Question

Determine the complex transfer function T(s) = V/V; for the circuit shown below. Specify it as a function of the complex frequency, s, and the symbols for the resistors and capacitor. On the attached graph, plot the magnitude of the complex transfer function T(jw) in decibels as a function of the frequency f of the source as f varies from 1 Hz to 1 MHz. Assume that the op amp is ideal. Use as the numerical values for the resistors and capacitors: R1 = 12 kN, R2 = 3 kN, R3 = 2 kN, R4 = 1 kN, R3 = 2 kN, R6 = 68 k12, and C = 1 nF. Compute pole and zero frequencies in Hertz and high and low frequency gains in decibels if applicable. R1 Vam + VO R2 R6 R5 WH R 4 C

Answer 1

Magnitude in dB = 20*log(magnitude)

Gwen crrautt under s domain is R1 MM uto v2 O R, By voltage drvision Rule RA NL AL R5 utes) = VEROR R4 sc Ritri = Vies) (36) 12K +35 utes)= Vics) 0 By nobl analysis of investing terminal 'CS) R3 vis) - Vols) Rs+ Roll (R4+'scj VTs) vis) - Vo(s) + Rot Ro('t R4SC) 1 + (R6+RAJSC Vis + 2K vis) - Vols) at + 68KC 1+ 1K (159) 1 + 69K (109 (VT) _ -9]{1+69(1793) 2x + 2(693x10^xcoms +686 +68X1oxicols vis + 24

vts)= Vis) - Vics) 5 >) V75) (VTs) -Vols)] [1769xő?s] 70k + 206x103s from ea + 5(2) [veco -15 Vol 9) 3 (1+69 vio?:) 5 (70 + 206 xőbs ) こわ Upcs)( 104206 yio's ] + 2 Věts) {1+69x1333] - 10 VOCs) [1 +69 xío?s] = Vycs) [ 70 +2 +206 xlo's + 138 xo’s ] = Vors) [16769o kids Vols) 72 +134906 Yeos 10 +690x1o3's Vlaso S+ 520.96 Voces Vels) 0.2 5+14.493 0.2 'S+ 520.96 TIS) = S+14.493 |

Put قال - ل 520.96 + juo T(60) 0.2 (14.493 +5w wt (520.96) 19.012 oir Vw²+(14.493² 2 at Trp) p2+ 89.949) f²+ (2-306² 6875-565 0.2 at f=143 (TIR)) 6.3176 - 154388 dB 655979 16.388dB 6974-565 at f= lotz ITCF) = 1.627 0.2 105-3176 * 4.23dB at f=100Ha 17(73) 0.259 -11.709 dB at f= 1kHz LTCP)] 0.2-0068 13.949 dB

at f= 10kHz (T(f)] = 0.2 - 13.979 dB at f= look (Tefl - 0-2 -13.979 dB at f = 1M HO ITCF7 - 0.2 = -13.979dB CdB) 216-388dB magnitude 4-2388 110709dB 13949dB 13.979dB TH3 lo7 100 Ik Tok OOK IM FCH3) S+ 520.96 TOS) 0.2 15+19.493 pole → S= -14.493 2 en 3) S = -52096 17.133 dB attro row freq garn = 16-1888dB (Ters) high frea garn Hep =- 13:9794dB

Please UPVOTE for my explanation. Thanks you.