1 / 12

Phasors (7.3); Complex Numbers (Appendix)

Phasors (7.3); Complex Numbers (Appendix). Dr. S. M. Goodnick September 8, 2003. Phasors. A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current:. Phasors (cont.). Time Domain: Frequency Domain:. Summary of Phasors.

zaide
Download Presentation

Phasors (7.3); Complex Numbers (Appendix)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Phasors (7.3);Complex Numbers (Appendix) Dr. S. M. Goodnick September 8, 2003 ECE201 Lect-6

  2. Phasors • A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current: ECE201 Lect-6

  3. Phasors (cont.) • Time Domain: • Frequency Domain: ECE201 Lect-6

  4. Summary of Phasors • Phasor (frequency domain) is a complex number: X = zq = x + jy • Sinusoid is a time function: x(t) = z cos(wt + q) ECE201 Lect-6

  5. Class Examples • Learning Extension E7.3 • Learning Extension E7.4 ECE201 Lect-6

  6. Complex Numbers • x is the real part • y is the imaginary part • z is the magnitude • q is the phase imaginary axis y z q real axis x ECE201 Lect-6

  7. More Complex Numbers • Polar Coordinates: A = z q • Rectangular Coordinates: A = x + jy ECE201 Lect-6

  8. Are You a Technology “Have”? • There is a good chance that your calculator will convert from rectangular to polar, and from polar to rectangular. • Convert to polar: 3 + j4 and -3 - j4 • Convert to rectangular: 2 45 & -2 45 ECE201 Lect-6

  9. Arithmetic With Complex Numbers • To compute phasor voltages and currents, we need to be able to perform computation with complex numbers. • Addition • Subtraction • Multiplication • Division ECE201 Lect-6

  10. Complex Number Addition and Subtraction • Addition is most easily performed in rectangular coordinates: A = x + jy B = z + jw A + B = (x + z) + j(y + w) • Subtraction is also most easily performed in rectangular coordinates: A - B = (x - z) + j(y - w) ECE201 Lect-6

  11. Complex Number Multiplication and Division • Multiplication is most easily performed in polar coordinates: A = AMq B = BMf A B = (AM  BM)  (q + f) • Division is also most easily performed in polar coordinates: A / B = (AM / BM)  (q - f) ECE201 Lect-6

  12. Examples • Find the time domain representations of V = 104V - j60V I = -1mA - j3mA at 60 Hz • If Z = -1 + j2 , then find the value of IZ + V ECE201 Lect-6

More Related