{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 20-22_v2

# Lecture 20-22_v2 - Spring 2011 ECE 2100 Cornell University...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 1 Lectures 20-22 Phasors and their uses Frequency-domain analysis Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 2 Generalizing complex exp. • Can describe a complex exponential as either – magnitude and phase (polar) – or as a weighted sum of real, imaginary (cartesian) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t B t A t V t m t m t V t m t V ϖ ϖ φ ϖ φ ϖ φ ϖ sin cos sin sin cos cos cos- =- = + = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t j jB A t V t j jm m t V t j j m j t j m t V ϖ ϖ φ φ ϖ φ φ ϖ exp exp sin cos exp exp exp + = + = = + = • Can describe a sinusoid either by – magnitude and phase (polar) – or as a weighted sum of sine, cosine (cartesian) cos( ω t) sin( ω t) A B m φ real imag A B m φ Spring 2011 ECE 2100, Cornell University, Prof. A. Molnar 3 The phasor transform • Converting phase/mag to Cartesian (complex notation): • Converting complex cartesian to angle + magnitude ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 φ φ ϖ φ ϖ sin , cos exp exp m B m A t j jB A j t j m t V = = + = + = • Allows intra-conversion between complex numbers and magnitude/phase real imag A B m φ ( 29 ( 29 ( 29 ( 29 ( 29( 29 =- + = + = + = + =- A B jB A jB A B A m t j jB A j t j m t V 1 2 2 tan exp exp...
View Full Document

{[ snackBarMessage ]}

### Page1 / 11

Lecture 20-22_v2 - Spring 2011 ECE 2100 Cornell University...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online