2 SKEE/SKEU v R(t) - Figure Q.1(a) Evaluate the transfer function of the network as

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Wendy Hawkins
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1 SKEE/SKEU 073 PART A Q. ) A trfer futio i ued to deribe the reltiohi betwee the iut d outut igl of ytem. Figure Q.) how RC etwork ued to form filter futio. V it) R + v Rt) - C + v t) - Figure Q.) i) ii) Evlute the trfer futio of the etwork. 4 mrk) With the id of Bode digrm, determie the tye of filter give by d, well the utoff frequey if 4.7Ω d mrk) b) A egieer i required to deig Chebyhev filter to filter out the high frequey omoet of hum voie. Give mximum rile A mx, tobd frequey.844rd, bd frequey d / d tteutio tobd 0dB ; i) Clulte the umber of order filter for thi litio ii) Obti the ormlized trfer futio, H), of the filter. 4 mrk) 3 mrk)

2 3 SKEE/SKEU 073 iii) Derive the tul trfer futio, H), of the filter if the 8rd. / 3 mrk) iv) Obti the tul Chebyhev vlue of the iruit d lerly idite the vlue of eh omoet i the iruit if the reite t the lod i give 00Ω d 0rd. / 7 mrk)

3 4 SKEE/SKEU 073 PART B Q. ) For eh of the igl give, determie if the igl i ymmetrilly eve, odd or either. i) xt) = 5 o t..5 mrk) ii) zt) = i t 90 o ).5 mrk) b) Retgulr wve, ft) i Figure Q.b)i) i fed ito Lier Time Ivrit LTI) ytem how i Figure Q.b)ii). Figure Q.b)i) Figure Q.b)ii) i) ii) Determie the mthemtil exreio for gt). Illutrte gt) i time domi grhil rereettio. 4 mrk) mrk)

4 5 SKEE/SKEU 073 iii) Exre mthemtilly the outut igl, ht) d determie ll igl oertio ivolved i thi ytem. 5 mrk) ) Coider the two ub-ytem H d G defied i Figure Q.)i). Figure Q.)i) i) Uig ub-ytem H d G, exre mthemtilly the ytem outut y[] i Figure Q.)ii) i term of the iut x[]. mrk) Figure Q.)ii) ii) If the iut igl, determie the ytem outut y[] i Q.)i). 4 mrk) iii) Determie the lierity roerty of the ytem, y[] i Figure Q.)ii). Jutify your wer. 3 mrk)

5 6 SKEE/SKEU 073 Q.3 ) Figure Q.3) how eriodi igl of ft): Figure Q.3) i) By uig igl oertio, keth vt)=f-t). mrk) ii) Exre mthemtilly the omlex exoetil Fourier Serie for vt) u to the 5th hrmoi. 3 mrk) b) Figure Q.3b) how ytem with iut igl xt), yt) d the outut igl of zt). xt) yt) + + Figure Q.3b) zt) Sigl xt) d yt) re idetified : ; 400 i) ii) iii) Exre grhilly igl xt) d yt). Cotrut the omlex exoetil Fourier erie for zt). Illutrte grhilly double ided etrum for zt). 3 mrk) 3 mrk)

6 7 SKEE/SKEU 073 ) Figure Q.3) how iruit with voltge oure vt). 3 mrk) Figure Q.3) The igl vt) i give : i) ii) v 0 Exre the Trigoometri-oie form Fourier Serie of vt) for u to the eod hrmoi. 4 mrk) Cotrut the Trigoometri-oie form Fourier Serie for the urret it) for u to the eod hrmoi. iii) Clulte the verge ower for it). 5 mrk) mrk)

7 8 SKEE/SKEU 073 Q.4 ) Fourier erie d Fourier trform re the tool ued i the re of igl lyi d igl roeig. Differetite the two tool briefly. mrk) b) By lyig the roertie of Fourier Trform, determie the fourier trform of the followig igl; i) mrk) ii) mrk) ) Figure Q4)i) below how Trmitter-Reeiver Lier Time Ivrit LTI) Sytem hvig iut igl xt). The Fourier Trform of xt), i give i Figure Q4)ii). gt) i idel Low P Filter with ut-off frequey of ω= 000 rd/ d gi =. bt) i the outut igl from the Trmitter Sytem tht i the reeived by the Reeiver Sytem. ht) i idel High P Filter with ut-off frequey of ω= 000 rd/ d gi =. Trmitter Reeiver xt) t) bt) dt) gt) ht) yt) t) = o000t) t) = o000t) Figure Q4)i)

