This lab will give you an opportunity to review ELEC 120 and ELEC 225-226 as you design electric circuits that behave as frequency-selective 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 make measurements to determine how closely your circuits come to achieving the design specifications. 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 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 5000 Hz.

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

4. Derive the analytical expression for the magnitude and phase 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/elec32006/lab1_freq.m
   to help you produce this plot. Compare the Bode plot with the design specifications.
   

   Tutorials on using 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. If you have time, 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, and a comparison of your measured results with the design specifications

Thank you, and have fun!