Sudry Sudirhm Alisis Rgki Lisrik Jilid Drpulic
Hk cip pd pulis, SUDIRHAM, SUDARYANO Alisis Rgki Lisrik Drpulic, Bdug r-7 disi Juli hp:-cf.rg Alm ps: Kyk D-3, Bdug, 435. Fx: 6 5347 Sudry Sudirhm, Alisis Rgki Lisrik
BAB rsfrmsi Furir Ki lh mmplri ggp frkusi dri suu rgki. Alisis dg mgguk rsfrmsi Furir yg k ki plri riku ii k mmprlus pmhm ki mgi ggp frkusi, ik mgi prilku siyl iu sdiri mupu rgkiy. Sli dri pd iu, pd rgkirgki ru diumpi kd dim mdl siyl d piri idk dp diyk mllui rsfrmsi Lplc k pi dp dilkuk mllui rsfrmsi Furir. pik-pik yg k ki hs mlipui: dr Furir, rsfrmsi Furir, sif-sif rsfrmsi Furir, d lisis rgki mgguk rsfrmsi Furir. Dlm ii ki mmplri ig hl yg prm, sdgk hl yg rkhir k ki plri di rikuy. Dg mmplri dr d rsfrmsi Furir ki k mmhmi dr Furir. mmpu mgurik uk glmg pridik mdi dr Furir. mmpu muk spkrum uk glmg pridik. mmhmi rsfrmsi Furir. mmpu mcri rsfrmsi Furir dri suu fugsi. mmpu mcri rsfrmsi lik dri suu rsfrmsi Furir... Dr Furir... Kfisi Furir Ki lh mlih hw siyl pridik dp diurik mdi spkrum siyl. Pguri suu siyl pridik mdi suu spkrum siyl idk li dlh pry fugsi pridik kdlm dr Furir. Jik f dlh fugsi pridik yg mmuhi prsyr Dirichl, mk f dp diyk sgi dr Furir : 3
4 Sudry Sudirhm, Alisis Rgki Lisrik [ ] si cs f. yg dp ki ulisk sgi lih su- 3. θ cs f. Kfisi Furir,, d diuk dg huug riku. > > ; si ; cs d f d f d f.3 Huug.3 dp diprlh dri.. Mislk ki mcri : ki klik. dg csk kmudi ki igrsik r smpi d ki k mmprlh cs si cs cs cs cs d k d k d k d k f Dg mgguk ksm igmri si si si cs cs cs cs cs αβ αβ β α αβ αβ β α mk prsm di s mdi
5 si si cs cs cs cs dd k k d k k d k d k f Kr igrl uuk su prid dri fugsi sius dlh l, mk smu igrl di rus k prsm ii rili l kculi su yiu k d k ik rdi yg cs lh kr iu cs d f Pd uk-uk glmg yg srig ki mui, yk dir kfisi-kfisi Furir yg rili l. Kd ii diuk lh ksimris fugsi f yg prh ki plri di B-3; ki k mlihy skli lgi dlm uri riku ii.... Ksimris Fugsi Simri Gp. Suu fugsi dikk mmpuyi simri gp ik f f. Slh su ch fugsi yg mmiliki simri gp dlh fugsi csius, cs cs. Uuk fugsi smcm ii, dri. ki dpk [ ] [ ] si cs d si cs f f Klu kdu fugsi ii hrus sm, mk hruslh, d f mdi [ ] cs f.4
6 Sudry Sudirhm, Alisis Rgki Lisrik CO OH-.: uk dr Furir dri uk glmg dr puls riku ii. Pylsi : Buk glmg ii mmiliki simri gp, mpliud A, prid, lr puls. π π π π si si si cs ; ; A A A d A A A Ad Uuk, 4, 6,. gp, ; hy mmpuyi ili uuk, 3, 5,. gil. cs cs si,, A A A A f gil gil π π π Pmhm : Pd uk glmg yg mmiliki simri gp,. Olh kr iu sudu fs hrmis θ yg rri θ. Simri Gil. Suu fugsi dikk mmpuyi simri gil ik f f. Ch fugsi yg mmiliki simri gil dlh fugsi sius, si si. Uuk fugsi smcm ii, dri. ki dpk [ ] si cs f v A
Klu fugsi ii hrus sm dg f mk hruslh [ cs si ] [ si ] d f.5 CO OH-.: Crilh dr Furir dri uk glmg prsgi di smpig ii. Pylsi: Buk glmg ii mmiliki simri gil, mpliud A, prid. ; ; v A A si si A d A d A cs cs A cs π cs π π Uuk gil csπ sdgk uuk gp csπ. Dg dmiki mk A 4A uuk gil π π A uuk gp π 4A v π si, gil Pmhm: Pd uk glmg dg smri gil,. Olh kr iu sudu fs hrmis θ u θ 9. 7
