Signal Processing and Linear Systems-B.P.Lathi copy

# 68b find t he laplace transforms a nd t he region of

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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 6.4-3 6 .4-1 6 .4-2 6 .4-3 F ind t he z ero-state response vo(t) of t he n etwork in Fig. P 6.4-l if t he i nput voltage f (t) = t e-tu(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. P6.4-2 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. P6.4-3 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 .4-8 ~ 0 in t he c ircuit of Fig. P6.4-4a for t he 6 4 66 C ontinuous-Time 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 6.4-10 t =0 a nd t he i nput ( a) u (t) ( b) e -'u(t). 6 .5-1 IH l OY F igure P 6.5-1a 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 6.5-1b 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 6.4-S R f (t) yet) c (a) F ig. P 6.4-9 6 .4-9 Ka H (s) = - s +a where Rb K = 1 +"if" a nd __ _ 1 a - RC F ig. P 6.5-1 6 .5-2 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 .6-1 Realize a a nd t hat t he t ransfer f unction for t he c ircuit in Fig. P 6.4-9b 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 6.4-9a IS given by K8 H (s) _ - (s H(s)=~ . · t· F 'g P 64-1O show t hat t he t ransfer f unction 6 .4-10 F or a s econd-order 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 .6-2 6s 2 H (s) = 2S2 + 38 + 10 + 6s + 5 R epeat P roblem 6.6-1 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 .4-11 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 .6-3 R epeat P roblem 6.6-1 i f H 8 _ ( ) - 58(8 2s +3 + 2)2(8 + 3) 468 6 C ontinuous-Time S ystem A nalysis U sing t he L aplace T ransform P roblems 4 69 Y (s) 6 .6-9 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 .6-10 Show o p a mp c anonical realization of t he t ransfer function H (s) = s2 3s + 7 + 4s + 10 6 .6-11 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.

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