1. Frequency Response Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

2. Contents Introduction Transfer Function The Decibel Scale Bode Plots Series Resonance Parallel Rosonance Passive Filters Active Filters Applications

3. Introduction Analysis with a constant frequency is already learned. To obtain the frequency response –Keep the amplitude and the phase of the sinusoidal source constant (amplitude=1, phase=0) –Sweep the frequency from a starting frequency to a stop frequency –Plot the amplitude and the phase of the desired voltage or current versus frequency

4. Transfer Function The transfer function H(  ) can be expressed as Zeros: the roots of N(  )=0 Poles: the roots of D(  )=0

5. Example 1 Phasor domain Time domain

6. Example 2

7. Example 3

8. The Thought of Bode Plots It is quite difficult to handle the plotting of the transfer function in a linear scale. If the transfer function is transformed to a logarithmic scale, then the plotting becomes much more easy.

9. The Decibel (dB) Scale

10. Bode Plots

11. Steps to construct a Bode plot: –Plot each factor separately –Additively combine all of them graphically because of the logarithms involved The mathematical convenience of the logarithm makes the Bode plots a powerful tool Straight-line plots used instead of actual plots

12. Bode Plots: A Gain K

13. Bode Plots: Zero/Pole at Origin

14. Bode Plots: Simple Zero 20 dB/decade

15. Bode Plots: Simple Pole -20 dB/decade -45  /decade

16. Bode Plots: Quadratic Pole

17. Bode Plots: Quadratic Zero

18. Summary

21. Example 1

22. Example 1 (Cont’d)

23. Example 2

24. Example 2 (Cont’d)

25. Example 3

26. Example 3 (Cont’d)

27. Series Resonance

28. When Resonance Occurs 1.The impedance is purely resistive. The LC series combination acts like a short circuit. 2.The voltage and the current are in phase, so the power factor is unity. 3.The impedance Z(  ) is minimum. 4.The voltage across L and C can be much larger than the source voltage.

29. Half-Power Frequencies

30. Quality Factor: Q

31. Summary Voltage across L and C QV m

32. Parallel Resonance

33. When Resonance Occurs 1.The impedance is purely resistive. The LC parallel combination acts like an open circuit. 2.The voltage and the current are in phase, so the power factor is unity. 3.The admittance Y(  ) is minimum. 4.The current flowing through L and C can be much larger than the source current.

34. Comparisons Series circuit Parallel circuit

35. Passive Filters Lowpass Highpass Bandpass Bandstop

36. Lowpass Filter

37. Highpass Filter

38. Bandpass Filter B

39. Bandstop Filter rejection frequency B

40. Active Filters A general 1st-order active filter Active 1st-order lowpass filter

41. Active 1st-Order Highpass Filter

42. Active Bandpass Filter

44. Bandreject (or Notch) Filter

46. Applications: Radio Receiver 2055 kHz rejected 2055 kHz

47. Touch-Tone Telephone (1/2)

48. Touch-Tone Telephone (2/2)

49. Crossover Network (Lowpass) (Highpass)