ELEC 226, Spring 2003
Prof. Rich Kozick

## Homework 12

Date Assigned: Monday, April 21, 2003
Date Due: Tuesday, April 29, 2003 by 3:30 PM, at my office (Dana 220)

1. The final exam for ELEC 226 is scheduled for Thursday, May 1, at 8:00 AM in room Dana 103.

The exam will be open book and open notes, and it will cover all of the material in ELEC 226. Since ELEC 226 is strongly dependent on ELEC 225, the final exam will effectively include all of the material that we discussed in ELEC 225 and ELEC 226, but the topics from ELEC 226 will be emphasized.

2. Reading: Please review Chapter 12 on Laplace transforms. Most of this material should be familiar to you from MATH 212, but pay particular attention to the definition of poles and zeros in Section 12.8.

Study Chapter 13 on circuit analysis in the s-domain. The main idea in Chapter 13 is that a circuit can be transformed into the s-domain, and then all of the circuit analysis methods that we studied in Chapters 1-5 can be applied. The s-domain also provides important insights for system analysis and design through the transfer function, poles, and zeros.

Also, look at Chapter 14 on frequency-selective circuits. We will revisit RL, RC, and RLC circuits, and we will study their transfer functions H(s), poles, and zeros. Then we will relate these quantities to the frequency response H(j omega), and we will gain a new perspective on low-pass, high-pass, and band-bass filters.

3. Please solve the following problems in Chapter 13. You may find it useful to refer to the notes on applying the Laplace transform in circuit analysis.
13.8
13.9 [Note that in parts (b) and (c), you should find Vo(s) and IL(s), which are the Laplace transforms of the voltage vo(t) and current iL(t), respectively.]
13.11
13.29

4. Please demonstrate your Lab 6 circuit to me on Thursday, April 24, unless you already demonstrated your circuit on April 17. Please follow the announced schedule, with students in Section A attending from 8:00 AM - 9:30 AM, and Section B attending from 9:30 AM - 11:00 AM.

The reports for Lab 6 will be due on Tuesday, April 29 by 3:30 PM. As noted on the Lab 6 description, each two-person lab group should submit one report. Be sure to include the following in your report:

• An accurate circuit diagram that shows all circuit components and their values.
• A brief explanation of the reasoning that you used to design your system and choose component values.
• The operating range of your system. That is, for each waveform, specify the range of amplitude values that you can achieve at 1000 Hz. Then for a particular amplitude value (say, 2 V), specify the range of frequencies that you can produce while maintaining the shape of the wave.
• Explain how your design can be modified to allow operation over a wider frequency range. That is, what would need to change in your circuit in order to produce waveforms with frequencies that are 10 times higher?
Thank you.