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Applied Electromagnetics EEE 161

Applied Electromagnetics EEE 161. Intro to Transmission Lines. LECTURE 1 – INTRO TO CLASS, Getting to know each other. Complex Numbers/Phasors at home reading. View the video about complex numbers: https :// www.youtube.com/watch?v=T647CGsuOVU View the phasor simulation:

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Applied Electromagnetics EEE 161

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  1. AppliedElectromagneticsEEE 161 Intro to Transmission Lines

  2. LECTURE 1 – INTRO TO CLASS, Getting to know each other

  3. Complex Numbers/Phasors at home reading • View the video about complex numbers: https://www.youtube.com/watch?v=T647CGsuOVU • View the phasor simulation: https://en.wikipedia.org/wiki/File:Circle_cos_sin.gif • Read chapter 1, sections on Complex numbers and phasors. • Post at least 1 “muddiest point” (most unclear) in this reading on the SacCT discussion Complex Numbers and Phasors. These are graded as extra credit. • Due Week 2, day before first class.

  4. Complex Numbers/Phasors at home reading • View the video about complex numbers: https://www.youtube.com/watch?v=T647CGsuOVU • View the phasor simulation: https://en.wikipedia.org/wiki/File:Circle_cos_sin.gif • Read chapter 1, sections on Complex numbers and phasors. • Post at least 1 “muddiest point” (most unclear) in this reading on the SacCT discussion Complex Numbers and Phasors. These are graded as extra credit. • Due Week 2, day before first class.

  5. Objective • In order to understand transmission lines we have to be able to describe sinusoidal signals first!

  6. Motivation • Here is an equation of a wave • Here is an equation of a sinusoidal signal How are they the same and how are they different? Use vocabulary to name green and yellow highlights.

  7. Sinusoidal Signal Describe this graph using at least 5 words!

  8. Sinusoidal signals can be represented using complex numbers!

  9. Complex Numbers

  10. Objective • To solve simple circuits we have to be able to apply basic arithmetic operations with complex numbers.

  11. Complex numbers Cartesian Coordinate System Polar Coordinate System For example: Euler’s Identity

  12. Quiz • Complex number Z=3+j2 is given. • Sketch the number in Cartesian coordinate system • Find the magnitude and phase • Write a complete sentence to explain magnitude and phase on the diagram

  13. Some concepts from complex #s Conjugate Division Addition It is easier to add/subtract complex numbers when they are in _____________ coordinates. It is easier to divide/multiply complex numbers when they are in polar coordinates.

  14. Which equation do we use to go from Polar to Rectangular coordinates?

  15. Euler’s equation A A A

  16. QuizWhat is the real and imaginary part of the voltage whose amplitude is 2 and phase is 45 deg? (no calc)

  17. Quiz

  18. Some more concepts Power and Square Root.

  19. Quiz Calculate and sketch the magnitude and phase of the following three complex numbers:

  20. Quiz Find the magnitude and phase of the following complex numbers:

  21. Where did we see division of complex numbers?example in EE: Find magnitude and phase of the current in the circuit below How can we find magnitude and phase of this current in terms of variables R, L, V and ω?

  22. Separately transfer R and OmegaL to FD

  23. Quiz • Find the magnitude and phase of the voltage on the mystery circuit if the current through it was measured to be • The complex equation to find the voltage is

  24. Homework 1 will be due soon!

  25. Interesting Case Study in an Electrical Engineering Laboratory Let’s look at two simple circuits

  26. Dr. M is measuring voltage in the laboratory using her handy-dandy Fluke. She measures voltages on the resistors and inductor to be as shown. She is shocked with the measurement on top and bottom circuit. Why? What do you think she expects, and what did she measure?

  27. Objective • Students will be able to solve simple circuits using phasors

  28. ac Phasor Analysis: General Procedure

  29. ac Phasor Analysis: General Procedure

  30. Example 1-4 (p.37): RL Circuit Cont.

  31. Example 1-4: RL Circuit cont.

  32. Graded Quiz TL#1 A series R-L circuit is given as shown in Figure below. Derive equations for magnitude and phase of current and voltages on resistor and inductor in the phasor domain. Assume that the resistance of the resistor is R, inductance of the inductor is L, magnitude of the sourse voltage is Vm and phase of the source voltage is θ. Note that you don’t have numbers in this step, so to find the magnitude and phase for current I and voltages VR and VLyou must first derive both numerator and denominator in polar form using variables R, omega, L, Vm, Vphase (do not use numbers). The solutions should look like equations in slide 24/27! In this step, assume that R=3Ω, L=0.1mH, Calculate magnitude and phase of I, VL and VR by plugging in the numbers in the equations for VL, VR and I you found above. Sketch the phasor diagram. Finally, write the two voltages and the current in the time domain.

  33. Socrative Quiz To use voltage divider eq the same current has to flow through both impedances.

  34. How are these two the same and how are they different? You can use voltage divider in both What is the difference between Xc=120Ohms and R=120Ohms What is the difference between Xc(reactance) and Zc (impedance)? To use voltage divider eq the same current has to flow through both impedances.

  35. How are these two the same and how are they different? You can use voltage divider in both What is the difference between Xc=120Ohms and R=120Ohms What is the difference between Xc(reactance) and Zc (impedance)? To use voltage divider eq the same current has to flow through both impedances.

  36. Objectives • Students will be able to explain why is the relationship between sinusoidal signals and phasors valid in the previous table • If a sinusoidal signal is given in time domain, they will be able to recognize and derive the phasor expression • If a phasor of a signal is given, they will be able to recognize and derive the time-domain expression

  37. Transformation • What is the transformation that we are using to transfer signals from time to frequency domain?

  38. Transformation • What is the transformation that we are using to transfer signals from time to frequency domain? That’s great, but why??

  39. Objective • Students will be able to explain how and why was the phasor transformation introduced

  40. Superposition • If we have two generators in a linear circuit: • Remove one, find currents and voltages • Remove the other, find currents and voltages • The total voltage or current is equal to the sum of responses from the two cases above.

  41. Backward Superposition • We have an existing cos(ωt) generator in the circuit • We add the second generator j*sin(ωt) • We find the currents and voltages in the circuit for the combined generator ejωt • Keep only the real part of the response

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