Question

For the circuit shown in Fig. 4.3, the op-amp is ideal and is operating in its linear region. (a) Determine the transfer function H (s) = Vo(s)/Vi(s). (b) Sketch and clearly label the Bode Magnitude-Phase plot of H(jo) (Your provided two graph papers. Use the first for the magnitude plot and the second for the phase plot). (c) What filter is represented by H(s)? Explain. 400 k 2 210 S2 50 nF 160 k92 내 mto 105 2 50 nF U + vo

Answer 1

Solution : For the circuit shown in figure above, finding the s domain transfer function of the circuit then substitute the s=jw to obtain the transfer function in frequency domain the varying the value of frequency and tabulating the data for magnitude and phase for different values of w then sketching the bode plot as shown below-

Solution: for the circuit Ry shown in of AM Here Ri= 1borr C2 Ra G= 500f R₂ = 400KR Rza a losr Ry =2102 vi 2 It -stage * stage 1 C2 SonF Transform the giren circuit into s-domain we get- RY R2 You ca nh + VO, 13) D Vols) Vils) - it stage 2 K --- and non- for stage 2 As current is zero on ideal op. Amp Using Vo,(s) – Vils) stage entering through investing inverting input terminals of NOWO, Ku At Node 'A' we get - = VA (3) su) Roo (+ sor) AS VA = Ug = ovat (lue to virtual ground of op. Amp) Cuev+) therefore 5 - VOSHE Rzx SC, 1 + SCR 1 R, +1 + I R 2 3 from eq Vits)

T Voors) Vits) SCR2 14 SGR, -SARR ero, [static] s(Retro) Sta) 0 Vors) Vils) s(R21R, 2 $+ 1 RICI) Verst dat * (vscz) Vo(s) I+I Voils) - 1152 for the stage 2 of op Amp count Using Kel At node 'c' we get Rz As Vels) = Vois) = ovout (alue to restual ground of op. Amp) Nowo, from eq" (3) Put Vels) we get > -Uots [ 56+ ☆ py VO, IS) = Ovout we R3 1+ Slq RY R3 Vols) Vo(s) -RUIR (1+SGRy) - Ral R3 Vois) = VO, 15) serv[st sehr]

00 Vo (3) Vols) Rg Ca 5 (st # Rinse) rikthin, tworld neroge Prorapes frontein HIS) Vors) Vitsi Vocs) Vols) Х Voils) Vi 13) 2 R₂ (2 Re RI ) X (st Rule) S+ atici) SG R2 (R4lR3) (+3C, RI) (1+5 C Ru) X SC R2 Ru RS Hes) 44 SCR4 + SCAT CC, R, RU) (SC, R2 Ry/R3) [s? (CICER, P4) +5 S (CR,+& R4) + 1] (SGRZRM) C1 C2 R, Ry $? + s (CRO + C2 Ru) + C1 C2R, Ry C1 C2 R, Ry 0 Hes) 1

s R2 1 + His) 2 RIR © si erant QRY . GRI Greg Ri Ry Now, fut the value of , Ago Ry, Go and ey in ega o 400XIOS 4.7619x105 A, Mg Ca 160x10) (105) XOOM") 1.1904x109 R, Ry Cola (Iboxiô x 210 x (50x109)?) 1 + + + 9.5363X104 Cq Ry 50X10 -9 GRI 160X703 Put the value of above parameter in ea (6) weget The Transfer of main His) > 4,7619x105 s [$+ (953cxxi's+(museexion] HIS) = stus (a) > 4.4619x10 Gw) (b) As sajoo Hejeros ( (11904X1t-w*) + 9-5363x1deju)]

A morgnitude of my | Hejw) 4.7619x10 w - (1.190uyot-w)'+(7.5363xso'm)? Magnitude inde a tejeo) bolo = 201090|tyvos. phase of Hijro) 9.5363 X 10" W (thon ( 1.19044107-co? = go-tant 9.536 3X104 w 1.1904mot-o? 10 the value varying a magnitude of 4-7 bixio - co and Tabularing the daten for and phase we get Alwal rondlec - lhej:)) = 0.04 V(1.1904x2 -12+(9.5363 xloº)? IndB) = |(tuji)lag = 2dogo (Heji)) Theja)do च de 5 -24.950 de

