Chapter 8. Microwave Filters

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Presentation transcript:

Chapter 8. Microwave Filters

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

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

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

Circuit realization V_AC SRC1 L L1 C C1 V_AC SRC1

Example #2 – 3rd order Butterworth filter

Example #2 – 3rd order Butterworth filter

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

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

Microstrip realization – Stepped impedance filter Example 8.6

Transmission line → T- network

Chevyshev filter

LPF-to-HPF transformation LPF→HPF

LPF→HPF

LPF-to-BPF transformation LPF→BPF

LPF-to-BRF transformation LPF→BPF

Real capacitor characteristics 유효 영역

Real inductor characteristics 유효 영역

8.5 Filter implementation Richard’s transformation

Kuroda’s identities

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.

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.

Figure 8.37 (p. 411) Amplitude responses of lumped-element and distributed-element low-pas filter of Example 8.5.

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.

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

LPF→BPF

Band pass filter implementation using resonators

Admittance inverter equivalents

Resonator coupling & resonant freq. split

Inter-resonant coupling - 등가 회로

Inter-resonator coupling

External Q 동일한 간격의 gap

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

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

Filter design by simulator Coupling 계수 구하기 Qex구하기

12-pole hair pin filter