Simri Sgh Glmg. Suu fugsi dikk mmpuyi simri sgh glmg ik f f. Fugsi dg sif ii idk ruh uk d iliy ik diivrsi kmudi digsr sgh prid. Fugsi sius misly, ik ki ki ivrsik kmudi ki gsr ssr π k kmli mdi sius. Dmiki pul hly dg fugsi-fugsi csius, glmg prsgi, d glmg sgiig. f [ cs π si π ] [ cs si ] Klu fugsi ii hrus sm dg f [ cs si ] mk hruslh d hrus gil. Hl ii rri hw fugsi ii hy mmpuyi hrmis gil s...3. Dr Furir Buk Ekspsil Dr Furir dlm uk spri. srig disu sgi uk sius-csius. Buk ii dp ki uh kdlm csius uk siyl sdr spri.. Skrg uk. k ki uh k dlm uk kspsil dg mgguk huug csα α α. Dg mgguk rlsi ii mk. k mdi 8 Sudry Sudirhm, Alisis Rgki Lisrik
9 θ θ θ θ θ cs f.6 Suku kig.6 dlh pumlh dri smpi. Jik pumlh ii ki uh muli dri smpi, dg pysui mdi, mdi, d θ mdi θ, mk muru.3 pruh ii rki si si cs cs d f d f d f d f θ θ θ.7 Dg.7 ii mk.6 mdi θ θ f.8 Suku prm dri.8 mrupk pumlh yg ki muli dri uuk mmsukk sgi slh su suku pumlh ii. Dg cr ii mk.8 dp diulis mdi θ c f.9 Iilh uk kspsil dr Furir, dg c dlh kfisi Furir yg mugki rup sr kmplks.
Sudry Sudirhm, Alisis Rgki Lisrik c θ. ik ; ik dg d > θ < θ θ c c. Jik d pd.3 ki msukk k. k ki dpk d f c. d dg. ii mk.9 mdi d f c f.3 Prsm. muukk hw c dlh mpliud dri hrmis k- d sudu fs hrmis k- ii dlh c. Prsm. upu. dp ki pdg sgi pguh siyl pridik f mdi suu spkrum yg rdiri dri spkrum mpliud d spkrum sudu fs spri lh ki kl di B-. Prsm.9 upu.3 mmrik f pil kmpsisi hrmisy c dikhui. Prsm. mdi cikl kl rsfrmsi Furir, sdgk prsm.3 dlh rsfrmsi liky. CO OH-.3: Crilh kfisi Furir c dri fugsi pd ch-.. Pylsi : si A A A d A c
.. rsfrmsi Furir... Spkrum Kiyu Dr Furir, yg kfisiy dirik lh. hy rlku uuk siyl pridik. Siyl-siyl pridik spri siyl kspsil d siyl k gg idk dp dirprssik dg dr Furir. Uuk mgi siyl-siyl dmiki ii ki mmrluk rsfrmsi Furir d ksp spkrum kiyu. Siyl pridik dipdg sgi siyl pridik dg prid k-higg. Jik diig hw π, mk.3 mdi f π f d f d.4 Ki lih skrg p yg rdi ik prid diprsr. Kr π mk ik mki sr, k mki kcil. Bd frkusi r du hrmis yg ruru, yiu π ug k mki kcil yg rri uuk suu slg frkusi ru umlh hrmis smki yk. Olh kr iu ik prid siyl diprsr muu mk spkrum siyl mdi spkrum kiyu, mdi d prmh frkusi ifiiisiml, d mdi puh kiyu. Pumlh pd.4 mdi igrl. Jdi dg mmu mk.4 mdi f f d d F d π π.5 dg F mrupk suh fugsi frkusi yg ru, sdmiki rup shigg
F f d.6 d F iilh rsfrmsi Furir dri f, yg diulis dg si F [ f ] F Prss rsfrmsi lik dp ki lkuk mllui prsm.5. F f CO OH-.4: Crilh rsfrmsi Furir dri uk glmg puls di smpig ii. Pylsi : Buk glmg ii dlh pridik yg hy mmpuyi ili r d, sdgk uuk yg li iliy l. Olh kr iu igrsi yg dimi lh.6 cukup dilkuk r d s. F A d si A A Ki digk rsfrmsi Furir.6 F f d dg kfisi Furir A c f d.7 Kfisi Furir c mrupk spkrum siyl pridik dg prid yg rdiri dri spkrum mpliud c d spkrum A v Sudry Sudirhm, Alisis Rgki Lisrik
