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Applied Electronic Circuit #9. Filter, S-plane, Active Filter. 제출일 : 2014. 05. 26. 생체의공학과 2010103789 박 준 환. Passive Filter( 이득이 없는 필터 ). 1. Filter. Active Filter. 필터의 주파수 분석. 1. Filter. . . . < Bandstop Filter(notch Filter)>. - PowerPoint PPT Presentation
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Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
1 Park Jun-hwan
Applied Electronic Circuit #9
제출일 : 2014. 05. 26.생체의공학과
2010103789 박 준 환
Filter, S-plane, Active Filter
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
2 Park Jun-hwan
1. Filter Passive Filter( 이득이 없는 필터 )
𝑣 𝑖 𝑣𝑜
Active Filter
𝑣 𝑖 𝑣𝑜
𝑣 𝑖 𝑣 𝑖
𝑣𝑜 𝒗𝒐
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
3 Park Jun-hwan
1. Filter 필터의 주파수 분석
|𝑯|
𝒘𝒘 𝒄
<Low Pass Filter> |𝑯|
𝒘𝒘 𝒄
<High Pass Filter>
|𝑯|
𝒘𝒘𝑯
<Band Pass Filter> |𝑯|
𝒘𝒘𝑯
<Bandstop Filter(notch Filter)>
𝒘 𝑳 𝒘 𝑳
* 신호의 주파수 성분을 알아야 Filtering 가능 . 신호와 Noise 의 주파수가 다를 때 : Filter 사용
신호와 Noise 의 주파수가 같을 때 : Shielding 이나 그 외 방법 사용
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
4 Park Jun-hwan
1. Filter Filtering 의 예시 ( 교재 Fig 3.2 에서 발췌 )
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
5 Park Jun-hwan
1. Filter 실제의 Filter
|𝑯|
𝒘𝒘 𝒄
<Low Pass Filter>
Pass Band Stop Band
TransitionBand
: Cutoff Frequency
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
6 Park Jun-hwan
1. Filter
+
-
i +
-
i
𝑉 (𝑠 )=𝑅 ∙ 𝐼 (𝑠) 𝑉 (𝑠 )= 1𝑠𝐶 ∙ 𝐼 (𝑠) 𝑉 (𝑠 )=𝑠𝐿∙ 𝐼 (𝑠)
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
7 Park Jun-hwan
1. Filter
𝑣 𝑖(𝑡) 𝑣𝑜(𝑡)𝐻“ 회로”
* 전압이득
𝐻 (𝑠 )=𝑣𝑜(𝑠)𝑣 𝑖(𝑠)
=𝑎𝑚 ∙𝑠𝑚+…+𝑎1 ∙𝑠+𝑎𝑜𝑎𝑛 ∙𝑠
𝑛+…+𝑏1 ∙𝑠+𝑏𝑜=𝑁 (𝑠)𝐷 (𝑠)
𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛
Filter 를 구현하기 위해 반드시 Capacitor 나 Inductor 가 필요하다 . - S 가 나와야 하기 때문
* 예시
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
8 Park Jun-hwan
2. S-plane S-plane(Pole-Zero Diagram)
𝝈
𝒋𝒘 ZeroPole
𝑠=𝜎+ 𝑗𝑤
Left Half Plane(LHP) Right Half Plane(RHP)
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
9 Park Jun-hwan
2. S-plane𝐻 (𝑠 )=
𝐴1
𝑠−𝑝1+
𝐴2
𝑠−𝑝2+…+
𝐴𝑛
𝑠−𝑝𝑛일때
* Case 1. ( 실근 ) : Pole 이 실근을 가질 경우
𝜎 𝑘>0
Diverge “ 시스템에서는 존재 X”
𝒘𝒘 𝒄
Die out
𝜎 𝑘<0
* BIBO Stability : Bounded Input Bounded Output →
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
10 Park Jun-hwan
2. S-plane𝐻 (𝑠 )=
𝐴1
𝑠−𝑝1+
𝐴2
𝑠−𝑝2+…+
𝐴𝑛
𝑠−𝑝𝑛일때
* Case 2. Pole 이 켤레복소수를 가질 경우
, Diverge
𝑡
* : 모든 pole 이 LHP 에 있음
- Natural Response : Die out ( 시간이 지나면 없어진다 = Transient Response) - Steady State Frequency Response 만 따짐
𝑡𝑡
