# ECE303L Signals and Systems Lab 4

### Objectives

1. Learn how to use the Cursor and FFT features of the oscilloscope.
2. Use SPICE to analyze second-order (RLC) circuits.
3. Investigate step function response of RLC circuits.
4. Investigate AC response of RLC circuits.
5. Conduct an open-ended design project (resistance/capacitance/inductance measurement system)

### Background

The following links contain information about the oscilloscope cursor and FFT features.

Our textbook covers RLC circuits on p 415-416. The following links contain additional information:

### Requirements

1. Demonstrate your ability to use the Cursor features of the oscilloscope by doing the following.
1. Display a sine wave on the oscilloscope. Manually adjust the cursors so that Y1 marks the minimum value of the signal, Y2 marks the maximum value of the signal, X1 marks a significant time feature (zero crossing, max, or min) and X2 marks the same feature one period later. Capture an image of your oscilloscope display.
2. Write a MATLAB script that queries the oscilloscope for the cursor values and uses them to calculate the amplitude, period, and frequency of the signal.

2. The oscilloscope uses dB (decibel) values relative to a 1 Volt rms sine wave, meaning that signal would have an amplitude of 0 dB. Verify this measurement by running the MATLAB script sine demo modified so that the frequency of the signal is set to the center frequency of the FFT display. Capture an image of the oscilloscope showing the FFT display for a peak-to-peak voltage of 1 Volt with the Y1 cursor set to the voltage peak.

3. The MATLAB script series demo uses the FFT feature of the oscilloscope to study the harmonics of a 50%-duty square wave. It prompts the user to mark the vertical peaks corresponding to the various harmonics, which are then captured into a MATLAB vector. The effect of changing the display time base is also shown. The MATLAB pause function is used to stop the script and allow the user to capture the oscilloscope display. The resulting harmonics can then be compared to calculated values. See Fourier series results.

Repeat the activities described above, but for a 25%-duty square wave. Note that the square wave above has only odd harmonics, whereas other duty-cycle values have both odd and even harmonics (although some are still missing). This means that the example script will need to be modified. Compare your measured harmonic coefficients to the theoretical values. Capture an example oscilloscope image showing the spectrum for your square wave.

4. Build a RLC series circuit. You can use substitution boxes or discrete components. If you use discrete components, choose values from the bag of mixed components, and when you are done return the components to the proper drawers in the cabinet. Measure the resistance, capacitance and inductance of your components using the impedance meter at the back of the lab. Choose sets of values to produce both over-damped (ξ > 1) and under-damped (ξ < 1) system.

5. Capture oscilloscope images showing both over-damped and under-damped responses to square-wave input. Compare your measured values with the theoretical values, as described in class.

6. Simulate the systems above in SPICE, showing the transient analysis for square-wave input.

7. Measure the frequency response of a R-LC circuit, using a MATLAB script. You should obtain measurements of frequency, amplitude of both channels, and phase shift. Plot the ratio of the amplitudes (Vout/Vin) and the phase as a function of frequency. Superimpose a theoretical plot over the experimental values. Choose parameter values that give the best match. Compare the parameter values you selected to those obtained from the impedance measurements.

8. Simulate the system above in SPICE, showing the AC analysis.

9. In the previous laboratory you designed an automated system, using MATLAB, to determine an unknown capacitance or resistance. Improve this system to determine inductance. Your system should recognize whether the component under test is a resistor, capacitor, or inductor. The lab assistant will again have you measure a selection of unknown values to demonstrate your system.

Maintained by John Loomis, last updated 29 September 2010