8 9 SKEE/SKEU 073 Xω) 4-80 Figure Q4)ii) 80 ω i) Illutrte grhilly etrum of Aω), Bω), Dω) d Yω). Y ew ω) 8 mrk) Figure Q4)iii) ω ii) Deig ew Reeiver Sytem i order to get ew outut igl yewt) with etrum Y ew ω) how i Figure Q4)iii). To hieve thi, determie the ew mthemtil exreio of igl t) d illutrte grhilly the ew etrum of H ew ω). Your wer mut lo how the ew etrum of D ew ω). 5 mrk)

9 0 SKEE/SKEU 073 Q.5 ) The Lle Trform w foud to be very ueful i the re of eletril d eletroi egieerig. Diu the mi dvtge d litio of the Lle Trform. 3 mrk) b) A Lier Time Ivrit LTI) ytem i how i Figure Q5). The iut igl for the ytem i give o0, d the imule reoe of the ytem i 0. o0 LTI Sytem 0 Figure Q5) i) Determie the Lle Trform of d. 3 mrk) ii) Exre the outut i term of it Lle Trform Y), d the by uig ivere Lle Trform, olve for. 5 mrk) iii) If the outut i delyed by 3 eod to yield ew igl,, determie the Lle trform for. mrk)

10 SKEE/SKEU 073 Ω Ω Ω Figure Q5b) ) Bed o the iruit i Figure Q5b) with vt) i equl to 6 ut) ; i) Produe the iruit i Figure Q5b) i -domi for t 0 d lbel the iruit ordigly. 4 mrk) ii) Exre the urret it) t t 0 i the iruit with the umtio tht the vlue of the iitil urret i0 ) = A. 8 mrk)

11 SKEE/SKEU 073 LAMPIRAN APPENDIX) F: Alog Filter Deig CHEBYSHEV mx 0log 0log log 0 A A, 0 0 mx A oh oh mx A oh oh 0... ) ) K T K H, ) ; 0 ) ; mx eve ge odd gjil K A BUTTERWORTH j H ),... ) ) B H j H 0 0log ) 0log 0log, 0log 0 0, 0 0, log 0 0 log 0 0

12 3 SKEE/SKEU 073 tu Jdul F.: Pegir frekuei udut jlur heti terorml,. Clultio of ormlized tobd gle frequey) Jei ei Tye of filter) Pei lulu redh, LPF Low P Filter) Pei lulu tiggi, HPF High P Filter) Frekuei udut jlur heti terorml, Normlized tobd gle frequey) Pei lulu jlur, BPF tuor) Bd P Filter) Pei jlur heti, BSF Bd Sto Filter) tuor), ilih yg lebih keil hooe mller vlue), ilih yg lebih keil hooe mller vlue)

13 4 SKEE/SKEU 073 Jdul F.4: Pekli ei Chebyhev utuk A mx 0.5,, d 3 db. Coeffiiet of Chebyhev filter for A mx 0.5,, d 3 db) db rile db rile db rile db rile

14 5 SKEE/SKEU 073 Jdul F.5: Trformi frekuei ei Frequey Trformtio of filter) Jei ei Trformi Tye of filter) Trformtio) Pei lulu redh, LPF Low P Filter),, bgi Butterwort h ) Pei lulu tiggi, HPF,, bgi Butterwort h ) High P Filter) Pei lulu jlur, BPF Bd P Filter) Pei jlur heti, BSF Bd Sto Filter) Jdul F.6): Pekli-ekli Poliomil Butterworth B ) = Coeffiiet of Butterworth Polyomil) / Jdul F.6b): Poliomil Butterworth dlm betuk emfktor Butterworth Butterworth Polyomil i Ftorized Form) B ) ) + + ) ) ) ) ) ) ) ) 7 + ) ) ) ) ) ) ) ) 9 + ) ) + + ) ) ) ) ) ) ) )

Chapter #3 EEE Subsea Control and Communication Systems

Chapter #3 EEE Subsea Control and Communication Systems EEE 87 Chter #3 EEE 87 Sube Cotrol d Commuictio Sytem Cloed loo ytem Stedy tte error PID cotrol Other cotroller Chter 3 /3 EEE 87 Itroductio The geerl form for CL ytem: C R ', where ' c ' H or Oe Loo (OL)