sudu fs c, d kduy mrupk spkrum gris idk kiyu, mmiliki ili pd frkusi-frkusi ru yg diskri. Smr iu rsfrmsi Furir F diprlh dg mgmgk prid siyl mdi k-higg gu mckup siyl pridik yg ki ggp sgi siyl pridik yg pridy k-higg. Fkr pd c diklurk uuk mmprlh F yg mrupk spkrum kiyu, ik spkrum mpliud F mupu spkrum sudu fs F. CO OH-.5: Gmrk spkrum mpliud dri siyl pd ch.4. Pylsi : Spkrum mpliud siyl pridik ii mrupk spkrum kiyu F. F si A -5 F 6π 4π π π 4π 6π Pmhm: Siyl ii mmpuyi simri gp. Sudu fs hrmis dlh l shigg spkrum sudu fs idk digmrk. Prhik pul hw F mmpuyi spkrum di du sisi, psiif mupu gif; ili l rdi ik si yiu pd ±kπ k,,3, ; ili mksimum rdi pd, yiu pd wku ili si. CO OH-.6: Crilh rsfrmsi Furir dri f [A α ] u d gmrk spkrum mpliud d fsy. Pylsi : 3
α α F A u d A d α A A uuk α> α α A F α θ F α F 5 Aα θ 9 9 Pmhm: Uuk α <, idk d rsfrmsi Furir-y kr igrsi mdi idk kvrg..3. rsfrmsi Blik Pd rsfrmsi Furir rsfrmsi lik srig dilkuk dg mgpliksik rlsi frmly yiu prsm.5. Hl ii dp dimgri kr pliksi frmul rsu rlif mudh dilkuk CO OH-.7: Crilh f dri Pylsi : f π F πδ πδ d α δ d α π πδ d 9 4 Sudry Sudirhm, Alisis Rgki Lisrik
Pmhm : Fugsi πδ dlh fugsi di kws frkusi yg hy mmpuyi ili di ssr π. Olh kr iu ug hy mmpuyi ili di ssr. Kr fugsi hy mmpuyi ili di mk igrl dri smpi cukup dilkuk dri smpi, yiu sdiki di wh d di s. Ch ii muukk hw rsfrmsi Furir dri siyl srh rmpliud dlh πδ. CO OH-.8: Crilh f dri Pylsi : f F πδ α πδ α d π α α α δ α d α Pmhm : α πδ α d π α Fugsi πδα dlh fugsi di kws frkusi yg hy mmpuyi ili di α ssr π. Olh kr iu ug hy mmpuyi ili di α ssr α. Kr fugsi hy mmpuyi ili di α mk igrl dri smpi cukup dilkuk dri α smpi α, yiu sdiki di wh d di s α. CO OH-.9: Crilh f dri πa F u α u α α Pylsi : [ ] 5
πa f [ u α u α ] d π α α πa A [] d π α α α α α α α A A si α A α α α Pmhm: Dlm sl ii F mmpuyi ili pd slg α<<α lh kr iu ug mmpuyi ili pd slg frkusi ii ug; dg dmiki igrsi cukup dilkuk r α d α. Hsil rsfrmsi lik f diyk dlm uk sixx yg rili ik x d rili ik x. Jdi f mcpi ili mksimum pd d muu l ik muu ik k rh psiif mupu gif. Kurv F d f digmrk di wh ii. F f A β β..3. Dri rsfrmsi Lplc k rsfrmsi Furir Uuk rp siyl, rdp huug sdrh r rsfrmsi Furir d rsfrmsi Lplc. Sgim ki khui, rsfrmsi Lplc didfiisik mllui 8. sgi s F s f d.8 6 Sudry Sudirhm, Alisis Rgki Lisrik
dg s σ dlh puh frkusi kmplks. Bs wh igrsi dlh l, riy fugsi f hruslh kusl. Jik f mmuhi prsyr Dirichl mk igrsi rsu di s k p kvrg ik σ, d frmulsi rsfrmsi Lplc ii mdi F s f d.9 Smr iu uuk siyl kusl igrsi rsfrmsi Furir cukup dilkuk dri l, shigg rsfrmsi Furir uuk siyl kusl mdi F f d. Buk. sm r dg.9, shigg ki dp simpulk hw uuk siyl f kusl d dp di - igrsi F F s σ rlku. Prsyr dp di-igrsi pd huug. dp dipuhi ik f mmpuyi dursi yg rs u cp muru muu l shigg igrsi f dri k kvrg. Ii rri hw pl-pl dri Fs hrus rd di slh kiri sumu imir. Jik prsyr-prsyr rsu di s dipuhi, pcri rsfrmsi lik dri F dp pul dilkuk dg md rsfrmsi lik Lplc. CO OH-.: Dg mgguk md rsfrmsi Lplc crilh rsfrmsi Furir dri fugsi-fugsi riku ggp α, β >. Pylsi:. f A. f c f 3 δ A α u α [ siβ] u 7
