{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EE40_Fall08_Lecture16-22

# EE40_Fall08_Lecture16-22 - EE40 Lecture 16-22 Connie...

This preview shows pages 1–14. Sign up to view the full content.

Slide 1 EE40 Fall 08 Connie Chang-Hasnain EE40 Lecture 16-22 Connie Chang-Hasnain October 6, 8, 10, 13, 15, 17, 20 Reading: Chap. 5, 6, Supplementary Reader Ch. 1, appendix on complex numbers

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 2 EE40 Fall 08 Connie Chang-Hasnain Chapter 5 • OUTLINE – Phasors as notation for Sinusoids – Arithmetic with Complex Numbers – Complex impedances – Circuit analysis using complex impdenaces – Dervative/Integration as multiplication/division – Phasor Relationship for Circuit Elements • Reading – Chap 5 – Appendix A
Slide 3 EE40 Fall 08 Connie Chang-Hasnain Example 1: 2nd Order RLC Circuit R + - C V s L t=0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 4 EE40 Fall 08 Connie Chang-Hasnain Example 2: 2nd Order RLC Circuit R + - C V s L t=0
Slide 5 EE40 Fall 08 Connie Chang-Hasnain Sinusoidal Sources Create Too Much Algebra ) cos( ) sin( ) ( wt B wt A t x P + = ) cos( ) sin( ) ( ) ( wt F wt F dt t dx t x B A P P + = + τ ) cos( ) sin( )) cos( ) sin( ( )) cos( ) sin( ( wt F wt F dt wt B wt A d wt B wt A B A + = + + + τ Guess a solution Equation holds for all time and time variations are independent and thus each time variation coefficient is individually zero 0 ) cos( ) ( ) sin( ) ( = - + + - - wt F A B wt F B A B A τ τ 0 ) ( = - + B F A B τ 0 ) ( = - - A F B A τ 1 2 + + = τ τ B A F F A 1 2 + - - = τ τ B A F F B Dervatives Addition Two terms to be general Phasors (vectors that rotate in the complex plane) are a clever alternative.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 6 EE40 Fall 08 Connie Chang-Hasnain Complex Numbers (1) x is the real part y is the imaginary part z is the magnitude θ is the phase ( 1) j = - θ z x y real axis imaginary axis Rectangular Coordinates Z = x + jy Polar Coordinates: Z = z ∠ θ Exponential Form: θ cos z x = θ sin z y = 2 2 y x z + = x y 1 tan - = θ (cos sin ) z j θ θ = + Z j j e ze θ θ = = Z Z 0 2 1 1 1 0 1 1 90 j j e j e π = = ∠ ° = = ∠ °
Slide 7 EE40 Fall 08 Connie Chang-Hasnain Complex Numbers (2) 2 2 cos 2 sin 2 cos sin cos sin 1 j j j j j j e e e e j e j e θ θ θ θ θ θ θ θ θ θ θ θ - - + = - = = + = + = j j e ze z θ θ θ = = = Z Z Euler’s Identities Exponential Form of a complex number

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 8 EE40 Fall 08 Connie Chang-Hasnain 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 (And later use multiplication by j ω to replace – Diffrentiation – Integration
Slide 9 EE40 Fall 08 Connie Chang-Hasnain Addition Addition is most easily performed in rectangular coordinates: A = x + jy B = z + jw A + B = ( x + z ) + j ( y + w ) Real Axis Imaginary Axis A B A + B

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 10 EE40 Fall 08 Connie Chang-Hasnain Subtraction Subtraction is most easily performed in rectangular coordinates: A = x + jy B = z + jw A - B = ( x - z ) + j ( y - w ) Real Axis Imaginary Axis A B A - B
Slide 11 EE40 Fall 08 Connie Chang-Hasnain Multiplication Multiplication is most easily performed in polar coordinates: A = A M ∠ θ B = B M ∠ φ A × B = ( A M × B M ) ( θ + φ ) Real Axis Imaginary Axis A B A × B

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Slide 12 EE40 Fall 08 Connie Chang-Hasnain Division Division is most easily performed in polar coordinates: A = A M ∠ θ B = B M ∠ φ A / B = ( A M / B M ) ( θ - φ ) Real Axis Imaginary Axis A B A / B
Slide 13

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern