University of Southern California School Of Engineering Department Of Electrical Engineering

Transcription

1 Unverty f Suthern afrna Sch Of Enneern Deartent Of Eectrca Enneern EE 48: ewrk nent # fa, Due 9/7/ ha Fure : The redrawn cnfuratn f "F P." t b t a Gven the fure, ne can wrte the fwn equatn: λ t t { λ } t b t b b λ t b t t t λ b λb NS. #.a t ad retance tted λb That t cncude that the reut btaned abve the ae a where the ad wa nfntey are, hwever; t nt the ae a rnay derved exren. b Snce a caactr w euate an en crcut at w frequence, th w ve u the an that derved n art a NS. #.b

2 c Fure : The cheatc t fnd utut retance I x b avn the cheatc abve, the equatn bew can be wrtten. x λb b x ut I x λ b x x NS. #.c d By nectn, n nfnty. NS. #.d e By nectn, te cntant the retance, that een by the caactr, te caactr tef. Therefre: τ ut NS. #.e f In a ne e yte, a n ur cae, the bandwdth f the tranfer functn equa t ne ver the te cntant. Thu, NS. #.f ut v By exann, the frt tw ectn, and f ectn, ne can arrve a reut that: ut b v λ NS. #. ut

3 ere, t advantaeu t have n ad deendence. ence, ne can den h crcut wthut wrryn abut the ad. h By un a f the equatn, ne can btan reut bew: v.78 τ.5 n NS. #.h f ut 56.5 Ω.8 9 rad 7. Mhz Fure a eactance f nductr at renance equa t nductance te that renant frequency rad/. ence, NS. #.a b We ut utze vtae dvder t fnd the tranfer functn. Therefre, r where NS. #.b

4 c In revu tw equatn, the frer enera fr f the atter. In rder t fnd, equate th antude functn t antude f zer an ver quare rt f tw. By un th equaty, ne can eay fuf fwn aebrac te t attan the vaue f frequency. S where S where NS. #.b 4 4

5 NS. #.c Nrazed rah f th w be a fw: w/w d W c S S W I W W S I NS. #.d W S Th y uet that the enery tranferred n between caactr and nductr. ence, there n tta enery dated. eferrn t art b f the ecnd quetn, ne can tranfr that frequency baed tranfer functn nt aace dan. The ny thn that t be dne that wtchn n between? and. a Once we atch th ecfc tranfer functn wth the enera tranfer functn ven n the quetn. One can eay fnd the fwn a they are wrtten.

6 c ζ n n n ζ NS. #.4a n ζ NS. #.4a The renant frequency eaure f bandwdth, and zeta eaure f tabty. b c c ζ n n v c v v e ζ n t { } n ζ t c ζ e e t v v t c c ζ n t e n ζ t n ζ t c ζ ζ v v c c c t n NS. #.4c NS. #.4b vetn ?.5?.9? ? tn --[wnt] Fure

7 d In th art, we have an errr functn and we d nt want th functn t be any arer than ne ercent f teady tate vaue. By nectn f th errr functn ne can ay that envee f th functn a decayn exnenta, th exnenta, becaue at eak nu are equa t ne r nu ne, thu we are eft wth exnenta ne. We, f ne take the dervatve f the errr functn ne fnd the axa f t by equatn t t zer, he can enure nt any arer errr than.. Dn ha ve u reut bew. e ζ nt t n ζ NS. #.4d e In rder t uarantee that errr never arer than. ercent, we hud fnd the frt axa f errr functn dn w ve u fwn reatn h: t n π π 4.65 ζ ζ ζ ζ π n π t ζ NS. #.4e 887. M z.86 4 Fure 5

8 a avn the cheatc n the fure, ne can wrte the equatn bew: I I I I NS. #.5a b One can ue enera band a exren t arrve at the reut. The thn nce we have thee enera exren n ntnc fr, and we ut need t atch enera and ecfc and fnd ut and?. NS. #.5b c In rder t fnd the renant frequency an f a band a fter, ne ut need t take rat f ceffcent f. In th cae, t equa t ne. T rve th t rea eay. We, at renant frequency: NS. #.5c cance ut the ne n dennatr d They can nt be cntred ndeendenty. hann,,, t chane? w certany affect t. wever, f ne de ny want t chane, he can d wthut affectn?. T d, hud be tuned. NS. #.5d e Of cure, t rtant tune and? wthut affectn each ther becaue ay yu want t fr.5 Mz t 6.7 Mz. T d yu w chane center frequency, but f yur fter the ne ke we have, when yu chane center frequency yu a chane. Fr exae, t fr.5 Mz t

9 6.7 Mz frequence, bacay yu w ncreae center frequency. T d, yu need t chane, r, r. hann thee w a chane ether akn t ber r aer. nd th w ntrduce ether a tabty r ne rbe. NS. #.5e 5 a Baed n the crcut abve, ne can wrte the equatn n tabe x x x x x fter rearrann th e, ne ha et fwn fna reut: 4 4 NS. #.5a Fure 6

10 fter the carn wth the enera exren reented n the quetn, we can arrve at: NS. #.5a 4 b If e nfnty, r dan factr e t zer, we w have catn n ur yte. ence, catn cndtn : 4 4 NS. #.5b c Fr tabty, ne need t nt zer r neatve, thu: < 4 NS. #.5c d If ne u, nt equatn fnd fr dbb frequency n rbe, he can eay hw that: 6 ence, NS. #.5d e Equatn the dennatr f enera exren, when.5, t zer ne et the e. Thu, NS. #.5e, ± 4, ± Fure 7

11 a Bacay, f ne ke t have w yte, he hud den h crcut wth rea e. NS. #.6a b By atchn the abve wth derved ne fr crcut n fure, ne can eay arrve at fwn reut: // NS. #.6b NS. #.6b k k

12 k k v t k e k v t c t k k t e k t k t fr k > fr k e NS. #.6c d..8 k vtn.6.4 k.5 k. k tn --[t] Fure 8 Fr the t, when k equa t ne we ha et wet yte. NS. #.6d e T T e. T. 9 NS. #.6e

13 f T fr >>.9 T NS. #.6f.95 T.9 T.95 T.9.9 T T NS. #.6f µ 5n 7.8 Ω µ Ω NS. #.6 The uatn rah and net-t are n the fwn tw ae. The buffer n th rbe can be redrawn a abve where: f a b Fure 9 NS. #.7a

14 tae n Wave D::v Syb rbe 6 urrent X.e-4 urrent Y8.9e- Dervatve.5e u u u 4u Te n TIME

15 Prbe 6 * * *.t t ue 5n 5n 5u u 5 5n 6..tran 5u 4u.end

16 frequency equa t ne ver ceffcent f, when the dennatr ntnc fr fr frt rder yte. ence, B NS. #.7b c Th vtae te n f hw t defned n revu ectn. Thu, NS. #.7c d ε. IM ε.9898 NS. #.7d 8 avn crcut n the fure, ne can eay wrte equatn t fnd nut edance. Thu, Fure I x G I I x I xgzg I x xgzg x I G Z G NS. #.9a Zn n GG G G x n