α. f A u fugsi kusl d dp di -igrsi A F s pl p α di kiri sumu img sα F α. f δ fugsi kusl d F s F α [ siβ] dp di - igrsi c. f3 A u fugsi kusl, dp A F s pl pα± β sα β A F α β α β α di - igrsi di kiri sumu im CO OH-.: Crilh f dri F 3 4 Pylsi : Jik ki gi dg s ki dpk F s s 3 s 4 Pl dri fugsi ii dlh p 3 d p 4, kduy di slh kiri sumu imir. k k F s s 3 s 4 s 3 s 4 k s 4 F s s 3 s 4 s3 rsfrmsi lik dri F dlh : f ; k 3 4 [ ] u s 3 s4 8 Sudry Sudirhm, Alisis Rgki Lisrik
.4. Sif-Sif rsfrmsi Furir.4.. Kliir Spri hly rsfrmsi Lplc, sif um rsfrmsi Furir dlh kliir. Jik mk : : F [ f ] F d F[ f ] F [ Af Bf ] AF BF F CO OH-.: Crilh rsfrmsi Furir dri v csβ. Pylsi:. Fugsi ii dlh -kusl; lh kr iu md rsfrmsi Lplc idk dp di rpk. Fugsi csius ii ki ulisk dlm uk kspsil. β β β β [ csβ ] F F[ ] F[ ] F Dri ch.8. ki khui hw F πδ β F Jdi [ csβ] πδ β πδ β.4.. Difrsisi Sif ii diyk sgi riku df F F.3 d Prsm.5 myk f π F d df d d π π F d F d d d d π F d df F F d 9
.4.3. Igrsi Sif ii diyk sgi riku. F F f x dx πf δ.4 Suku kdu rus k.4 mrupk kmp srh ik skiry d. Fkr F rki dg f; ik digi dg l k ki dpk F f d CO OH-.3: Crilh rsfrmsi Furir dri f Au. Pylsi: Md rsfrmsi Lplc idk dp dirpk uuk fugsi k gg. Dri ch.. ki dpk hw F [ δ ]. Kr fugsi k gg dlh igrl dri fugsi impuls, ki dp mrpk hug.4 rsu di s. F.4.4. Pmlik [ u ] F δ x dx πδ Pmlik suu fugsi f dlh mggi dg. Jik ki mmlikk suu fugsi, mk uru kdi dlm fugsi yg ru rlw dg uru kdi pd fugsi smul. rsfrmsi Furir dri fugsi yg dilikk sm dg klik dri rsfrmsi Furir fugsi smul. Scr frml hl ii dp diulisk sgi [ f ] F mk F[ f ] F JikF.5 Muru.6 Sudry Sudirhm, Alisis Rgki Lisrik
F [ f ] F f [ f ] F[ f τ ] d ; f τ f τ Mislk τ τ τ dτ dτ F Sif pmlik ii dp ki mfk uuk mcri rsfrmsi Furir dri fugsi sigum d fugsi kspsil du sisi. CO OH-.4: Crilh rsfrmsi Furir dri fugsi sigum d kspsil du sisi riku ii. v u v α α u u kspsil du sisi : sigum : sg u α α u α u Pylsi : Ch.3. mmrik F [ u ] πδ mk F [ sg ] F[ u u ] α F u mk Ch.. mmrik [ ] α α [ ] [ ] α α F F u u α α α.4.5. Kmp y d Imir dri F α Pd umumy rsfrmsi Furir dri f, F, rup fugsi kmplks yg dp ki ulisk sgi
F f d A B F f cs d θ f si d dg A f cs d ; B f si d.6 B F A B ; θ.7 A Jik f fugsi y, mk dri.6 d.7 dp ki simpulk hw. Kmp riil dri F mrupk fugsi gp, kr A A.. Kmp imir F mrupk fugsi gil, kr B B. 3. F mrupk fugsi gp, kr F F. 4. Sudu fs θ mrupk fugsi gil, kr θ θ. 5. Ksimpul d mgkik : klik F dlh kug-y, F A B F *. 6. Ksimpul 5 mgkik : F F F F * F. 7. Jik f fugsi gp, mk B, yg rri F riil. 8. Jik f fugsi gil, mk A, yg rri F imir..4.6. Ksimris Sif ii diyk scr umum sgi riku. Jik [ f ] mk F[ F ] π f F F.8 Sif ii dp diuruk dri frmulsi rsfrmsi lik. Sudry Sudirhm, Alisis Rgki Lisrik
π f Jik F d diprukrk d π f.4.7. Prgsr Wku Sif ii diyk sgi riku. Jik F mk : π f F d [ f ] F mk F[ f ] F d F.9 Sif ii mudh diuruk dri dfiisiy..4.8. Prgsr Frkusi Sif ii diyk sgi riku. [ ] β F f mk F [ F β ] f Jik F.3 Sif ii ug mudh diuruk dri dfiisiy..4.9. Pskl Sif ii diyk sgi riku. JikF [ f ] F mk F[ f ] F.3.5. Rigks l-. riku ii mmu psg rsfrmsi Furir sdgk sif-sif rsfrmsi Furir rmu dlm l-.. 3
