## ECE 209: Circuits and Electronics Laboratory

### Laboratory 5: Properties of Second-Order Circuits

As discussed in the course policies, all pre-laboratory assignments are individual assignments; they are NOT to be submitted by a group. You may discuss the assignment with other classmates, but the work you turn in to me should be your own and reflect your personal comprehension of the laboratory material. Do NOT split pre-lab work up among several people; each student should complete the pre-laboratory assignment in its entirety and should provide a unique submission to me at the beginning of the class.

INDIVIDUAL pre-laboratory assignment (out of 100 points): (due from each student at the beginning of class)

1. (25 points) Complete part (1.1) of the laboratory exercises. Show your work! Some hints:
• Remember that the s-domain impedance of:
• a resistor with resistance R is R
• an inductor with inductance L is s L
• a capacitor with capacitance C is 1/(s C)
• Recall how to find the output of a voltage divider.

2. (25 points) Complete part (1.2) of the laboratory exercises. Submit your MATLAB code! Some hints:
• See the somewhat outdated Appendix at the end of the laboratory exercises.
• Given a MATLAB LTI system formed by h = tf(A,B), both step(A,B) and step(h) do the same thing.
• Similarly, freqs(A,B) is very similar to bode(A,B) or bode(h).
• Grids can be turned on with grid on and turned off with grid off.
• The more up-to-date MATLAB examples on the lab 5 section of the course web page may be helpful.

3. (25 points) Complete part (2.1) of the laboratory exercises. Show your work! Some hints:
• The circuit is a Sallen–Key filter.
• The operational amplifier is in a negative feedback configuration, and so the Vo output signal tied to the inverting (i.e., "-") input will match the signal at the non-inverting (i.e., "+") input. Any other effects of the operational amplifier can be ignored.
• Setup node voltage equations at the two unnamed nodes, and substitute one equation into the other to solve for Vo(s)/Vin(s).

4. (25 points) Complete part (2.2) of the laboratory exercises. Submit your MATLAB code!

5. BONUS (5 points): Re-derive the transfer function from part (2.1) for the generic filter topology. That is, replace the passive components with generic Z1, Z2, Z3, and Z4 impedances and derive the transfer function. Show your work!

6. BONUS (5 points): As with laboratory reports, a pre-laboratory assignment submission generated with any flavor of TeX (e.g., LaTeX) will earn the author 5% extra credit on that assignment.

We will discuss the solutions in class. Website and original documents Copyright © 2007–2010 by Theodore P. Pavlic Licensed under a CC-BY-NC 3.0 License