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MT-144

MT-144. NETWORK ANALYSIS Mechatronics Engineering (13). Sinusoids and Phasors. Contents. Introduction Sinusoids Phasors Phasor Relationships for Circuit Elements Impedance and Admittance Kirchhoff’s Laws in the Frequency Domain Impedance Combinations Applications. Introduction.

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MT-144

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  1. MT-144 NETWORK ANALYSIS Mechatronics Engineering (13)

  2. Sinusoids and Phasors

  3. Contents • Introduction • Sinusoids • Phasors • Phasor Relationships for Circuit Elements • Impedance and Admittance • Kirchhoff’s Laws in the Frequency Domain • Impedance Combinations • Applications

  4. Introduction • AC is more efficient and economical to transmit power over long distance. • A sinusoid is a signal that has the form of the sine or cosine function. • Circuits driven by sinusoidal current (ac) or voltage sources are called ac circuits. • Why sinusoid is important in circuit analysis? • Nature itself is characteristically sinusoidal. • A sinusoidal signal is easy to generate and transmit. • Easy to handle mathematically

  5. Sinusoids

  6. Sinusoids (Cont’d) • A period function is one that satisfies f(t) = f(t+nT), for all t and for all integers n. • The period T is the number of seconds per cycle • The cyclic frequency f = 1/T is the number of cycles per second

  7. Sinusoids (Cont’d)

  8. Sinusoids (Cont’d) • To compare sinusoids • Use the trigonometric identities • Use the graphical approach

  9. The Graphical Approach

  10. Phasors • Sinusoids are easily expressed by using phasors • A phasor is a complex number that represents the amplitude and the phase of a sinusoid. • Phasors provide a simple means of analyzing linear circuits excited by sinusoidal sources.

  11. Phasors (Cont’d)

  12. Important Mathematical Properties

  13. Phasor Representation

  14. Phasor Representation (Cont’d)

  15. Phasor Diagram

  16. Sinusoid-Phasor Transformation

  17. Phasor Relationships for Resistor Phasor diagram Time domain Phasor domain

  18. Phasor Relationships for Inductor Phasor diagram Time domain Phasor domain

  19. Phasor Relationships for Capacitor Phasor diagram Time domain Phasor domain

  20. Impedance and Admittance

  21. Impedance and Admittance (Cont’d)

  22. Impedance and Admittance (Cont’d)

  23. Impedance and Admittance (Cont’d)

  24. KVL and KCL in the Phasor Domain

  25. Series-Connected Impedance

  26. Parallel-Connected Impedance

  27. Y- Transformations

  28. Example 1

  29. Example 2

  30. Example 3 -Y transformation

  31. Applications: Phase Shifters Leading output

  32. Phase Shifters (Cont’d) Lagging output

  33. Example

  34. Applications: AC Bridges

  35. AC Bridges (Cont’d) Bridge for measuring L Bridge for measuring C

  36. Summary • Transformation between sinusoid and phasor is given as • ImpedanceZ for R, L, and C are given as • Basic circuit laws apply to ac circuits in the same manner as they do for dc circuits.

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