l.. Psg rsfrmsi Furir. Siyl f F Impuls δ Siyl srh ks π δ Fugsi k gg u πδ Sigum sg Expsil kusl α u α Ekspsil du sisi α Ekspsil kmplks α α β π δ β Ksius csβ π [ δ β δ β ] Sius siβ π[ δ β δ β ] l.. Sif-sif rsfrmsi Furir. Sif Kws Wku Kws Frkusi Siyl f F Kliir A f B f AF BF Difrsisi Igrsi df F d F f x dx π F δ Klik f F Simri F π f Prgsr wku f F Prgsr frkusi β f F β Pskl f F 4 Sudry Sudirhm, Alisis Rgki Lisrik
Sl-Sl Dr Furir Buk Sius-Csius.. uk dr Furir dri glmg sgiig riku ii. v ms 5V. 5V v ms V. c. d. v v v ms ms ms 5V 5V V. 5V. Siklus prm dri dr puls diyk sgi v u u u u 3 Gmrk siklus prm rsu d crilh kfisi Furiry sr gmrk spkrum mpliud d sudu fsy. 5
3. Suu glmg kmpsi diuk dg mumlhk gg srh V dg glmg prsgi yg mpliud puck k puck-y V. Crilh dr Furiry d gmrk spkrum mpliudy. Dr Furir Buk Ekspsil. 4. Crilh kfisi kmplks dr Furir uk glmg riku.. 5V v v ms ms 5V V. v V ms ms c. 5V v 5V d. v ms ms V. 5V 6 Sudry Sudirhm, Alisis Rgki Lisrik
rsfrmsi Furir 5. Crilh rsfrmsi Furir dri uk-uk glmg riku: A. v [ u u ];. π v Acs u u 4 4 A c. π v cs u u d. v u ;. v sg 6u f. v [ u sg ] δ g. v u u 6. uk rsfrmsi lik dri fugsi-fugsi riku: π α. F ; α πa β. F [ u β u β ] c. F 5 ; d. F 5. F 5 ; f. F 5 7
8 Sudry Sudirhm, Alisis Rgki Lisrik g. 5 5 5 F ; h. 5 5 5 F i. 5 5 5 F ;. 5 5 δ F k. πδ 4 F ; l. πδ 4 4 F m. 4 4 πδ F ;. πδ 4 F. 4 4 4 πδ πδ πδ F
BAB Alisis Rgki Mgguk rsfrmsi Furir Dg pmhs lisis rgki dg mgguk rsfrmsi Furir, ki k mmpu mlkuk lisis rgki mgguk rsfrmsi Furir. mmpu mcri ggp frkusi... rsfrmsi Furir d Hukum Rgki Kliir dri rsfrmsi Furir mmi rlkuy rlsi hukum Kirchhff di kws frkusi. Rlsi HK misly, ik dirsfrmsik k lgsug mmrik huug di kws frkusi yg sm uky dg rlsiy di kws wku. Mislk rlsi HK ik dirsfrmsik : v v : V V v 3 3 V 3 Hl iipu rlku uuk KCL. Dg dmiki mk rsfrmsi Furir dri suu siyl k mguh pry siyl di kws wku mdi spkrum siyl di kws frkusi p mguh uk rlsi hukum Kirchhff, yg mrupk slh su prsyr rgki yg hrus dipuhi dlm lisis rgki lisrik. Prsyr rgki yg li dlh prsyr lm, yg dp ki prlh mllui rsfrmsi huug gg-rus krkrisik i-v lm. Dg mmfk sif difrsisi dri rsfrmsi Furir, ki k mmprlh rlsi di kws frkusi uuk rsisr, idukr, d kpsir sgi riku. Rsisr Idukr Kpsir : V : : V I R L C RI R LI L CV C Rlsi dis mirip dg rlsi hukum Ohm. Dri rlsi di s ki dpk impdsi lm, yiu prdig r gg d rus di kws frkusi 9
Z R R ; Z L L ; ZC. C Buk-uk. lh ki kl sgi impdsi rus lklik. Dri uri di s dp ki simpulk hw rsfrmsi Furir suu siyl k p mmrik rlsi hukum Kirchhff di kws frkusi d huug gg-rus lm mdi mirip dg rlsi hukum Ohm ik lm diyk dlm impdsiy. Dg dsr ii mk ki dp mlkuk rsfrmsi rgki, yiu myk lm-lm rgki dlm impdsiy d myk siyl dlm rsfrmsi Furiry. Pd rgki yg dirsfrmsik ii ki dp mrpk kidh-kidh rgki d md-md lisis rgki. ggp rgki di kws wku dp diprlh dg mlkuk rsfrmsi lik. Uri di s prll dg uri mgi rsfrmsi Lplc, kculi su hl yiu hw ki