Af = 10 Mode/sec ! I mejios) hyn 614 X/06 = 0.390 J (1.19098/07-102) + (9-5363X105 )? - 7. 985 dB In dB => lujoslarg = 2019.oltujion) AT W = 10² radisocor 476196104 | Hejroy) Vch-rgovzro* -604) = 3:123 -109*+(9:6 368 x106)? Indoa - 9.893 dB | H1j02)) = 2010910|Che jio”)] 4rw5 ° Colec - HVì v°) = 4-16 Tổ 4.961 1-19048810 - 1979+(9-5363X17)" IndB Huwag = gulay. My may = 13-4148 1 | Hejro")) = *#614x709 Afw=10' rollsec = =4.972 V (1:1604x10* -100)*+(9:5363X10°)? Meno") las = 2010g. (Hejio')]) = 13.98 dB At w=10° roadsee on Theiros)) = hu#6198 16° JOH:1904 RT-5:00)*+(3-5 32X10)" Indo a = 3.448 Indo litres late = 2010g. Hijue) = 10.752 dB

At W = 106 had see in 0.444 | Myio) = 4.8819 xlo" |(1-1909874 -10)* + (9-5363X10%)? In de + Hygios ) ) on = 20 lagio I Hejross] ligos) Ion = .6.403 dB and som-. Phase Calculation in 9.5363x/6960 CH(jw) = 90-tao'( 1.19 041107 - W? ago 9-5363 X70Y tan 는 1907X107 -1 At W = 1radisec Zheji) ZHje) = 89.54 9.5363X105 Ar w=lo rad|se in Zrujo) = 90° tamil 1.1904 y/of - -102 ZHGjiO)= 85.4199 1-1904 X107 -104 At w=104 rodsec :v (Hejoy = goº - tom( 9.5363x16 Zhejvoj= 51.27° ATW = 10% radisec iv Zhejio%) = 96 - Tari'( 9.5363 x70 19oyx107 106 Lycje 10:7120 +

AT W=10"radisoc in 9.5363X108 Zhejions = 90 - Toni' por goexiot - (100) = 90 100 tan <mejor) = -5.24 9. 5363X700 8.809x107 Khupio") = 90°-tamil (9-536px10 AT wapo handiaAc in yol goyxlot - (100) go - 100 than I g. 5363 8109 9.988x109 :) -46.329 10 9.5363X10 amin Ar w=106 modlibce s krojek) = go-tart ( 1.190vxro - 002) to plainly 4-100] Amejioa) = -84.55 Taburering ta for Magnitude 9.5363X100 9.99470 and so on. data and phose 103 109 105 109 1 10 Wrondisec ) 10-752d0 -6.9030B. || HIJWldB -24.900B - 4.985.des 9-89348 13.4118 13-93dB CHijo) 89.549 25-44457-27° 10.12 -5.27 -46.32 -04:59 and so on.

Skerching the Bode plot 13.13 dB 13.400 10-752dB 9-09310 14T worlog 4-6-483 dB 0-7-98510 - 27.950B 10 10 103 104 106 to Cradlsee) loy scale Mavide (0) 89.54 q 85.41 kom) 51270 316.712 95.240 - 46.32 -4.5 to challsee) ly scare Phase peab

from the Bode Plut ( consider magnitude plot) We seen the giren circuit implementation behaves as tandpuf Now, in order to comment the nature of filter from Promates storicim chething the response of thes, ac ropatively or S=0 pleo HIS) dyrt 01981055 5+19.5369x1099s +(1-1904x604) хо Ans=o 9 Ro) Q= As sto lim Hes) = lim + 4-+61X0S x 0+0 +(1.1904 18167) 4.7481058 1 + (6.5369Xro) + 4+8805 +91X61011 -0 0 # H10) =0 and HIX) n This shows the nature of filter is Band paus lype": Answei