Chapter 9 - Chapter 9 Sinusoids and Phasors SJTU 1...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
SJTU 1 Chapter 9 Sinusoids and Phasors
Background image of page 1

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

View Full DocumentRight Arrow Icon
SJTU 2 Sinusoids A sinusoid is a signal that has the form of the sine or cosine function. angle phase ument t frequency angular amplitude Vm where t V v m = = + = = + = φ ω arg ) cos(
Background image of page 2
SJTU 3 ) cos( φ ω+ = t V v m φ ϖ t f T π ϖ 2 2 = = radians/second (rad/s) f is in hertz(Hz)
Background image of page 3

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

View Full DocumentRight Arrow Icon
SJTU 4 ) cos( ) ( ) cos( ) ( 2 2 2 1 1 1 φ ϖ + = + = t V t v t V t v m m Phase difference: θ by v lags v by v leads v phase in are v and v phase of out are v and v if t t 2 1 0 2 1 0 2 1 0 2 1 0 ) ( ) ( 2 1 2 1 < = - = + - + =
Background image of page 4
SJTU 5 Complex Number form l exponentia form sinusoidal form polar form r rectangula φ j re z jrsin rcos z r z jy x z = + = = + = φ
Background image of page 5

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

View Full DocumentRight Arrow Icon
SJTU 6 Phasor a phasor is a complex number representing the amplitude and phase angle of a sinusoidal voltage or current. Eq.(8-1) and Eq. (8-2) Eq.(8-3)
Background image of page 6
SJTU 7 When Eq.(8-2) is applied to the general sinusoid we obtain E q.(8-4) The phasor V is written as Eq.(8-5)
Background image of page 7

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

View Full DocumentRight Arrow Icon
SJTU 8 Fig. 8-1 shows a graphical representation commonly called a phasor diagram. Fig. 8-1: Phasor diagram Two features of the phasor concept need emphasis: 1. Phasors are written in boldface type like V or I 1 to distinguish them from signal waveforms such as v(t) and i1(t) . 2. A phasor is determined by amplitude and phase angle and does not contain any information about the frequency of the sinusoid.
Background image of page 8
SJTU 9 In summary, given a sinusoidal signal , the corresponding phasor representation is . Conversely, given the phasor , the corresponding sinusoid is found by multiplying the phasor by and reversing the steps in Eq. (8-4) as follows: E q.(8-6) ) cos( ) ( φ ω+ = t V t v m = Vm V Time domain representation Phase-domain representation
Background image of page 9

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

View Full DocumentRight Arrow Icon
SJTU 10 Properties of Phasors additive property Eq.(8- 7) Eq.(8-8) Eq.(8-9)
Background image of page 10
SJTU 11 derivative property Eq.(8- 10) V j dt dv ϖ Time domain representation Phase-domain representation
Background image of page 11

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

View Full DocumentRight Arrow Icon
SJTU 12 Integral property Time domain representation Phase-domain representation ϖ j V vdt The differences between v(t) and V: 1.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/06/2010 for the course EE 102 taught by Professor Pingli during the Fall '08 term at Shanghai Jiao Tong University.

Page1 / 44

Chapter 9 - Chapter 9 Sinusoids and Phasors SJTU 1...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online