idk myu-yu g kdisiwl. Hl ii dp difhmi kr s igrsi dlm mcri rsfrmsi Furir dlh dri smpi. Hl ii rd dg rsfrmsi Lplc yg s igrsiy dri k. Jdi lisis rgki dg mgguk rsfrmsi Furir mgiku srk sluruh kdi rmsuk kdi uuk <. Olh kr iu cr lisis dg rsfrmsi Furir idk dp diguk ik kdi pd < diyk dlm uk kdisi wl. Pd dsry rsfrmsi Furir dipliksik uuk siyl-siyl -kusl shigg md Furir mmrik ggp rgki yg rlku uuk smpi. CO OH-.: Pd rgki sri r rsisr R d kpsir C dirpk gg v. uk ggp rgki v C. Pylsi: Prsl rgki rd prm ii lh prh ki gi pd lisis rsi di kws wku mupu kws s mgguk rsfrmsi Lplc. Di sii ki k mgguk rsfrmsi Furir. v R C v C 3 Sudry Sudirhm, Alisis Rgki Lisrik
rsfrmsi Furir dri rgki ii dlh : gg msuk V, impdsi rsisr R rhuug sri dg impdsi kpsir. C Dg kidh pmgi gg ki dpk gg pd kpsir dlh V C ZC C RC V V V R Z R C RC C gg kpsir rgug dri V. Mislk gg msuk v rup siyl k gg dg mpliud. Dri l.. gg ii di kws frkusi dlh V πδ. Dg dmiki mk V C RC RC πδ RC πδ RC RC RC Fugsi impuls δ hy mmpuyi ili uuk, shigg pd umumy Fδ Fδ. Dg dmiki suku kdu πδ RC rus k prsm di s πδ. Suku prm RC dp diurik, d prsm mdi V C πδ RC Dg mgguk l.. ki dp mcri rsfrmsi lik v C sg RC RC [ ] u [ ] u Pmhm : Hsil yg ki prlh muukk kd rsi gg kpsir, sm dg hsil yg ki prlh dlm lisis rsi di kws wku di B-4 ch 4.5. Dlm mylsik prsl ii ki idk myiggug sm skli mgi kdisi wl pd kpsir kr rsfrmsi Furir lh mckup kd uuk <. V R C V C 3
CO OH-.: Bgimkh v C pd ch.. ik gg yg dirpk dlh v sg? Pylsi: Dri l.. ki prlh F [ sg ] mk V C d uriy dlh. Dg dmiki V C RC RC rsfrmsi liky mmrik RC Pmhm: v C sg RC u Prsl ii mlik siyl -kusl yg mmrluk pylsi dg rsfrmsi Furir. Suku prm dri v C mmrik ifrmsi g kd pd <, yiu hw gg kpsir rili kr suku kdu rili l uuk <. Uuk >, v C rili RC u yg mrupk gg rsi yg ili khiry dlh. Di sii rlih ls hw lisis dg mgguk rsfrmsi Furir mmrik ggp rgki yg mckup sluruh srh rgki muli dri smpi. Gmr v C dlh spri di wh ii. v C -4-4 sg - - sg RC u RC u 3 Sudry Sudirhm, Alisis Rgki Lisrik
.. Kvlusi d Fugsi Alih Jik h dlh ggp rgki rhdp siyl impuls d x dlh siyl msuk, mk siyl klur y dp diprlh mllui igrl kvlusi yiu y h τ x τ dτ. Dlm igrl kvlusi ii s igrsi dlh τ smpi τ kr dlm puru frmulsi ii h d x mrupk uk glmg kusl. Jik s igrsi rsu diprlr muli dri τ smpi τ,. mdi h τ x τ dτ.3 τ y Prsm.3 ii mrupk uk umum dri igrl kvlusi yg rlku uuk uk glmg kusl mupu -kusl. rsfrmsi Furir uuk kdu rus.3 dlh F Y F [ y ] τ τ h τ x τ dτ h τ x τ dτ Prukr uru igrsi pd.4 mmrik d.4 Y τ τ h τ h τ x τ x τ ddτ ddτ.5 Mgig sif prgsr wku pd rsfrmsi Furir, mk.5 dp diulis Y τ τ h τ h τ τ τ X dτ dτ X H X.6 33
Prsm.6 muukk huug r rsfrmsi Furir siyl klur d msuk. Huug ii mirip uky dg prsm yg mmrik huug msuk-klur mllui fugsi lih s di kws s yiu Ys s Xs. Olh kr iu H disu fugsi lih uk Furir. CO OH-.3: ggp impuls suu sism dlh α α h. Jik sism ii diri msuk siyl sigum, sg, uklh ggp rsiy. Pylsi: Dg l.. didpk H uuk sism ii α α α α H F α Siyl msuk, muru l.. dlh Siyl klur dlh X F α Y H X α yg dp diurik mdi k k k 3 Y α Y α Y [ sg ] k k k3 Y α α α α α α α α α α α α α α α α α α α α αα α α αα 34 Sudry Sudirhm, Alisis Rgki Lisrik
