UC (Dr. Hny Hmmd) 9/9/6 ecture # ignl flw grph: Defitin. Rule f Reductin. Mn Rule. ignl-flw grph repreenttin f : ltge urce. ive gle-prt device. ignl Flw rph A ignl-flw grph i grphicl men f prtryg the reltinhip mng the vrile f et f ler lgeric equtin. Origlly trduced y.j. Mn. Cnider ler netwrk tht h N put nd utput prt. Which i decried y et f ler lgeric equtin. N i j ij I j i,,, N Thi y tht the effect i t the i th prt i um f g time cue t it N prt. i repreent the dependent vrile (effect), nd I j re the dependent vrile (cue). Nde r junctin pt f the ignl-flw grph repreent thee vrile. COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 ignl Flw rph Brnche ij Nde r Junctin t Cefficient r g f rnch the cnnect the i th dependent nde with the j th dependent nde. ignl Flw rph A ignl-flw grph cn e ued nly when the ytem i ler. A et f lgeric equtin mut e the frm f effect functin f cue efre it ignl-flw grph cn e drwn. A nde i ued t repreent ech vrile. Nrmlly, thee re rrnged frm left t right, fllwg i uccein f put (cue) nd utput (effect) f the netwrk. Nde re cnnected tgether y rnche with n rrw directed twrd the dependent nde. ignl trvel lng the rnche nly the directin f the rrw. ignl I k trvelg lng rnch tht cnnect nde i nd I k i multiplied y the rnch g ik. The dependent nde (effect) i i equl t the um f the rnch g time the crrepndg dependent nde (cue). COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 Exmple Output f ytem i cued y tw put nd repreented y the equtin. Cue Fd it ignl-flw grph. lutin Exmple Effect Output f ytem i cued y tw put nd repreented y the equtin. Fd it ignl-flw grph. lutin rnch nde Cue Exmple The put-utput chrcteritic f tw-prt netwrk re given y the et f ler lgeric equtin. Fd it ignl-flw grph. lutin COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 Ccde cnnectin f tw prt netwrk A A A A B B B B A B A A B B A A A A A B B B B B Exmple The fllwg et f ler lgeric equtin repreent the pututput reltin f multiprt netwrk. Fd the crrepndg ignlflw grph. R R 7Y Y Y Y lutin R R COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 Exmple R 7Y R 7 R Y Exmple Y R R 7 Y COMM (9) ecture # 5
UC (Dr. Hny Hmmd) 9/9/6 Exmple Y Y R R 7 Y Y Defitin (Input nd Output nde) Input R Input R 7 Y Cnvertg ny nde t n utput nde y ddg unity g rnch. Input Nde: Nde with nly utgg rnche. Output Nde: Nde with nly cmg rnche. COMM (9) ecture # 6
UC (Dr. Hny Hmmd) 9/9/6 Defitin (Input nd Output nde) Cnvertg ny nde t n put nde y rerrngg the equtin R R R R 7 Y Defitin (th) A cntuu uccein f rnche trvered the me directin i clled the pth. It i knwn frwrd pth if it trt t n put nde nd end t n utput nde withut hittg nde mre thn nce. The prduct f rnch g lng pth i defed the pth g. th g etween nd R R th th /(+) R 7 Y COMM (9) ecture # 7
UC (Dr. Hny Hmmd) 9/9/6 Defitin (p) A lp i pth tht rigte nd end t the me nde withut encunterg ther nde mre thn nce lng it trvere. When rnch rigte nd termte t the me nde, it i clled elf-lp. The pth g f lp i defed the lp g. elf p R R 7 Y p -/(+) p Rule f Reductin (Rule ) When there i nly ne cmg nd ne utgg rnch t nde (i.e. tw rnche re cnnected erie), it cn e replced y direct rnch with rnch g equl t the prduct f the tw. 5 R COMM (9) ecture # 8
