1. Chapter 8. Microwave Filters

2. Passive filter Common filter responses Low-pass filter
High-pass filter
Band-pass filter
Band-reject filter

3. Lumped element filter synthesis
H(s) +
Vout -
Vin
: conservation of energy

4. Example #1- 1st order low pass filter
Pole 의 부호는 (–)인 것을 선택한다
(+)인 것은 physically unrealizable

5. Circuit realization
V_AC
SRC1 L L1 C C1
V_AC
SRC1

6. Example #2 – 3rd order Butterworth filter

7. Example #2 – 3rd order Butterworth filter

8. Low pass filter proto-types : Ladder type
로 정한 필터
Butterworth filter
Value of n g1 g2 g3 g4 g5 g6 g7 1
2.000
1.000 2
1.414 3 4
0.7654
1.848 5
0.6180
1.618
0.618 6
0.5176
1.932

9. Filter transformation
1. Impedance transformation
Filter
Filter
2. Frequency transformation

10. Microstrip realization – Stepped impedance filter
Example 8.6

11. Transmission line → T- network

12. Chevyshev filter

13. LPF-to-HPF transformation
LPF→HPF

14. LPF→HPF

15. LPF-to-BPF transformation
LPF→BPF

17. LPF-to-BRF transformation
LPF→BPF

19. Real capacitor characteristics
유효 영역

20. Real inductor characteristics
유효 영역

21. 8.5 Filter implementation
Richard’s transformation

22. Kuroda’s identities

23. Example 8.5
Figure 8.36a (p. 409) Filter design procedure for Example 8.5. (a) Lumped-element low-pass filter prototype. (b) Using Richard’s transformations to convert inductors and capacitors to series and shunt stubs. (c) Adding unit elements at ends of filter.

24. Figure 8. 36b (p. 410) (d) Applying the second Kuroda identity
Figure 8.36b (p. 410) (d) Applying the second Kuroda identity. (e) After impedance and frequency scaling. (f) Microstrip fabrication of final filter.

25. Figure (p. 411) Amplitude responses of lumped-element and distributed-element low-pas filter of Example 8.5.

26. Impedance and admittance inverter
Figure 8.38a/b (p. 412) Impedance and admittance inverters. (a) Operation of impedance and admittance inverters. (b) Implementation as quarter-wave transformers.

27. Low pass filter using admittance inverter
L, C 가 모두 필요하므로 제작하기 어려움. L을 제거.
C값이 여러 가지
이므로 제작하기 어려움.
하나의 C값으로 통일.

29. LPF→BPF

30. Band pass filter implementation using resonators

31. Admittance inverter equivalents

32. Resonator coupling & resonant freq. split

33. Inter-resonant coupling - 등가 회로

34. Inter-resonator coupling

35. External Q
동일한 간격의 gap

36. Example – Inter-resonator coupling
Gap을 변화시키면서 resonant freq.의 차이가
Proto-type에 의해 정해진 값이 나오게 한다.
약하게 coupling 시킨다.

37. Example – External coupling
Gap을 변화시키면서 3dB bandwidth가
Proto-type에 의해 정해진 값이 나오게
한다.
동일한 간격의 gap

38. Filter design by simulator
Coupling
계수 구하기
Qex구하기

39. 12-pole hair pin filter