Jdi Y α α shigg α α y sg u u α α [ ] u [ ] u ] Gmr dri hsil yg ki prlh dlh spri di wh ii. CO OH-.4: uk ggp frkusi dri sism pd ch-.3. Pylsi : Fugsi lih sism rsu dlh -4 4 [ α ] u y - α H. α Kurv H ki gmrk dg sgi sis d hsily dlh spri gmr di wh ii. H [ α ] u - - 35
Pd, yiu frkusi siyl srh, H rili sdgk uuk iggi H muu l. Sism ii kr spri lwpss filr. Frkusi cuff rdi ik H H α α c c α α.644α.3. Ergi Siyl Ergi l yg diw lh suu uk glmg siyl didfiisik sgi W l p d dg p dlh dy yg dirik lh siyl kpd suu. v Jik rup rsisr mk p i R ; d ik R y dlh rsisr Ω mk WΩ f d.7 dg f rup rus upu gg Prsm.7 diguk sgi dfiisi uuk myk rgi yg diw lh suu uk glmg siyl. Dg k li, rgi yg dirik lh suu glmg siyl pd rsisr Ω mdi pry kdug rgi glmg rsu. rm Prsvl myk hw rgi l yg diw lh suu uk glmg dp dihiug ik di kws wku mupu kws frkusi. Pry ii diulisk sgi W Ω f d π d F.8 Kr F mrupk fugsi gp, mk.8 dp diulisk π W Ω F d.9 36 Sudry Sudirhm, Alisis Rgki Lisrik
Jdi di kws wku rgi glmg dlh igrl uuk sluruh wku dri kudr uk glmg, d di kws frkusi rgiy dlh π kli igrsi uuk sluruh frkusi dri kudr sry ili mulk rsfrmsi Furir dri siyl. Puru rm ii dimuli dri.7. W dd π Ω f d f F Igrsi yg rd di dlm d kurug dlh igrsi rhdp d uk rhdp. Olh kr iu f dp dimsukk k dlm igrsi rsu mdi W d π d Ω f F Dg mmprukrk uru igrsi, k diprlh W Ω π π π F f F dd f F F d π F dd d rm Prsvl mgggp hw igrsi pd prsm.8 upu.9 dlh kvrg, mmpuyi ili rhigg. Siyl yg rsif dmiki disu siyl rgi; sgi ch: siyl kusl kspsil, kspsil du sisi, puls prsgi, sius rdm. Jdi idk smu siyl mrupk siyl rgi. Ch siyl yg mmpuyi rsfrmsi Furir pi uk siyl rgi dlh siyl impuls, siyl k gg, sigum, d sius p hi. Hl ii uk rri hw siyl ii, k gg d siyl sius misly, idk dp diguk uuk mylurk rgi hk pylur rgi k rlgsug smpi k higg; usru kr iu i idk disu siyl rgi mlik disu siyl dy. 37
CO OH-.5: Hiuglh rgi yg diw lh glmg v u V Pylsi: [ ] Ki dp mghiug di kws wku WΩ [ ] d [ ] Uuk mghiug di kws frkusi, ki cri lih dulu V. W Ω 6 π d π π π π Pmhm: Kdu cr prhiug mmrik hsil yg sm. Fugsi F muukk krp rgi dlm spkrum siyl. Prsm.4 dlh rgi l yg dikdug lh sluruh spkrum siyl. Jik s igrsi dlh d mk ki mmprlh prsm J W F d. π yg muukk rgi yg dikdug lh glmg dlm slg frkusi d. Jik huug r siyl klur d msuk suu pmrss siyl dlh Y H X mk rgi siyl klur dlh W Ω H X d. π Dg huug-huug yg ki prlh ii, ki dp mghiug rgi siyl lgsug mgguk rsfrmsi Furiry p hrus mghui uk glmg siyly. J d 38 Sudry Sudirhm, Alisis Rgki Lisrik
CO OH-.6: uk lr pi yg diprluk gr 9% dri l rgi glmg xpsil v [ ] u V dp diprlh. Pylsi: Buk glmg [ ] u v V Ergi l : W Ω 6 π d π π J π Mislk lr pi yg diprluk uuk mmprlh 9% rgi dlh β, mk β β W9% 6 π d π β π Jdi 9 β β π.9 π β 63 rds 39
