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University of CincinnatiCollege of Engineering & Applied ScienceSchool of Dynamic SystemsCourse Code: 20-MECH-3070CCourse Title: Circuits & Sensing LabExperiment Number: 3Experiment Title: Dynamic Response of InstrumentsDate(s) Performed: June 29 July 15, 2015Date Submitted: July 22, 2015Group Code: 0-00Group Members: LAST NAME, First Name: LAST NAME, First NameInstructor: Professor NameExperiment Results = _/40Analysis/Discussion= _/30Answers to Questions= _/20Writing= _/10-TOTAL SCORE= _/100ABSTRACTUse Ez_Heading1 for the abstract title and use Ez_AbstractText when writing the body of the abstract. Try to be as concise as possible. Give a general overview of the experiments and your results. Do not give too much detail in this section. One or two paragraphs are acceptable, enough to fill half of this abstract page.Table of ContentsABSTRACT2Table of Contents3Glossary of Terms1. Objectives52. Theoretical Background63. Experimentation63.1 Time response of a first order (low pass) instrument simulated as an RC circuit63.1.1 Summary of Procedure63.1.2 Results73.1.3 Analysis & Discussion83.2 Frequency response of a first order (low pass) instrument simulated as an RC circuit83.2.1 Summary of Procedure83.2.2 Results93.2.3 Analysis & Discussion93.3 Time response of a first order (high pass) instrument simulated as an RC circuit93.3.1 Summary of Procedure93.3.2 Results93.3.3 Analysis & Discussion113.4 Frequency response of a first order (high pass) instrument simulated as an RC circuit113.4.1 Summary of Procedure113.4.2 Results113.4.3 Analysis & Discussion123.5 Time response of a second order lightly damped instrument simulated as an RLC circuit123.5.1 Summary of Procedure123.5.2 Results123.5.3 Analysis & Discussion133.6 Frequency response of a second order lightly damped instrument simulated as an RLC circuit133.6.1 Summary of Procedure133.6.2 Results133.6.3 Analysis & Discussion144. Answers/Solutions to Questions145. Conclusions14APPENDICES15A EQUIPMENT LIST15B Lab Notes16C Matlab Code17Glossary of Terms1. ObjectivesAt the end of this experiment, the students are expected to: Objective 1 Objective 2 Objective 32. Theoretical BackgroundProvide relevant theory and principles that were tested during the experiment by referring to your class lecture materials and book(s). Information provided in this section will aid the reader in understanding why the experiment was conducted in such manner. Equations can also be provided in this section so that they may not need to be re-written in the succeeding sections of the experiment report.3. Experimentation3.1 Time response of a first order (low pass) instrument simulated as an RC circuit3.1.1 Summary of ProcedurePut a summary of the procedure here. There is no need to narrate the step-by-step procedure. The description of the procedure should be sufficient so that the reader will have an understanding of what you did and how the measurements were made.Placing the circuit setup or drawing the circuit diagram in this section will allow the reader to understand your summary better. Just remember to put figure captions. (Hint: Right-click on the figure and select “Insert Caption”. After typing the necessary figure description, highlight the figure text and select “Ez_FigureCaption” from Styles. Should you need to reference to the figure in your text, select the “Insert” ribbon, then go to the “Links” section and hit “Cross-reference”. From “Reference-type”, select “Figure”, then from “Insert reference to:”, select “Only label and number”, then select the appropriate item under “For which caption”, then press “Ok”. Then it should display, Error! Reference source not found., on your text. Should you decide to insert another figure or table at the middle of your report, which would render the original numbering inaccurate, just go through the process just mentioned above. Once finished, highlight on the text with referenced figures or simply select all text by hitting “Ctrl+A”, right-click on the highlighted-text, then choose “Update field”. This will ensure that the figure numbers are sequentially correct and figures are referenced properly in the text.Figure 1. A low pass RC circuit3.1.2 ResultsPut your results here. Use the tables provided and re-encode your data.Table 1: RC circuit component valuesComponentNominal ValueMeasured Value% DifferenceR (k)C (F)Table 2: Low pass circuit parametersComponentComputed ValueMeasured Value% Error (ms)kssFigure 2. Step response of a low-pass RC circuitFigure 3. Piece-wise integral of sample periodic functionsFigure 4. Output waveforms from a low pass RC circuitRelevant and related graphs should also be put here. Remember to properly label tables and figures. Follow the procedure as when inserting a caption for a figure, but select “Ez_TableCaption” from “Styles”.Just below the table, provide sample computations used to generate the data in the previous table. Use the equation editor to write the equations.3.1.3 Analysis & DiscussionA concise, but still comprehensive, analysis is important. Be sure to briefly discuss the theoretical concept/idea that is being tested in this portion of the experiment. Refer to your data to illustrate how this concept is validated with the experiment that was just performed.Again, use the automatic referencing option for convenience. To reference the previous table, use the procedure as specified in the previous section: Insert Links Cross-reference Reference type table Insert reference to: Only label and number for which caption choose the appropriate table ok. Like so, Error! Reference source not found.Comment on any difference between the measured parameters and the expected or theoretical values. Also, comment on possible sources of errors.3.2 Frequency response of a first order (low pass) instrument simulated as an RC circuit3.2.1 Summary of Procedure3.2.2 ResultsTable 3: RC circuit component valuesComponentNominal ValueMeasured Value% DifferenceR (k)C (F)Table 4: Low pass FRF parameters from MatlabParameterComputed Valueb (rad/sec)kssTable 5: Low pass filter FRF parameters for select frequenciesFrequency(Hz)Vi(V)Vo(V)Gain, Vo/Vi|dB(dB)Time Delay, td(sec)Phase Angle, (deg, )102040801603206403.2.3 Analysis & Discussion3.3 Time response of a first order (high pass) instrument simulated as an RC circuit3.3.1 Summary of ProcedureFigure 5. A high pass RC circuit3.3.2 ResultsTable 6: RC circuit component valuesComponentNominal ValueMeasured Value% DifferenceR (k)C (F)Table 7: High pass circuit parametersComponentComputed ValueMeasured Value% Error (ms)kssFigure 6. Step response of a high-pass RC circuitFigure 7. Piece-wise first order derivative of sample periodic functionsFigure 8. Output waveforms from a high pass RC circuit3.3.3 Analysis & Discussion3.4 Frequency response of a first order (high pass) instrument simulated as an RC circuit3.4.1 Summary of Procedure3.4.2 ResultsTable 8: RC circuit component valuesComponentNominal ValueMeasured Value% DifferenceR (k)C (F)Table 9: High pass FRF parameters from MatlabParameterComputed Valueb (rad/sec)kssTable 10: High pass filter FRF parameters for select frequenciesFrequency(Hz)Vi(V)Vo(V)Gain, Vo/Vi|dB(dB)Time Delay, td(sec)Phase Angle, (deg, )102040801603206403.4.3 Analysis & Discussion3.5 Time response of a second order lightly damped instrument simulated as an RLC circuit3.5.1 Summary of ProcedureFigure 9. An RLC circuit3.5.2 ResultsTable 11: RLC circuit component valuesComponentNominal ValueMeasured Value% DifferenceRL + R (k)L (H)C (F)Table 12: RLC circuit parameters - TheoreticalParameterComputed Valuen (rad/sec)kssFigure 10. Step response of an RLC circuitTable 13: RLC circuit time response parameters - MeasuredParameterComputed Valuetp (s)POts.2% (ms)td (s)kss3.5.3 Analysis & Discussion3.6 Frequency r
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