R02 - ENEE 241 02 READING ASSIGNMENT 2 Thu 02/05 Lecture...

This preview shows pages 1–2. Sign up to view the full content.

ENEE 241 02* READING ASSIGNMENT 2 Thu 02/05 Lecture Topic: n th root of a complex number; continuous-time sinusoids; phasors Textbook References: sections 1.3 and 1.4 Key Points: The equation z n = e , where φ is a given angle, has n roots of the form z = e ; these are obtained by setting θ = ( φ + 2 ) /n , where k = 0 ,...,n - 1. The functions cos θ and sin θ are both periodic with period 2 π (radians), and are shifted versions of each other. The generic time-dependent sinusoid A cos(Ω t + φ ) has three parameters: amplitude A , an- gular frequency Ω (rad/sec) and initial phase φ . The cyclic frequency f (Hz) and period T (sec) are related to Ω by f = 1 /T = Ω 2 π The stationary phasor of A cos(Ω t + φ ) is the complex number Ae . The sum of two (or more) sinusoids of arbitrary amplitudes and phases but of identical frequency Ω is a sinusoid of frequency Ω. Sinusoids of identical frequency can be added together by taking the complex sum of their stationary phasors. Theory and Examples: 1 . The equation z n = v , where z is a complex variable and v is a complex constant, has n complex roots (this is true for any polynomial of degree n ). These roots can be found using the following observations:

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.

This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

Page1 / 4

R02 - ENEE 241 02 READING ASSIGNMENT 2 Thu 02/05 Lecture...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online