1. Some Mathematics Time Response Significant Figures Statistics http://antwrp.gsfc.nasa.gov/apod/ap040117.html

2. IAH: EET 3022 First Order Response b(t)=b i +(b f -b i )(1-e -t/tau ) b i = initial value of the exponential change b f = final value of the exponential change tau = the time constant of the first order process Step change

3. IAH: EET 3023 Graphs of First order Responses b(t)=b i +(b f -b i )(1-e -t/tau )

4. IAH: EET 3024 2 nd order response 2 time constant circuit Like an RLC electrical circuit Can be: –Pure 2 time constant exponential –Damped sinusoid: Ve -t/tau Sin(ωt) Higher order circuits are similar, but have additional time constants.

5. IAH: EET 3025 Measurement Error DMM: +- one least significant digit So for a measurement of.102 amps, it is accurate to +- 1 mA. Assume you have a 100Ω, 5% resistor Calculating the Voltage across the resistor: V=IR = (100Ω +-5%)(.102A+-.001A) How to calculate the error? Use Square Root of Sum of Squares technique

6. IAH: EET 3026 Square Root of Sum of Squares So, this describes the accuracy of the measurement Volts

7. IAH: EET 3027 Significant Figures Some common mathematical rules used in electronics (for both homework and lab assignments) are: Use 3 significant figures for solutions (for a result that is correct to 3 significant figures, you must use more than 3 significant figures in all of the intermediate calculations). e.g. if your answer is 12E-6, write 12E-6 or 1.2E-5, if your answer is 1.47678E-3, write 1.48E-3 Use standard rounding e.g. if your answer is 1.034567, write 1.03 Give the numerical solution to problems (unless the problem asks for a formula or equation). e.g. don't write  79, write 8.89, don't write 127/9, write 14.1 (calculators are required when doing homework, labs, and tests)

8. IAH: EET 3028 Statistics Mean –Average –DC Standard Deviation –rms

9. IAH: EET 3029 An example using Excel

10. IAH: EET 30210 STDEV using Excel

11. IAH: EET 30211 Normal Probability (Bell) Curve http://www.cquest.utoronto.ca/geog/ggr270y/notes/not09d.html http://www.cquest.utoronto.ca/geog/ggr270y/notes/not09d.html This is probably the most important of all the probability distributions. Among other things, people's weights, heights and shoe sizes are normally distributed, as are annual rainfall and temperatures of a region, IQ scores, test scores, and most natural phenomena in general. Many more variables can be approximated very well by normal distributions.

12. IAH: EET 30212 Normal Distribution and Data 27.1 0 C 27.1 – 21.6 =5.5 0 C

13. IAH: EET 30213 Summary 1 st and 2 nd order time response Measurement Error –Square Root of Sum of Squares –Significant Figures in Calculations Statistics –Mean –Standard Deviation –Normal Probability Curve (Bell Curve)