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Introduction to Complex Numbers and Phasors in Transmission Lines

Learn about complex numbers, phasors, and their application in circuits. Explore Euler's formula, Cartesian and polar coordinates, and Phasor Analysis to solve circuits. Practice calculating magnitude and phase of complex numbers. Engage with video resources and discussions to enhance understanding.

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Introduction to Complex Numbers and Phasors in Transmission Lines

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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. EEE 161 Week 1, Lecture 1, Video 1 Sinusoidal signals

  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. EEE 161 Week 1, Lecture 1, Video 2 Complex Numbers

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

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

  11. 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

  12. 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.

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

  14. Euler’s equation A A A

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

  16. Quiz

  17. Some more concepts Power and Square Root.

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

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

  20. 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?

  21. Separately transfer R and OmegaL to FD

  22. EEE 161, Week 1, Lecture 1 Concepts: application of Complex numbers to circuits

  23. Example 1 HW problem complex numbers

  24. Example problem complex numbers Z1=5<-60, z2=4<45z1*z2=20<-15z1+z2=5.33-j1.55<-60=5*e^j(-60)Euler’s formula 5e^j(-60)=5(cos(-60)+jsin(-60))=5/2-j5*sqrt(3)/2 - cartesian

  25. 2. Example 2 HW problem complex numbers

  26. 2. Example problem homework 1 Z1=3-j2, Z2=-4+j3Polar form?Z1=sqrt(13)<arctg(-2/3)

  27. 3. Example problem how complex numbers are used in circuits • Find the magnitude and phase of the voltage on the mystery circuit if the current through it was measured to be • And the complex equation to find the voltage is

  28. 4. Sinusoidal Signals and Complex numbers relationship Sinusoidal signals can be represented using complex numbers!

  29. 5. Watch complex numbers video and post on discussion board https://www.youtube.com/watch?v=T647CGsuOVU Post on Week 1 Lecture 1 summary of what you have learned (or know really well) and at least one question that is still unclear. Respond to one other student.

  30. Homework 1 will be due soon!

  31. Optional but interesting3Blue1Brown explains complex numbers (6min)https://www.youtube.com/watch?v=F_0yfvm0UoU

  32. EEE 161 Week 1, Lecture 2, Video 1 Measurement Mystery

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

  34. 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?

  35. EEE 161 Week 1, Lecture 2, Video 2 Process to solve circuits using phasors

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

  37. ac Phasor Analysis: General Procedure

  38. ac Phasor Analysis: General Procedure

  39. EEE 161, Week 1, Lecture 2 Concept: phasors

  40. Objective • Students will be able to solve a simple circuit using phasors

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

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