[Reference Appendix B for additional information] 1. Open the Excel file with your captured data. Columns A, B, and C contain data about the capture. Column D is the time data. There will be 2500 data points in this column, and the data in row 2500 minus that in row 1 should equal the oscilloscope time per division (250 Us/div) times 10. Perform this calculation in your note book to insure that the values are the same. 553 CCCC905 AM AMPLITUDE MA FR Figure 27: Example of Captured Waveform Data in Excel 2. The data in column E is the waveform amplitude data. There is one value for each time value. Scan the data and make sure the highest value (peak) compares with the signal generator settings. 3. In column F, calculate the theoretical value expected for the sine wave, using Eqn. 1. Use the time values in column D for the equation time values (1). A, and frequency (f) come from the signal generator settings (reference experiment procedures. [Note: V,#Veel). Start with and B set to zero. 4. Plot both sine waves on the same graph: experimental (column E) and theoretical (column F) vs. time (column D). The waves will be offset (not aligned). 5. In column G take the difference (residual) between columns E and F for each time value. 6. Create another data set in column H by squaring the values in column G. 7. Sum all 2500 values in column H to be used as a fit indicator. 8. There will be an arbitrary phase offset between the captured signal and theoretical signal caused by the arbitrary trigger level in the scope. It will be necessary to shift the value of in 23 the equation to get alignment. As you vary, the minimum value of the sum will indicate a best fit. You will also need to adjust the amplitude (A.) and offset (B) values. By adjusting these values, you can adjust the theoretical equation (column F) to fit the experimental data and minimize the sum. [Note: Look at your plot from step 4 to see the adjustments you are making and how well the waves align.] How well does your theoretical signal fit your captured signal? Include your updated theoretical sine equation and fit indicator. 9. Plot the residuals versus time. Figure 28 illustrates an example plot. How do the residual values correlate with the values expected from an 8 bit ADC? Explain. 0015 -0.001 0.015 0.01 -0.01 0.015 Time (s) 0.001 0.0015 Residuals Figure 28: Difference between Captured and Theoretical Data The first signal (a) is a sine wave. The line voltage that runs household appliances is perhaps the best known example of a sine wave. A generic sine wave can be expressed as A(t)- Ao sin(2nft+6) +B Eq. 1 1