Use MATLAB Control System Toolbox and the Linear System Analyzer Applications to plot the Bode diagrams. Present the MATLAB code and the plots below. How can you relate the frequency response with the filter type? Which type of filter is that $($e$.$g$.,$ low$-$pass, high$-$pass, band$-$pass, band$-$stop$)?$ Can you identify the cutoff and$/$or central frequency from the graph?

Calculate the cutoff and$/$or central frequency $($find the right equations$).$ Present the hand calculations below. Does the calculated frequency match with the measured frequency?

Change the resistor value. Try to increase and decrease the resistance $R($e$.$g$.,R=1$ and $R=24).$ Present the hand calculation for the new transfer function below. Plot the Bode diagrams. Present MATLAB code and the plots below. Plot the magnitude and phase response of the circuit for the $3-$resistor values in the same graph. How does the resistor affect the system's frequency response?

Repeat part $9.$ For the inductor $L($e$.$g$.,L=\frac{1}{2}H$ and $L=20H).$ Present the hand calculation for the new transfer function below. Plot the Bode diagrams. Present MATLAB code and the plots below. Plot the magnitude and phase response of the circuit for the $3-$inductor values in the same graph. How does the inductor affect the system's frequency response?

Repeat part $10.$ for the capacitor $C($e$.$g$.,C=\frac{1}{2}F$ and $C=\frac{1}{12}F).$ Present the hand calculation for the new transfer function below. Plot the Bode diagrams. Present MATLAB code and the plots below. Plot the magnitude and phase response of the circuit for the $3-$capacitor values in the same graph. How does the inductor affect the system's frequency response?

Instructions:

Label all the figures. Label both x $-$ and y $-$axis and add a title for each figure. Add a legend when you have multiple plots in the same graph.

Format properly the report. Choose a formatting style and be consistent.

Add figures$/$code$/$results at the end of each section.

Add the entire code at the end of the document as Appendix.

Answer all the questions$/$comments otherwise you will only get partial credits. Understanding the results and being able to comment on them and interpret them is the most important part of the project.

You can work in a group of a maximum of $2$ students. I expect all students that choose to work in a group to equally contribute to the project and to the report.

The grade of the final project consists of $2$ parts:

a$.50\%$ : final report clarity and format.

b$.50\%$ : correctness of solutions and project understanding

Contact your instructor for any clarification you might need or to make sure you are on the right path for project completion. Answer $7-11$