Question

RI + + v(t) C1 HE C2 volt)

with Creating a block diagram of this circuit,

Find the C(s)/R(s) with Block Diagram Reduction Method and Sginal Flow Diagram Method?

Answer 1

Sel The laplace dornain Circuit de the given Circuit R₂ MWL w t Viu) 1 25,00 as daw Vols) E - Applying RYL 1st loop ViW = R.I,L) + s (3,0 -1,0) Vils) = (2, + t hs) I, Cs) - 1 / 2 I 2 (s) Vils) - cis 120) = (2+)1,6) ILS) viu) (Ritus is (12, + + 3 2,6) وه (R, GS+1) Riasti - 0 Applying kul to and loop J2 (6) Dr & as [ I. ) - T, co 1 cas I LW) -o

) 1 1 ) ( + cis Cis ( 1 [ + ] (مدة (2+ Cis cs (: R₂ Cast + Gstas as las ردیا۔ 32 [B2, C5 +((i+G)] = GST() 1) C₂ s I, (S) R₂ Gas +(6+(₂)S from the Circuit Vols) و = (یاء زی CS 1, 2 3 The block- diagram ا using equation's can be represented CS أل (د) رد Rigst کل)+یع RGSTI

from the above we Cas find block diagram by reduction. tranfer tunction Step 1: Miner feed-back loop with as GL) = Raast+ (Cita) - Ho) - Ricist I Tu = Gis) 1 +64) Hu) as Reaast+(atas ور) 12269 + (4+G) (RESTI)

TI) = (5 (RIGS+1) (Rasti) [R.G 45+ (C,+G)] tas ais (R. C.St1) as (Ricist I) (2.49H1) (R6145 (+45) tas ة Step ² The three Cascade open loup tuctions care in :16) es frs (Rigs +1) (Ras + 1) [Reag5+ Citastas Vice) x (Rigs+1) You) vis) ais R, R₂ C2 Cast Ralatas Racest + (tl) stas (لاه cis Vis) RIR 6,2 (₂ 83 + [R.G+ (R1 + R2) Col5 + (6 +26)

b) from the block diagram can represent the Signal frow graph الا GS Rash(HG)S Ricisti & Vils). Ricisti By wing Maron's Gain formula from the can 1 tunction find the transfer Signal flow graph. above TCS) = { APK

Forward path gain P = CS (Rist) [P2 C, (2 87 (c + 5) Р. cs (Rast) (22 665+ (4+4)3] Individual loop gaine کت (R 4,5+1) [post+ (C+9)57] = 1-2 (246) [22465 & Clith)] (RIGS+1) [Reaks +(( + C2 )s) + (as. (P.C;8+1) [imgast + Catal] T(S) = į E Pelua ĥ Pai A=1 [ There is part of the graph not touching with no which in the toward patts

. 10) (R. Cyan) [R2 CA (Catals R, as+1) (Reaks + (6 + 6) tas (Resti) (Racias (citals TC) CS R, 2 G2 ₂5 + Rico (ata) 5 + REGGS +(6+G) stas CS TU) RIGGS + R, G+ (R+ (22) E, C) 5 citas tas + IT) 11 cis R Racin 23 +[Rc7 + (RAB) Ca] 5 +66 +26) The transfer functions obtained in both the Care is one.