ECE634 Signals and Systems II, Spring 2009 - Lecture 17, March 2 4.8 Frequency Response of an LTIC System This section assumes that s = + j = 0 + j = j , i.e. we are only concerned with the steady-state component of the response. Since the frequenc
ECE634 Signals and Systems II, Spring 2009 Homework 3 Solutions Show all work and write legibly for full credit.
1. For the differential equations that you solved in problem 5 of HW2, determine the zero-input and zero-state components.
y (t ) Y (
ECE634 Signals and Systems II, Spring 2009 Homework 4 The color-codes correspond to the colors you randomly selected in class. Do the problems that match your color. Show all work and write legibly for full credit. While some problems are not requir
ECE634 Signals and Systems II, Spring 2009 Homework 5 The color-codes correspond to the colors you randomly selected in class. Do the problems that match your color. Show all work and write legibly for full credit. While some problems are not requir
ECE634 Signals and Systems II, Spring 2009 - Lecture 1, January 21 Background knowledge quiz problems with solutions: Q.1. Express 2e j 3 in rectangular coordinates. A.1. Using Eulers identity: 2 cos ( 3) + 2 j sin ( 3) 1.980 + 0.282 j Q.2. Find the
ECE634 Signals and Systems II, Spring 2009 - Lecture 2, January 23 B.5 Partial Fraction Expansion: B.5-1 Method of Clearing Fractions T1 ( s ) = 4s 3 + 16s 2 + 14s = A B C D + + + 2 s + 1 s + 2 ( s + 2) s + 3
( s + 1)( s + 2 ) ( s + 3)
2
Clear frac
ECE634 Signals and Systems II, Spring 2009 - Lecture 4, January 30 4.1 The Laplace Transform: The unilateral (one-sided) Laplace Transform is the only one of interest here. It is defined as
X ( s ) = x ( t )e st dt
0
where X ( s ) is a function
ECE634 Signals and Systems II, Spring 2009 - Lecture 7, February 6 4.2 Some Properties of the Laplace Transform: Table on p.369 in the text Time shifting For x ( t ) u ( t ) X ( s ) ,
x ( t t0 ) u ( t t0 ) X ( s ) e st0 for t0 0
Exercise E4
ECE634 Signals and Systems II, Spring 2009 - Lecture 8, February 9 4.3 Solution of Differential and Integro-Differential Equations: Example 4.10 (pp.371-372) (Linear differential equation with constant coefficients) Solve the second-order linear dif
ECE634 Signals and Systems II, Spring 2009 - Lecture 11, February 16 4.4 Analysis of Electrical Networks in the Frequency Domain: Example 7.28 (G. E. Carlson, Signal and Linear System Analysis) Circuit to equation in the time domain Consider the el
ECE634 Signals and Systems II, Spring 2009 - Lecture 14, February 23 4.5 Block Diagrams: Fig. 4.18 (assumes no loading between blocks)
a)
Y (s)
X (s) Y (s)
= H (s)
b)
X (s)
=
W (s) Y (s) = H1 ( s ) H 2 ( s ) X (s) W (s)
b)
Y (s)
X (s)
ECE634 Signals and Systems II, Spring 2009 Homework 3 The color-codes correspond to the colors you randomly selected in class. Do the problems that match your color. Show all work and write legibly for full credit. While some problems are not requir
ECE634 Signals and Systems II, Spring 2009 Homework 2 Solutions Show all work and write legibly for full credit.
1. Find the inverse Laplace transforms of the following:
4s 2 + 16s + 18 a) 3 s + 5s 2 + 6s
b)
5s + 6 s + 5s 2 + 6 s
3
c)
s + 5 s
Bode Plot Examples: Lathi Example 4.25
Sketch Bode plots for the transfer function
H ( s) =
( s + 2 )( s + 10 )
20 s ( s + 100 )
Rearranging into Bode plot form,
s 100 s 1 + 100 H ( s) = s s 1 + 2 1 + 10
Note: for Bode plots s = +
Course Syllabus
ECE 634 Signals & Systems II
Spring 2009
Department of Electrical and Computer Engineering, University of New Hampshire Catalog Description: Transient response analysis of linear systems using Laplace transforms, application to fe
UNIVERSITY OF NEW HAMPSHIRE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE651- Electronic Design II FALL 2007
DUE DATE: Monday 17 September
Text problems: 4.1, 4.2, 4.8, 4.19, 4.20, D4.22
ECE651FL2007HW1
UNIVERSITY OF NEW HAMPSHIRE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE651- Electronic Design II FALL 2007
DUE DATE: Monday 24 September
Text problems: Chapter 1: 1.39, 1.40, 1.41, 1.42, 1.43, 1.44, 1.46
ECE651FL2007HW1
UNIVERSITY OF NEW HAMPSHIRE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE651- Electronic Design II FALL 2007
DUE DATE: Friday 5 October
Text problems: Chapter 4: D4.34, D4.35, 4.42, 4.44, D4.55, 4.58, D4.60, D4.66
ECE651FL2007HW3
Rules for Making Bode Plots
Term
Constant: K Real Pole:
s
0
Magnitude
20log10(|K|) Low freq. asymptote at 0 dB High freq. asymptote at -20 dB/dec Connect asymptotic lines at 0,
Phase
K>0: 0 K<0: 180 Low freq. asymptote at 0. High freq. asymptote at
Daniel Brogan
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ECE634 Signals and Systems II, Spring 2009 Homework 1 Show all work and write legibly for full credit. 1. Express the following number in polar form and Cartesian form: A =
( 2 + j )(1 2 j )
1 e
j 3 /4
2. Express the following number in polar fo
ECE634 Signals and Systems II, Spring 2009 Homework 1 Solutions Show all work and write legibly for full credit. 1. Express the following number in polar form and Cartesian form: A =
( 2 + j )(1 2 j )
A = (4 3 j)
0.5
=
(
4 + ( 3) e
2 2
j ta
ECE634 Signals and Systems II, Spring 2009 Homework 2 The color-codes correspond to the colors you randomly selected in class. Do the problems that match your color. Show all work and write legibly for full credit. While some problems are not requir
ECE634 Signals and Systems II, Spring 2009 - Lecture 15, February 25 4.6 System Realization Recall the Time-Integration Property For x ( t ) X ( s ) , X (s) x ( ) d s
t 0
Thus, Fig. 4.19 (Lathi) shows that an integrator block in the time domain