Unformatted text preview: nstantaneously a t t = O. D etermine t he c urrent yet) for t > 0
.
HInt: Use t he T hevenin equivalent. F ig. P 6.43 6 .41 6 .42 6 .43 F ind t he z erostate response vo(t) of t he n etwork in Fig. P 6.4l if t he i nput voltage
f (t) = t etu(t). F ind t he t ransfer function relating the o utput vo(t) t o t he i nput
f (t). From t he t ransfer function, write t he differential equation relating vo(t) t o f (t).
T he s witch in t he circuit of Fig. P6.42 is closed for a long time a nd t hen o pened
i nstantaneously a t t = O. F ind a nd s ketch t he c urrent yet).
F ind t he c urrent yet) for t he p arallel resonant circuit in Fig. P6.43 if t he i nput is
( a) f (t) = A cos w otu(t)
( b) f (t) = A sin w otu(t)
Assume all initial conditions t o b e zero. 2 wo 1 = LC 6 .48 ~ 0 in t he c ircuit of Fig. P6.44a for t he 6 4 66 C ontinuousTime S ystem A nalysis U sing t he L aplace T ransform 4 6, P roblems 1 /8n + + . l..n 1F 2 u(t) 8 f (t) Vo ( t) F ig. P 6.4"T
F ig. P 6.410
t =0 a nd t he i nput ( a) u (t) ( b) e 'u(t).
6 .51
IH l OY F igure P 6.51a s hows two resistive l adder s egments. T he t ransfer f unction o f e ach
segment ( ratio o f o utput t o i nput v oltage) is~. F igure P 6.51b shows t hese t wo
segments c onnected i n cascade.
( a) Is t he t ransfer f unction ( ratio o f o utput t o i nput v oltage) o f t his cascaded network WW=~? ( b) I f your a nswer is affirmative, verify t he a nswer by d irect c omputation o f t he
t ransfer f unction. Does t his c omputation c onfirm t he e arlier value ~? I f n ot, why?
( c) R epeat t he p roblem w ith R 3 = R 4 = 200. D oes t his r esult suggest t he a nswer t o
t he p roblem i n p art ( b)? F ig. P 6.4S R f (t) yet) c
(a) F ig. P 6.49 6 .49 Ka H (s) =  s +a where Rb
K = 1 +"if" a nd __ _
1
a  RC F ig. P 6.51 6 .52 I n Fig. 6.18, h l(t) a nd h 2(t) a re t he i mpulse responses o f s ystems w ith t ransfer functions H I(s) a nd H2(S), respectively. D etermine t he i mpulse response o f t he c ascade,
a nd p arallel c ombination o f H I(s) a nd H2(S) s hown in Fig. 6.18b a nd c. 6 .61 Realize a a nd t hat t he t ransfer f unction for t he c ircuit in Fig. P 6.49b is given b y (b) (a) S how t hat t he t ransfer f unction which relates t he .aut.put v oltage y (t) t o t he i nput
v oltage J (t) for t he o p a mp c ircuit in Fig. P 6.49a IS given by K8 H (s) _
 (s H(s)=~ . · t· F 'g P 641O show t hat t he t ransfer f unction
6 .410 F or a s econdorder o p a mp ClrcUi I II I .
.,
).
b
H (s) r elating t he o utput v oltage vo(t) t o t he i nput v oltage J (t given y by canonical, series, a nd p arallel forms.
6 .62 6s 2 H (s) = 2S2 + 38 + 10 + 6s + 5 R epeat P roblem 6.61 if 3 s(s + 2) ( a) H (s) _
 (s + 1)(8 2 + 2s + 2) ( b) H(8) = (8 s
H (s) = s 2+8s+12
U sing t he i nitial a nd final value t heorems, find th~ i nitial a nd final value of t he zero6 .411
state r esponse o f a s ystem w ith t he t ransfer functIOn s (s + 2) + 1)(s + 3)(s + 4) + 2)(82 + 4) 2s  4 6 .63 R epeat P roblem 6.61 i f H 8 _ ( )  58(8 2s +3 + 2)2(8 + 3) 468 6 C ontinuousTime S ystem A nalysis U sing t he L aplace T ransform P roblems
4 69 Y (s) 6 .69 Show two different op a mp c ircuit realizations of t he t ransfer function H (s) Y(s) +2
3
= ;s:t:5 = 1  ;:t:5 6 .610 Show o p a mp c anonical realization of t he t ransfer function H (s) = s2 3s + 7
+ 4s + 10 6 .611 Show o p a mp...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.
 Spring '13
 Bayliss
 Signal Processing, The Land

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