ELEC 320, Fall 1998
Prof. Rich Kozick

## Laboratory 1 Analog Filter Analysis and Design

This lab will give you an opportunity to review EE 102 and ELEC 220 as you design electric circuits that behave as first-order and second-order filters. You will analyze and design your filters using basic circuit analysis concepts. The computer software package MATLAB will be used to verify your designs. Then you will build the filters and measure whether the design specifications are actually achieved. Each student will submit a written lab report that includes an explanation of your filter design procedures, an analysis of your filters, and your experimental measurements.

Review Materials: Please review the items listed on the Homework 1 assignment sheet, as well as any other materials that will help you design the filters specified below.

Important Note: Your objective in this lab should be to understand the basic concepts used to analyze and design the filters. You will also become familiar with some MATLAB commands. What you should not do is look up a circuit in a textbook or handbook, plug numbers into a formula to get the circuit R, L, and C values, and then build the circuit, with little or no understanding about how or why it works!

The filter design specifications and lab activities are as follows.

1. Design a first-order, low-pass filter with a passband gain of -5 volt/volt at low frequencies and a cutoff frequency of approximately 500 Hz.

2. Design a first-order, high-pass filter with a passband gain of -5 volt/volt at high frequencies and a cutoff frequency of approximately 5000 Hz.

3. Design a band-pass filter with a passband gain of -20 volt/volt, a low cutoff frequency of approximately 1000 Hz, and a high cutoff frequency of approximately 2000 Hz.

4. Derive the analytical expression for the magnitude of the frequency response for each filter. Explain how this formula is used to choose the circuit component values to achieve the design specification. Produce a Bode plot of each frequency response magnitude using MATLAB. An example MATLAB program is available at
http://www.eg.bucknell.edu/~kozick/elec32098/lab1_freq.m
to help you produce this plot. Compare the Bode plot with the design specifications.

Tutorials on using the Sun computers and MATLAB are available at
http://www.eg.bucknell.edu/~kozick/tutorials.html

5. Construct your filters and measure each frequency response. Measure the frequency response at enough different frequencies to clearly indicate the gain in the pass-band and the roll-off in the stop-band. Compare the measured results with the analytical Bode plot. This can be done conveniently in MATLAB, as shown in the example program lab1_freq.m

6. Measure the unit step response of each circuit, and try to interpret the results. Are they consistent with your concepts of low-pass, high-pass, and band-pass filters?

Lab reports: Each student will individually prepare and submit a written lab report that includes the following:

• An explanation of the reasoning behind the filter design procedures that you used
• The analysis of your filters and the formulas that you used in the design
• A presentation of your experimental measurements of the frequency response of each filter, along with a discussion about the extent to which your filter meets the design specifications
The due date for the lab reports will be announced later. Please see Homework 7 and Homework 9 for more information about the lab reports.

Thank you, and have fun!