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EE202 Supplementary Materials for Self Study

EE202 Supplementary Materials for Self Study

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EE202 Supplementary Materials for Self Study

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  1. EE202 Supplementary Materialsfor Self Study Circuit Analysis Using Complex Impedance Passive Filters and Frequency Response

  2. Acknowledgment Dr. Furlani and Dr. Liu for lecture slides Ms. Colleen Bailey for homework and solution of complex impedance Textbook: Nilsson & Riedel, “Electric Circuits,” 8th edition

  3. Steady-State Circuit Response to Sinusoidal Excitation - Analysis Using Complex Impedance

  4. Why Sinusoidal?US Power Grid 60Hz Sinusoidal

  5. Household Power Line

  6. Household Circuit Breaker Panel 240V Central Air 120V Lighting, Plugs, etc.

  7. Single Frequency Sinusoidal Signal

  8. Sinusoidal Signal Amplitude Peak-to-peak Root-mean-square Frequency Angular Frequency Period

  9. Trigonometry Functions Appendix F

  10. Other Periodic Waveforms Fundamental and Harmonics

  11. Resistor Only Circuit I=V/R, i(t)=v(t)/R Instantaneous Response

  12. R-L Circuit Transient Steady-state

  13. Phase Shift Time Delay or Phase Angle: t / T *2 or *360-degree

  14. Phasor – Complex Number Z Real(Z)+j Imag(Z) Y Imag(Z) tan-1(Y/X) X Real(Z) Reference

  15. Complex Number

  16. Phasor Solution of R-L Circuit

  17. Observations Single Frequency for All Variables Phasor Solution of Diff Eq. Algebraic equation Extremely simple Phase Delay between variables Physical Measurements Real part of complex variables v = Real{V}; i = Real{I}

  18. Resistor

  19. Instantaneous Response

  20. Inductor

  21. Capacitor

  22. Impedance in Series Complex Impedance Resistance, Reactance

  23. Example =5000 rad/sec

  24. Apply ZL=jL, ZC=1/j C Zab=90+j(160-40)=90+j120=sqrt(902+1202)exp{jtan-1(120/90)} =150  53.13 degree I=750  30 deg / 150  53.13 deg = 5  -23.13 deg=5exp(-j23.13o)

  25. Impedance in Parallel Complex Admittance Conductance, Susceptance

  26. Example =200000 rad/sec

  27. Apply ZL=jL, ZC=1/j C Series: Use Z; Parallel: Use Y Y=0.2  36.87 deg; Z=5  -36.87 deg V=IZ=40  -36.87 deg

  28. Kirchhoff’s Laws Same Current at a Node Addition of current vectors (phasors) Voltage Around a Loop or Mesh Summation of voltage vectors (phasors)

  29. Delta-T Transformation

  30. Example

  31. Delta-T Transformation

  32. Series, Parallel, Series

  33. Another Delta-T Transformation

  34. Thevenin and Norton Transformation

  35. Thevenin Equivalent Circuit

  36. Norton Equivalent Circuits

  37. Voltage divider Vo=36.12-j18.84 (V)

  38. Find VTh Vx=100-I*10, Vx=I*(120-j40)-10*Vx; solve Vx and I VTH=10Vx+I*120=784-j288 (V)

  39. Find ZTh Calculate Ia Determine Vx Calculate Ib ZTh=VT/IT=91.2-j38.4 (Ohm)

  40. Transformer Time differentiation replaced by  j

  41. AC Sine Wave, Ideal Transformer Voltage and Current Power Conserved

  42. Transformer • Power Applications • Convert voltage • vout=(N2/N1)  vin • Signal Applications • Impedance transformation • Xab=(N1/N2)2  XL • Match source impedance with load to maximize power delivered to load

  43. Power Calculations

  44. Frequency Response of Circuits • Analysis Over a Range of Frequencies • Amplifier Uniformity • Filter Characteristics • Low pass filter • High pass filter • Bandpass filter • Equalizer

  45. RC Filters High Pass Low Pass