UC (Dr. Hny Hmmd) 9/9/6 Rule f Reductin (Rule ) Tw r mre prllel pth cnnectg tw nde cn e merged t gle pth with g i equl t the um f the rigl pth g. 5 5 Rule f Reductin (Rule ) A elf lp f g t nde cn e elimted y multiplyg it put rnche y /(-). rf COMM (9) ecture # 9
UC (Dr. Hny Hmmd) 9/9/6 Rule f Reductin (Rule ) A nde tht h ne utput nd tw r mre put rnche cn e plit uch wy tht ech nde h jut ne put nd ne utput rnch. C C C C C C C 5 C 5 C C Rule f Reductin (Rule 5) Thi i imilr t rule. A nde tht h ne put nd tw r mre utput rnche cn e plit uch wy tht ech nde h jut ne put nd ne utput rnch. C C C C C 5 C C 5 C C C COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 Mn Rule Rti T f the effect (utput) t tht f the cue (put) cn e fund ug Mn rule fllw: T k k k Where, i i the g f the i th frwrd pth () () () () () () () () () Mn Rule tnd fr the um f ll firt-rder lp g. tnd fr the um f ll ecnd-rder lp g. Dente the um f the firt-rder lp g tht d nt tuch pth ny nde. Dente the um f the ecnd-rder lp g tht d nt tuch pth ny nde. Dente the um f the firt-rder lp g tht d nt tuch pth ny nde. ecnd-rder lp g i the prduct f tw firt-rder lp tht d nt tuch t ny pt. Third-rder lp g i the prduct f three firt-rder lp tht d nt tuch t ny pt. COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 COMM (9) ecture # Mn Rule = (um f ll different lp g) + (um f prduct f ll pir f lp g, fr nn-tuchg lp) (um f prduct f ll triple f lp g, fr nn-tuchg lp) + k = k th pth frm put t utput. k = The quntity, ut with ll lp tuchg the k th pth, k, remved. T k k k Exmple 7 A ignl-flw grph f tw-prt netwrk i given Figure Ug Mn rule, fd it trnfer functin Y/R. lutin 6 6 5 5 R Y 6 R Y
UC (Dr. Hny Hmmd) 9/9/6 COMM (9) ecture # ignl-flw grph repreenttin f vltge urce I - E I I E I E lected cident E E E E E ignl-flw grph repreenttin f vltge urce I - E Input Output
UC (Dr. Hny Hmmd) 9/9/6 ignl-flw grph repreenttin f pive gleprt device I I I I - Exmple 8 Impednce termte prt f tw-prt netwrk hwn Figure. Drw the ignl flw grph nd determe the lectin cefficient t it put prt ug Mn rule lutin Tw-prt netwrk d Tw-prt Netwrk COMM (9) ecture #
UC (Dr. Hny Hmmd) 9/9/6 Exmple 8 (nther pile lutin) Rule Rule 5 Rule Exmple 8 (nther pile lutin) Rule Rule COMM (9) ecture # 5
UC (Dr. Hny Hmmd) 9/9/6 Exmple 9 A vltge urce i cnnected t the put prt f tw-prt netwrk nd the ld impednce termt it utput, hwn. Drw it ignlflw grph nd fd the utput lectin cefficient ut. lutin urce Tw-prt netwrk d Tw-prt Netwrk ut ut ut ut ut Exmple The ignl-flw grph hwn repreent vltge urce tht i termted y pive ld. Anlyze the pwer trnfer chrcteritic f thi circuit nd etlih the cnditin fr mximum pwer trnfer. lutin Output pwer f the urce wer lected ck t the urce wer delivered y the urce d wer cident n the ld wer lected frm the ld wer red y the ld d?? COMM (9) ecture # 6
UC (Dr. Hny Hmmd) 9/9/6 COMM (9) ecture # 7 Exmple d d T mximize we huld mimize the dmtr ) )( ( j j T mimize the dmtr the prduct mut e pitive nd pure rel * * *