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D: 0.BUN 7 8 4 B5 6 36 6....................................... 36 6.................................... 37 6.3................................... 38 6.3....................................... 38 6.4.......................................... 38 6.5..................................... 39 7 40 8 40 8. RCL.......................... 4 8............................ 4 8.3........................... 43 9 44 9. Op Amp................ 44 9. RC.................................... 47 9.3.......................... 48 9.4...................................... 49 9.5..................................... 50 9.6................................. 5 9.7................................... 5 9.8............................... 53 0 55 0...................................... 55 0. RC.............................. 56 0.3 ω s.............................. 57 0.4................................... 58

35

6 6. D.C..5V D.C. = Direct Current A.C. 00V 60Hz A.C. = Alternative Current V.5V 0 t V V 0 0 t 4. 0 60Hz 0 36

4 6. 43 V 0 ω t Vt= V 0 sin ω t (49) sin cos ω t ω t + π/ π/=90 ωt V V 0 43. t Vt 43 V y t θ = ω t (50) θ ω ω /s rad/s 37

6.3 fhz fhz Hz ωrad/s f f ω = π f (5) ωrad/s 6.3. Tsf f T = f = π ω (5) 6.4 sin θ θ 43 = f ω θ = ω t = π f t 38

6.5 3 49 V 0 V 0 V R P = V 0 /R V 0 V V 0 P = V 0 /R V e eff 00V e 00V eff V ( = V e 00V 00 = 4 V to 30V p p to 39

7 49 V 0 cos ωt iv 0 sin ωt V 0 cos ωt + iv 0 sin ωt Vt= V 0 cos ωt + iv 0 sin ωt i = e iθ = cos θ + i sin θ (53) Vt= V 0 e iωt (54) It= I 0 e iωt (55) V I 8 R V I 40

I = V R C L R Ż I = V Ż I V Ż Ż ż Ż ω f π ω f 8. RCL R Ż = R Ż f R R C Ż = iωc = i πfc Ż f Ż f L Ż = iωl = i πfl Ż Ż f f ω = f = 0 I = 0 I 4

8. ω RCL R Ż = R iy R x = Re i 0 ω Ż = C iωc = i ωc iy i ωc x = ωc e i π ω ω L Ż = iωl iy iωl x = ωle i π ω ω 4

8.3 R σ = R Ż Ẏ = Ż Ż = + inpeadance resistance reactance Ẏ = + admitance condactance susceptance L C 43

9 9. Op Amp v i v o v o = G v i (56) G = + R r (57) Op Amp G 0 G 0 R/r R r G = R r (58) 7 v i 3 + G 0 4 6 R r v o 44. G Gain = = = f = 0f c f c Op Amp G 0 44

0V E v i = E + v i V V 0 t 0 E t 45. C E 0V C R R 46. C R C R CR high pass filter f = 0 Hz f c f c f c = πrc (59) f c 3dB =.. 0.7 f = 0 45

DC GND AC DC AC GND 0V 0V 46

9. RC R C R /iωc ż = R + iwc = R i ωc R iy R θ x ż ωc R ż i/ωc ż ż ż = R + ω C e iθ (60) iy ωc R C x ω ż = R + e iθ (6) ω R C ( ) θ = tan ωrc ż z 0 R + (6) ω R C z 0 ω z 0 ω ω 0 z 0 θ 90 ωc ω z 0 R θ 0 R R R ω 47

9.3 44 r R ż ż ż ż 57 Ġ = + ż ż 58 ż ż (63) Ġ = ż ż (64) 3 + 7 v 3 + 7 i v i 6 6 G 0 v o G 0 v o 4 4 ż R ż C r 47. 48. 47 ż r C R 48 Ġ 64 ż = r i ωc ż = R Ġ = R r i ωc 6 r i ωc = r + ω r C e iθ tan θ = ωrc /e iθ = e iθ 48 ż (65) 48

