Chapter 3: Frequency Response of AC Circuit

1. Chapter 3: Frequency Response of AC Circuit EKT 119ELECTRIC CIRCUIT II

2. TRANSFER FUNCTION(TF) • Frequency response can be obtained by using transfer function.

3. DEFINITION: Transfer function, H() is a ratio between output and input.

4. TRANSFER FUNCTION Output signal Input signal

5. 4 condition of TF: Because there is no unit, they are called GAIN

6. KUTUB DAN SIFAR (POLES AND ZEROS) • Transfer function is written in fraction • The numerator and denominator can be existed as a polynomial

7. The roots of numerator also known as ZEROS. Zeros exist when N()=0 • The roots of denominator also known as POLES. Poles exist when D()=0

8. Poles and Zeros • The symbol for pole is x • The symbol for zero is o • Complex s-plane is used to plot poles and zeros.

9. POLES/ZEROS quadratic zero Poles/zeros at the origin real zero real pole quadratic pole

10. LOCATION OF POLES/ZEROS • Zeros/poles at the origin: Zeros/poles that are located at 0 • Real Zeros/poles: Zeros/poles that are located at real axis (-1,-2,1,2,10,etc) • Quadratic Zeros/poles:Zeros/poles that are not located at imaginary or real axis (-1+j2, 2+j5, 3-j3, etc)

11. EXAMPLE

12. ZEROS • Let numerator, N()=0

13. POLE • Let denominator, D()=0

14. FREQUENCY RESPONSE PLOT USING SEMILOG GRAPH

15. MAGNITUDE PLOT AND PHASE PLOT • magnitude plot • phase angle plot

16. HOW TO DO MAGNITUDE AND PHASE PLOT • Transform the time domain circuit (t) into freq. domain circuit (ω) • Determine the TF, H(ω) • Plot the magnitude of that tf, H(ω)against ω. • Plot the phase of that tf, (º) against ω.

17. BODE PLOTS • Bode plots are semilog plots of magnitude (in decibels) and phase (in degrees) of a transfer functionversus frequency

18. DECIBEL SCALE • Logarithm

19. BODE PLOT CHARACTERISTIC FOR POLES AND ZEROS

20. Logarithm of tf:

21. GAIN • Gain is measured in bels

22. Decibel (dB)

23. TRANSFER FUNCTION

25. GENERAL EQUATION OF TF • Before draw, make sure the general equation of tf is obtained first:

26. EX. COMPARE

28. BODE PLOT OF A CONSTANT,K

29. (1) (GAIN) constant

30. Magnitude for constant is : Phase angle for constant is: CHARACTERISTICS

31. magnitude plot phase plot f BODE PLOT FOR CONSTANT

32. BODE PLOT FOR ZERO AT THE ORIGIN

33. (2) ZERO AT THE ORIGIN (jω)N

34. Magnitude: Straight line with 20dB/dec of slope that has a value of 0 dB at =1 Phase: CHARACTERISTIC OF (jω)N

35. MAGNITUDE PLOT

36. PHASE PLOT

37. BODE PLOT OF POLE AT THE ORIGIN

38. (3) POLE AT THE ORIGIN 1/(jω)N @ (jω)-N

39. Magnitude: Straight line with -20dB/dec of slope that has a value of 0 dB at =1 Phase: CHARACTERISTIC OF(jω)-N

40. MAGNITUDE PLOT

41. PHASE PLOT

42. BODE PLOT OF REAL ZERO

43. (4) REAL ZERO

44. CHARACTERISTIC OF (1+jω/z1)N • Magnitude: • Phase:

45. MAGNITUDE PLOT

46. PHASE PLOT

47. BODE PLOT OF REAL POLE

48. (5) REAL POLE

49. CHARACTERISTIC OF (1+jω/p1)-N • Magnitude: • Phase:

50. MAGNITUDE PLOT