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Midterm Exam with Solution for Linear System Analysis I | ECE 311, Exams of Electrical and Electronics Engineering

Colorado State University (CSU)Electrical and Electronics Engineering
Prof. William D. Eads

Material Type: Exam; Professor: Eads; Class: Linear System Analysis I; Subject: Electrical and Computer Engineering; University: Colorado State University; Term: Fall 2007;

Typology: Exams

Pre 2010

Uploaded on 03/18/2009

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EE311 - Linear Systems I Name: . 5(? L-U T7 ()/JS
Mid-Term Exam . October 25,2007 9:30 -10:45 a.m.
Open Book, Open Notes, Calculator (not computer) Allowed. SHOW YOUR WORK!
Answer the following three questions. Box all answers.
1. (30Points) Consider thecirc~it below: .
~ R2
L R1
o----rYYY'
vj(t)
a) . What is the Ordinary Differential Equation describing vo(t) with Vj(t) as an input?
( . _A : , \ , ,.J,.) r),.) ,L1-) - - IIp:)
~t-) =- L~+If; L-( t) . vo~ .=:;- -1'2 l(f :::?-) L(L'- ~
.'. V~ (t) := -!:::::- dV7JCt')_S·Vpft..)
IZZ- tJb/ Rz..
or
b) Is this circuit CaUSal?'y"- Is it BIBO stable? +
c) Another circuit is described by:
dy(t) +3y(t) =2x(t)
dt
What transfer func.tion H(s) describes this circuit?
l-iCs '):::
What is the steady state response yss(t) ofthis circuit to the input x(t) =2cos(4t) ?
pf3

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Download Midterm Exam with Solution for Linear System Analysis I | ECE 311 and more Exams Electrical and Electronics Engineering in PDF only on Docsity!

EE311 - Linear Systems I Name:. 5 (? L-U T7 ()/J S

Mid-Term Exam. October 25,2007 9:30 -10:45 a.m.

Open Book, Open Notes, Calculator (not computer) Allowed. SHOW YOUR WORK!

Answer the following three questions. Box all answers.

  1. (30Points) Consider thecirc~it below:. ~ R L R o----rYYY' vj(t)

a). What is the Ordinary Differential Equation describing vo(t) with Vj(t) as an input? ~ (^ t-) =- L.^ ~ _A^ :^ + If; L-( ,^ t). \ vo~^ ,^ ,.J,.) .=:;- -1'2r),.) l (f :::?-) L ,^ (L'- L1-)^ -^ -^ II ~p:) .'. V~ (t) := -!:::::- d V7JCt')_S· Vpft..)

IZ Z- tJb/ Rz..

or

b) Is this circuit CaUSal?'y"- Is it BIBO stable? + c) Another circuit is described by: dy(t)dt + 3 y(t) = 2x(t)

What transfer func.tion H(s) describes this circuit? l-i Cs ')::: What is the steady state response yss(t) ofthis circuit to the input x(t) = 2cos(4t)?

  1. (30 points) Consider the linear time-invariant system with impulse response:

h(t) = (2e-Zt - e~3t)uCt)

where u(t) is the unit step function. a)

b) (^) Similarly, the response to a 5 v. step input (i.e. x(t) = 5u(t) ) for another system is:

YCt) = 10(1- e-Zt)u(t)

What is its impulse response? Same hint as in a) above! ktt) ~ (^) -------.. d C {. ( 10 C I ~e~2+ ,)4)J

d-::t

~. Lf e-_ 2_t-~.

d+ --rIO

What it the transfer function R(s) for this system? & St£) /;1^ tc'J^ e -S+J^ t ~.. --6&^ (IJJ^ -I e -(2,+S)^ \A^ L-tj t

....(Lt'C':;.)___ --^ '-I^^ ..•^ e -("2-+^^ s)1u,^ OQ^ ~- 51-L L(

l-{[S) ~. S-t-Z What dlnary Differential Equation describes this system?