Question

Derive the transfer function, vo/vi(s), in terms of G1, G2, G3, G4, G5 where Gį = 1/Zį. Z2 N Via Z1 Z3 ο νο a. Derive the transfer function, vo/vi(s), if Z1 = R1, Z2 = R2,23 = R3 (i.e., resistors) and 24 = 1/sC1,25 = 1/sC2 (i.e., capacitors). b. Using Excel/Matlab/Python, etc., to draw the Bode plot of the magnitude using the following design values: R1=180k22, R2=180k12, R3=100522, C1=100nF, C2=25nF. c. What are the values of w, and Q?

Answer 1

V. (S) - la) Z1 = R Ez = R2 Zz = R3 Zu anter : -31H4BH AL zs = 15 By KCl at wag Yes 3, 2014 mart wat) vedy, vy(. 109 1509[**, *** - voch te test .. Volt- $) Volu) Z, ' +++ Zal = 249 22 23. - - -- - - . G₂ +G4 | = N; (5) G, + G₂ Vo(s) t G3 Vy (3) -- lij - -- P4 ксi au va, -- - 1,19 K c), vice - Vole. -- 23 25 E By due to virtual grounding, Vyle) = 0: (i) Youn A - ..or - V (8) Gz = Go Vo (3) or, (y) =- VOCs) - Gill Preting (ü) in equation lis - af v.Cu) (+ 6,4G,+ G4 )= G,V19) + G_ Voc) + Gratis

. on, Govice) - - am ( 14 62 493 +)]6.09 2, vich -- Las ( 65y + an] vecs Vicky Peter ( 914 6 4 63 + Gay] : Vols) 2, = R1 = 180k ini ; G = Too xius v Zz = R2 = 180k ; Gz = iso x163 v Zz = Rg = 100 kn ; G3 = 100x103 a 2x = 5, ; Gq = sa = louxio's 25 - 5ć, i G5 = scz 2 es xio's. vo(s) Vics) / 1807109 (25x109 s I 180 X 100 tis +100x100 X103 180 %10?> (180 xiusGoo xio) L" 180 1+ 4505 [6.11.410 5+ 105+ (100x109)57 1 + 450s (21114185 + 10*) 3 - 1 +64025410) * + (65x16 55 /(4.5x155). 22222.222 SP +211•1S+22222.222 Sa+ ofa 9.49957103 2 4.5x105 S 4.5X105

Command Window >> n=[-22222.222]; >> d=[1 211.1 22222.222]; >> g=tf(n,d) -2.222e04 3^2 + 211.1 3 + 2.222e04 Continuous-time transfer function. >> bode (g) Warning: MATLAB has disabled some advanced graphics rendering features by switching to software OpenGL. For more information, click here.

gure 1 LU Edit View Insert Tools Desktop Window Help Bode Diagram Magnitude (dB) -80 180 Phase (deg) 100 101 103 104 - 10² Frequency (rad/s)

(C) compairing the denominator with general and order characteristic equation, .82 + 250.s t W -0. i wo = 1222 22.222 radls = 149. OH raaks - Wo is natural frequency. and 290o = 2.11-1 ; q: camping ratio . +90 2114 = 0.70805 .:. Quality factor, Q = 25 = 2x0.76805 Y 2x 149.07) 2 * 2070 616. -- - -- ----