1. Filter Design (1) Jack Ou ES590

2. Outline • Butterworth LPF Design Example • LPF to HPF Conversion • LPF to BPF Conversion • LPF to BRF Conversion

3. Butterworth Filter (Attenuation of the Butterworth filter) Avoid ripples in the passband. As n increases, the responses assumes a sharper transition. The 3dB bandwidth remains independent of n.

4. Low Pass Filter Design Requirement • fc=1 MHz • Attenuation of 9 dB at 2 MHz.

5. Determine the number of elements in the filter 9 dB of attenuation at f/fc of 2.

6. Low Pass Filter

7. Frequency and Impedance Scaling

8. Impedance Scaling

9. Simulation Results

10. Design Requirement for a Butterworth Low Pass Filter The cut-off frequency is not known in this design specification.

11. Design Process Since f2=2f1, then n=3. (fo=1.45 MHz)

12. Elementary Prototype Value

13. Calculation of Component Values

14. Simulation Results

15. LPF to HPF Conversion

16. High Pass Filter Design Requirement • fc=1 MHz • Attenuation of 9 dB at 0.5MHz.

17. Determine the number of elements in the filter (fc/f) 9 dB of attenuation at fc/f of 2.

18. Low Pass Filter

19. LPF to HPF Transformation Swap L with C, and C with L. 2. Use the reciprocal value.

20. Frequency and Impedance Scaling (same as before)

21. Impedance Scaling

22. HPF

23. LPF to BPF Conversion

24. LPF TO BPF Conversion

25. Determine f3

26. Typical Bandpass Specifications When a low-pass design is transformed into a bandpass design, the attenuation bandwidth ratios remain the same.

27. Determine n using f/fc

28. Transformation from LPF to BPF • The Actual Transformation from LPF to BPF is accomplished by resonating each low-pass element with an element of the opposite type and of the same value. All shunt elements of the low-pass prototype circuit becomes parallel resonant circuits, and all series elements become series-resonant circuits.

29. Transformation Example Resonate each low-pass element with an element of the opposite type and of the same value.

30. Calculate Component Values

31. Fourth Order Butterworth Filter

32. Transformation

33. Component Calculation

34. Schematic

35. Av on Log(f)

36. Av on Linear f

37. Band Rejection Filter

38. LPF to BRF Conversion Substitute BWC/BW for fc/f on the normalized frequency axis.

39. Design Example f1=2472.5 MHz f2=2472.72 f3=2494.28 f4=2494.5 MHz (22)/(21.56)=1.0204 Center Freq: 2483.5 MHz

40. Determine # of Stages Hmm…. not enough suppression.

41. Design Example f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz (98)/(45)=2.1778 Thus fc/f=2 Center Freq: 58.1 MHz

42. Determine # of Stages fc/f

43. Transformation from LPF Replace each shunt element with a shunt series resonant circuit. Replace each series element with a series parallel resonant circuit. Both elements in each of the resonant circuits have the same normalized value.

44. Component Calculations

45. Band Rejection Filter

46. LPF Elementary Prototype

47. BRF Transformation

48. Band Rejection Filter f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz