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Unformatted text preview: ECE 24001 LABORATORY #4 Magnitude and Phase Frequency Response of a Second Order System February 8, 2008 Professor Hanson Jonathan Gold Lab Partner : Jonathan Gold 1. Abstract The main objective of this lab was to use different methods of making frequency and phase measurements on a second order RLC circuit using the transfer function, H(s). In order to achieve this, we had to compare our experimental results obtained with the use of a circuit, to the theoretical values obtained by the automated measurements taken by MATLAB, proving to be very close. This lab shows that the values gathered by an automatic program are just as good as values taken manually. These values match with that of the theoretical values, showing that they are correct. These values are those found with a second order RLC circuit including the frequency and phase response. 2. Procedure and Data A. In this experiment we used an RLC circuit, which consisted of an independent voltage source, an inductor, a resistor and a capacitor. Where the value of the resistor was 2.10 k, the inductor had a value of 31.8 mH. The inductors internal resistance RL was of 35.1, and the capacitor had a value of 14.88 nF. Figure A is a diagram of the circuit we used. Figure A. RLC Circuit The function generator that provided that input to the RLC circuit was set to a sine wave with a 10V peak to peak value and frequency of 500 Hz. The function generator was hooked up to the entire circuit as well as channel 2 of the oscilloscope. The output voltage read across the capacitor was hooked up to channel 1 of the oscilloscope. B. As we increased the frequency from 500Hz up to 10,000Hz at increments of 500 Hz, we measured the amplitude of the input x (t) and output y (t), as well as the phase difference between them. Using RMS values, we recorded these results along with the corresponding frequency, input and output voltage, and magnitude frequency. Our experimental results measured in RMS values, can be found in Table 1, taken from EXCEL. Frequenc y Input Output Magnitude Phase Auto( sfreq ) Auto( sfreq ) magH(ML) phaseH(ML) RMS (v) RMS (v) Frequency Difference Magnitude Phase 500 Hz 7.02 0.360 0.051282051 67 0.0509 67.50 0.05190 1.18230 1000 Hz 7.05 0.705 0.100000000 73 0.0972 74.16 0.10050 1.29450 1500 Hz 7.08 1.050 0.148305085 74 0.1476 72.9072....
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 Winter '08
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