ELEC 470, Spring 1998
Prof. Rich Kozick

## Homework 5

Date Assigned: Wednesday, February 11, 1998
Date Due: Monday, February 16, 1998

1. Exam 1: We will have our first exam on Wednesday, February 18.

2. Reading: Please read Sections 3.1 - 3.9, with emphasis on Sections 3.1 - 3.4.

3. Please do problem 2.23 in the text for practice with pre-envelope concepts. Assume that fm << fc. For 2.23 part (b), also find the complex envelope
4. I have installed an interactive tutorial on amplitude modulation on the PCs in rooms 348 and 347. The tutorial was created by Hewlett-Packard. You can find it under the Programs menu with the title AM Fundamentals. Please go through these lessons - they include questions and animations, and they may help you to visualize AM concepts.

Try to answer the following question as you study these lessons: What are the advantages and disadvantages of single sideband (SSB) modulation compared with other methods of AM?

5. Before class on Friday, February 13: Please download the following files into your Sun account: am_env.mdl, am_env_filt.mdl, dsb_coh.mdl, costas_init.m, and costas_demo.mdl.
These are Simulink demonstrations of amplitude modulation, and they are available from the course home page under Demonstrations and Class Notes. Instructions for running the programs are given on the Web page.

6. Questions to answer related to the Simulink programs (we will begin working on these in class on Friday):
1. In the AM demo am_env.mdl, what are the considerations in choosing the gain ka?
2. In the DSB-SC demo dsb_coh.mdl, investigate the effect of a phase shift between the transmitter and receiver oscillator. Relate your observations to the analysis on page 137 of the text.
3. In the DSB-SC demo dsb_coh.mdl, investigate the effects of a frequency error between the transmitter and receiver oscillator. Perform an analysis of this effect by solving problem 3.11. Appendix 11 contains trigonometric identities that you might find useful.
4. In the DSB-SC demodulator using a Costas phase-locked loop in program costas_demo.mdl, what is the effect of the "Slider Gain" that amplifies the signal prior to being input to the VCO? What happens if this gain is too small? What happens if this gain is too large? Consider the filter that immediately precedes the Slider Gain: what signal is this filter designed to remove? Recall that in this program, you can change the phase in the "TX Carrier" to cause the Costas loop to hunt for a new phase-lock.

[CONTINUED ON BACK OF PAGE]

7. Graduate Students: (extra credit for undergraduates!)
Develop a Simulink program that modulates two separate messages m1(t) and m2(t) onto a single carrier frequency using quadrature amplitude modulation (QAM) as described on page 139 of the text. Can you use a Costas receiver to synchronize with the carrier phase? Demonstrate the effects of phase errors on the demodulated signals, and explain your results analytically by answering Problem 3.14.

It would be great if you can demostrate this on Monday, February 16, but it will be OK if you complete it by Friday, February 20.

Thank you.