Sl-Sl. Sklr S pd rgki riku lh rd di psisi muli. Pd i dipidhk kpsisi d p pd psisi smpi. Jik v V, v V, uk v i, V i, V, v. S µf v v v i kω. Sklr S pd rgki riku lh rd di psisi muli. Pd i dipidhk kpsisi d p pd psisi smpi. uk v i, V i, V, v, ik v V, v 5 V. S v v v i kω µf 3. Sklr S pd rgki riku lh rd di psisi muli. Pd i dipidhk kpsisi d p pd psisi smpi. uk v i, V i, V, v, ik v V, v V. S v v v i H,5 kω 4. Sklr S pd rgki riku lh rd di psisi muli. Pd i dipidhk kpsisi d p pd psisi smpi. uk v i, V i, V, v, ik v V, v V. v v v 4 Sudry Sudirhm, Alisis Rgki Lisrik
v S v v i,5 kω H v 5. Sklr S pd rgki riku lh rd di psisi muli. Pd i dipidhk kpsisi d p pd psisi smpi. uk v i, V i, V, v, ik v V, v V. S v v v i H Ω 6. Pd suh rgki sri L H, C µf, d R kω, dirpk gg v s sg V. uk gg pd rsisr. 7. ggp impuls suh rgki liir dlh h sg. Jik gg msuk dlh v s δ u V, uk gg klury. 8. uk ggp frkusi rgki yg mmpuyi ggp impuls h δ u. 9. uk gg klur rgki sl 8, ik diri msuk v s sg.. Jik gg msuk pd rgki riku dlh v cs V, uk gg klur v. µf kω kω v v v 4
. Ulgi sl uuk siyl yg rsfrmsiy V 4. uk gi yg diw lh siyl v 5 u V. uk pul rp prs rgi yg dikdug dlm slg frkusi rds. 3. Pd rgki filr RC riku ii, gg msuk dlh 5 v u V. v kω µf kω v uk rgi l msuk, prss rgi siyl klur v rhdp rgi siyl msuk, prss rgi siyl klur dlm slg pssd-y. 4. Pd rgki riku ii, gg msuk dlh 5 v u V. µf kω kω v uk rgi l msuk, prss rgi siyl klur v rhdp rgi siyl msuk, prss rgi siyl klur dlm slg pssd-y. v 4 Sudry Sudirhm, Alisis Rgki Lisrik
Dfr Pusk. Sudry Sudirhm, Alisis Rgki Lisrik, Pri IB, ISBN 979-999-54-3.. Sudry Sudirhm, Pgmg Md Ui Oupu Uuk Prhiug Susu Ergi Pd Pyulg gg Mgh, Mgrf, 5, limid pulici. 3. Sudry Sudirhm, Pgr Rgki Lisrik, C Kulih El, Pri IB, 7. 4. Sudry Sudirhm, Alisis Hrmis Dlm Prmslh Kulis Dy, C Kulih El 64, 8. 5. P. C. S, Pwr Elcrics McGrw-Hill, 3rd Rpri, 99, ISBN -7-45899-. 6. Rlph J. Smih & Richrd C. Drf : Circuis, Dvics d Sysms ; Jh Wily & S Ic, 5 h d, 99. 7. Dvid E. Jhs, Jhy R. Jhs, Jh L. Hilur : Elcric Circui Alysis ; Pric-Hll Ic, d d, 99. 8. Vic Dl r : Elcric Pwr Sysms, Pric-Hll Iril, Ic., 99. 9. Rld E. hms, Alr J. Rs : h Alysis Ad Dsig f Liir Circuis,. Pric-Hll Ic, 994.. Dugls K Lidr : Irduci Sigls d Sysms, McGrw-Hill, 999. 43
Dfr si v u v : gg sgi fugsi wku. V : gg dg ili ru, gg srh. V rr : gg, ili r-r. V rms : gg, ili fkif. V mks : gg, ili mksimum, ili puck. V : fsr gg dlm lisis di kws fsr. V : ili mulk fsr gg. Vs : gg fugsi s dlm lisis di kws s. i u i : rus sgi fugsi wku. I : rus dg ili ru, rus srh. I rr : rus, ili r-r. I rms : rus, ili fkif. I mks : rus, ili mksimum, ili puck. I : fsr rus dlm lisis di kws fsr. I : ili mulk fsr rus. Is : rus fugsi s dlm lisis di kws s. p u p : dy sgi fugsi wku. p rr : dy, ili r-r. S : dy kmplks. S : dy kmplks, ili mulk. P : dy y. Q : dy rkif. q u q : mu, fugsi wku. w : rgi. R : rsisr; rsissi. L : idukr; iduksi. C : kpsir; kpsisi. Z : impdsi. Y : dmisi. V s : fugsi lih gg. I s : fugsi lih rus. Y s : dmisi lih. Z s : impdsi lih. µ : gi gg. β : gi rus. r : rsissi lih, rsrsisc. g : kduksi; kduksi lih, rscducc. 44 Sudry Sudirhm, Alisis Rgki Lisrik