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EEN 307 Exam 1
Fall 2009
Prof. Murthi
PLEASE EXPLAIN YOUR STEPS AND REASONING FOR
FULL CREDIT. I CANNOT READ YOUR MIND!
Problem 1: Cousider the circuit below, and assume that you can use
the ideal op-amp approximations. At time ¢ = 0, the switch closes, and the
current source i,(t) is connected Lo the circuit.
(a) Write the differential equation characterizing the relaliouship between
the output voltage v(t) and the input current 2.{t} Zor t > 0.
“(b) For i,(t) = 5mA, find the output voltage vp(é).
=o (Ne carcect \tho the
Neb Tet Ay teneiover Bag terminal)
Gwe Com OX aint
Te SeRREe = V8) =
ce
Nem
Vette} = ve) t vite
Le ‘ reuler
woe por u
es
Vo) = Rye
Pie Jey Stace Ast Cans pont -
Oot Lk = 2ye (Sxlo 3)
&? . 5
° 1° — Ast] = SXt0 A
3
= 2 5 x19
k= a5 x a fos
= 9.5Xt0 % Sees oT
Noi Det yh = a= Les
v®) TAL we Ve (2)
eA go we tAfect
Auk Ce? / Vc () = ASH R, = Rey
\
(hen
veley= Ry + », = Oo
of ke _ fey
- (25
“Thom _t
ye (seh +625 £278
CS
Ace] = Cael
pet
_¢
= c(t )e 4
bo
\ -3 7s
Al = [Fee x 125 ) c tis
[oOo
~3 ~t Q
— éf ee
zea) — £08
2 al(e) — ARS
= ~*- fax'(“Iee)
what ‘ype a lla!
Cxamtee th (9 |
wee o ine
F
Cc) Ceo. wh = Olxte
Rp pole 0 = jo Xte ye
t = 3. [a ber te * We «= ISG He
We = pe = 1° Qn
“ Rye. “
-~¢ 3 _ -~2
ReC= o-lxte x joxle = ie
Ry JR, = (
hye fo Vyltl= Ae cod (vot 1 2)
Tne ootpet +
Volkl= Agl Hla) Idea (wat + B+ LH/e))
Sa for each cor, fad HMI ZH)
\. Mot 3, Wy? en 5°, g=43"
f= Sodz.
wees) ey = 0454 Coat beats
\ ange y at (59H)
+ ( Jn? Ss ia The pat
Sd ,
Problem 3: Consider the following observed input-output properties of
various systems. For each system, explain why or why not the system is a
linear time-invariant (LTT) systom.
(a) input iQ = ef + ef, ontput y(t) = e*
(b) input f(t) = 7cos(3t); ontput y(t) — 4+ 17 cos(3l + 53°).
(c) inpué /(Q = 7coa(St — 44°) + e™*; output y(t) = 49 cos(St + 14”)
DY eilstgitn/s)
(d) input f(d)
(e) input (id)
output y(t) = dei("/?),
5;
5; output y(t) = Se’.
L
" 7 cool34) fy 44 eeslt3t + 53°)
Ny Re Sasem no not LL.
Ne {raeae Suslan C&A feat az Cond Toa
at tty eatyet (4 abave) ied we (NM
Ceathat at Th inpud .
f-
Cc) Feoal Stas) eo
TF tste whe nei
Woe Syston is Magen,
F b00(St— 44") [9 FF cos (StH ge)
, [Ho] £45)
Ba
b&
ae = h are lt sg)
yO?
[How, — ZAC3)
(4) S as oe! ba 5)
d
“This implia AB He) = }
Laktckh = Net allowed fr
LwTt sqateos (Hs) Canact be
eo, Nel (rrean / complex)
Ce) 6 4}a 5"
= 7
bays er Hel YS Thy iy
O ° Allows , Se linear.
9