Ġ = R e iθ tan θ = r ωrc + ω r C iθ Ġ Ġ0e Ġ 0 G 0 = R r + ω r C (66) ( ) θ = tan ωrc (67) G 0 Ġ θ tan θ 48 v i G 0 θ v i 9.4 G 0 θ G 0 θ 49

66 67 ω 9.5 ω ω s = ω r C (68) ω s 66 G 0 = R r + ωs (69) ω s 7 R/r 49 Bode Diagram 0.5 G 0 r/r 0. 0. 0 00 ω s 49. G 0 50

9.6 RC 0.5 G 0 0. 0. 0 00 ω s 50. ω s = G 0 = = 0.7 5

9.7 49 ω s = (70) ω s G 0 ω s G 0 = R/r ( ) G0 ω s =. ω s = f c ω c ω s = ω r C = (7) ω c = r C f c = π r C (7) 59 7 ω s = 66 ω = /r C G 0 = R r. =. 0.707 R r (73) 0.7 = 3 db db db A 0 log 0 AdB 0log 0 0.7= 3 5

r =kω 9.8 f = 0 Hz 00 0Hz r = k R = 00k G 0 = R r = 00 = 00 r C r C 7 f c = 0Hz, r = kω C = πf C R. =. 0.6 f C R = 0.6 0 0 3 =.6 0 5 F = 6 µf /π 0.595 π. =. 0.6 v i 3 + 7 G 0 4 6 v o R =00K C = 6 µf r =K E + v i v o = E + Ġ E =0Hz 00 5 v i C i =0.6µF r i =00kΩ 3 + 7 G 0 4 6 v o R =00kΩ 53 C = 6 µf v i

5. r i Op Amp v i 0 r i r i =00kΩ C i 0Hz C i 59 7 f c = 0Hz, r i = 00kΩ C i. =. = 0.6 f c r i 0.6 0 0 5 =.6 0 7 F = 0.6 µf 54

0 0. ż ż 5 a v i ż ż v o b a b ż v i ż v i ż v o ż v o a b 5. v i ż ż v o v o = Ġ v i (74) = ż ż + ż v i (75) v o v i Ġ = ż ż + ż (76) v i v o v o = Ġ v i Ġ 55

0. RC 53 RC R v i C v o 53. RC Ġ ż = R ż = iωc 76 ωcr θ Ġ = iωc R + = 0 x iωcr + iωc 54. ωcr + iy iωcr + = + ω C R e iθ θ = tan (ωcr) Ġ Ġ = + ω e iθ C R θ θ Ġ = + ω C R e iθ (77) θ = tan (ωcr) (78) Ġ Ġ G 0 77 Ġ G 0 e iθ (79) 56

G 0 θ + ω C R = tan (ωcr) (80) G 0 e iθ θ 0.3 ω s ω ω s ωcr 3 G 0 + ω s θ = tan (ω s ) ω s = ωcr (8) C R ω s G 0 θ ω s CR Ġ0 Ġ G 0 / θ ω s 0 G 0. =. 0.7 ω S 0 log 0 G 0 0 0.5 log 0 ω s 0 log 0 G 0 db 0 3 0 log 0 ω s θ 0 45 90 7. G 0 θ ω s 57

G 0 θ (Bode Diagram) 0 0 7 G 0 5 4 3 0 0 5 0 0 5 0 5 30 0 ω s θ 45 60 75 90 0 5 0 0 5 0 ω s 55. CR G 0 0.4 55 G 0 ω s = 0 0 = (8) ω s G 0 58

ω s 8 θ 45 CR C R ω c f c ω s = ωcr = ω c = CR f c = πcr (83) 33 ω s = 3 ω = /R C G 0 =. =. 0.707 0.7 3 db db A xdb= 0 log 0 A (84) 0.7 0log 0 0.7= 3dB A 0.00 0.0 0. 0 00 000 x db 60 40 0 0 0 40 60 A 0.5 0.7 x db 6 3 0 3 6 E XB= log 0 E B Bell db /0 xdb= 0 log 0 (85) 59

84 85 = E = A 0 log 0 E = 0 log 0 A C v i R v o 56. CR 6 db/oct 0 db/dec / /0 60

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