Lecture 191 Phasors

Lecture 192 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

Lecture 193 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).

Lecture 194 Set Phasors on Vaporize 6.Fundamentals of impedance and admittance (some of Section 8.5) 7.Phasor diagrams (some of Section 8.6)

Lecture 195 Phasors A phasor is a complex number that represents the magnitude and phase of a sinusoid:

Lecture 196 Phasors (cont.) Time Domain: Frequency Domain:

Lecture 197 Complex Numbers x is the real part y is the imaginary part z is the magnitude  is the phase  z x y real axis imaginary axis

Lecture 198 More Complex Numbers Polar Coordinates: A = z   Rectangular Coordinates: A = x + jy

Lecture 199 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 

Lecture 1910 Summary of Phasors Phasor (frequency domain) is a complex number: X = z   = x + jy Sinusoid is a time function: x(t) = z cos (  t +  )

Lecture 1911 Examples Find the time domain representations of X = -1 + j2 V = 104V - j60V A = -1mA - j3mA

Lecture 1912 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

Lecture 1913 Addition Addition is most easily performed in rectangular coordinates: A = x + jy B = z + jw A + B = (x + z) + j(y + w)

Lecture 1914 Addition Real Axis Imaginary Axis AB A + B

Lecture 1915 Subtraction Subtraction is most easily performed in rectangular coordinates: A = x + jy B = z + jw A - B = (x - z) + j(y - w)

Lecture 1916 Subtraction Real Axis Imaginary Axis AB A - B

Lecture 1917 Multiplication Multiplication is most easily performed in polar coordinates: A = A M   B = B M   A  B = (A M  B M )  (  )

Lecture 1918 Multiplication Real Axis Imaginary Axis A B A  B

Lecture 1919 Division Division is most easily performed in polar coordinates: A = A M   B = B M   A / B = (A M / B M )  (  )

Lecture 1920 Division Real Axis Imaginary Axis A B A / B