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Filter Design (1)

Filter Design (1). Jack Ou ES590. Outline. Butterworth LPF Design Example LPF to HPF Conversion LPF to BPF Conversion LPF to BRF Conversion. Butterworth Filter. (Attenuation of the Butterworth filter). Avoid ripples in the passband .

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Filter Design (1)

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  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

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