Phasors

1
Phasors
2
Set Phasors on Stun

• How do we learn to use these phasors?
• 1. Sinusoids-amplitude, frequency and phase
  (Section 8.1)
• 2. Phasors-amplitude and phase (Section 8.3 sort
  of)
• 2a. Complex numbers (Appendix B).
• 3. Complex exponentials-amplitude and phase

3
Set Phasors on Kill

• 4. Relationship between phasors, complex
  exponentials, and sinusoids
• 5. Phasor relationships for circuit elements
  (Section 8.4)
• 5a. Arithmetic with complex numbers (Appendix B).

4
Set Phasors on Vaporize

• 6. Fundamentals of impedance and admittance (some
  of Section 8.5)
• 7. Phasor diagrams (some of Section 8.6)

5
Phasors

• A phasor is a complex number that represents the
  magnitude and phase of a sinusoid

6
Phasors (cont.)

• Time Domain
• Frequency Domain

7
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
8
More Complex Numbers

• Polar Coordinates A z ? q
• Rectangular Coordinates A x jy

9
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
• Convert to rectangular 2 ? 45?

10
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)

11
Examples

• Find the time domain representations of
• X -1 j2
• V 104V - j60V
• A -1mA - j3mA

12
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

13
Addition

• Addition is most easily performed in rectangular
  coordinates
• A x jy
• B z jw
• A B (x z) j(y w)

14
Addition
15
Subtraction

• Subtraction is most easily performed in
  rectangular coordinates
• A x jy
• B z jw
• A - B (x - z) j(y - w)

16
Subtraction
17
Multiplication

• Multiplication is most easily performed in polar
  coordinates
• A AM ? q
• B BM ? f
• A ? B (AM ? BM) ? (q f)

18
Multiplication
Imaginary Axis
A ? B
B
A
Real Axis
19
Division

• Division is most easily performed in polar
  coordinates
• A AM ? q
• B BM ? f
• A / B (AM / BM) ? (q - f)

20
Division
Imaginary Axis
B
A
Real Axis
A / B