approximation plot $($by$-$hand$)$ and then simply get the above values from your by$-$hand sketch. Show your work.