, Die out , oscillation
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
11 Park Jun-hwan
2. S-plane
𝑣𝑜(𝑡)𝐻 ( 𝑗𝑤)𝑣 𝑖(𝑡)
𝑣 𝑖( 𝑗𝑤) 𝑣𝑜( 𝑗𝑤)
- 주파수는 같으나 크기와 위상이 변함
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
12 Park Jun-hwan
3. Active Filter First Order Active Filter
* Low Pass Filter
𝑣𝑜(𝑡)𝑣 𝑖(𝑡)
|𝑯|
𝒍𝒐𝒈𝒘𝒍𝒐𝒈 𝟏
𝑹𝟐𝑪
<Bode Plot>
𝟐𝟎𝒍𝒐𝒈 𝑹𝟐𝑹𝟏
−𝟐𝟎𝒅𝑩 /𝒅𝒆𝒄−𝟑𝒅𝑩
* : w 가 10 증가할 때마다 -20dB 만큼 변화함
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
13 Park Jun-hwan
3. Active Filter First Order Active Filter
* High Pass Filter
𝑣𝑜(𝑡)𝑣 𝑖(𝑡)
𝒍𝒐𝒈𝒘
−𝟐𝟎𝒅𝑩/𝒅𝒆𝒄
𝑤0
|𝑯𝟎|𝒅𝑩
|𝑯|𝒅𝑩
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
14 Park Jun-hwan
3. Active Filter First Order Active Filter
* Band Pass Filter(Capacitor 와 pole 의 수가 같다 )
𝑣𝑜(𝑡)
𝑣 𝑖(𝑡)
𝒍𝒐𝒈𝒘
−𝟐𝟎𝒅𝑩 /𝒅𝒆𝒄
𝑤𝐿
|𝑯𝟎|𝒅𝑩
|𝑯|𝒅𝑩
𝑤𝐻
−𝟐𝟎𝒅𝑩 /𝒅𝒆𝒄
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
15 Park Jun-hwan
3. Active Filter First Order Active Filter
* Phase Shifter(All pass filter)
𝑣𝑜(𝑡)𝑣 𝑖(𝑡)𝑖 𝑖
𝑣𝑝
𝑣𝑝𝑉 𝑖 𝑉 𝑜
𝝈
𝒋𝒘
1𝑅𝐶
− 1𝑅𝐶
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
16 Park Jun-hwan
3. Active Filter First Order Active Filter
* Phase Shifter(All pass filter) 이어서
∗𝐻 (𝑠)=𝑉𝑜 (𝑠)𝑉 𝑖 (𝑠 )
=1−𝑠𝑅𝐶1+𝑠𝑅𝐶 ,𝐻
( 𝑗𝑤 )=1− 𝑗𝑤𝑅𝐶1+ 𝑗𝑤𝑅𝐶 =1∠−2 tan−1(𝑤𝑅𝐶)
𝒍𝒐𝒈𝒘
|𝑯|𝒅𝑩
이득 1 : 진폭감쇄가 없다
𝒍𝒐𝒈𝒘
∠𝑯𝑤0=
1𝑅𝐶0.1 1
𝑅𝐶 1 0 1𝑅𝐶
− 2𝜋
−𝜋
신호의 Amplitude 를 바꾸지 않으면서 위상만을 변화시키고자 할 때 사용
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
17 Park Jun-hwan
3. Active Filter Second Order Active Filter
* 의 값의 범위에 따라 다른 값의 근이 나온다
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
18 Park Jun-hwan
3. Active Filter Second Order Active Filter
𝝈
𝒋𝒘* ζ > 1 ( 서로 다른 실근 2 개 ) - overdamped : 2 개의 pole 이 LHP - Natural Response 는 2 개의 지수함수의
합
* 0 < ζ < 1 (Complex Conjugate) - - Natural Response : Damped Sinusoid
* ζ = 0 (Undamped) - Natural Response : Oscillation
* ζ < 0 (diverge : unstable)
𝝈
𝒋𝒘
𝝈
𝒋𝒘
𝝈
𝒋𝒘
(ζ > 1)
(0 < ζ < 1)
(ζ = 0) (ζ < 0)
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
19 Park Jun-hwan
3. Active Filter Second Order Active Filter
* 종합
𝝈
𝒋𝒘
(ζ = 1)
(ζ < 0)
(ζ < 0)
(ζ < 1)
(0 < ζ < 1)
(ζ = 0)
(ζ = 0)
𝐻 ( 𝑗𝑤 )= 𝑁 ( 𝑗𝑤 )
1−( 𝑤𝑤𝑜 )2
+( 𝑗 𝑤𝑤𝑜 )𝑄
,(𝑄= 12 ζ )
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
20 Park Jun-hwan
3. Active Filter Second Order Active Filter
* LPF
1. << 1 , “ ” 2. >> 1 , “ ”
3. = 1 , “ ” Cutoff frequency 에서 값은 Q 에 따라 변화
소자의 값에 따라 결정된다 (R, C)
|𝑯|
𝒍𝒐𝒈𝒘
(1 차 )
(2 차 )
𝑄
2 차 Filter 가 1 차 보다 성능은 좋으나 Q 값에 따라 파형이 바뀜
Dept. of Biomed. Eng. BME303:Applied Electronic Circuit Kyung Hee Univ.
21 Park Jun-hwan
감사합니다 .