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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. <High Pass Filter>. <Low Pass Filter>. <Band Pass Filter>. < Bandstop Filter(notch Filter)>.

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applied electronic circuit 9

Applied Electronic Circuit #9

Filter, S-plane, Active Filter

제출일 : 2014. 05. 26.

생체의공학과

2010103789 박 준 환

1 filter1

필터의 주파수 분석

1. Filter

<High Pass Filter>

<Low Pass Filter>

<Band Pass Filter>

<Bandstop Filter(notch Filter)>

* 신호의 주파수 성분을 알아야 Filtering 가능.

신호와 Noise의 주파수가 다를 때 : Filter 사용

신호와 Noise의 주파수가 같을 때 : Shielding이나 그 외 방법 사용

1 filter3

실제의 Filter

1. Filter

<Low Pass Filter>

Transition

Band

Stop Band

Pass Band

: Cutoff Frequency

1 filter5

“회로”

1. Filter

* 전압이득

Filter를 구현하기 위해 반드시 Capacitor나 Inductor가 필요하다.

- S가 나와야 하기 때문

* 예시

2 s plane

S-plane(Pole-Zero Diagram)

2. S-plane

Pole

Zero

Right Half Plane(RHP)

Left Half Plane(LHP)

2 s plane1

2. S-plane

* Case 1. (실근) : Pole이 실근을 가질 경우

Diverge “시스템에서는 존재 X”

Die out

* BIBO Stability

: Bounded Input Bounded Output →

2 s plane2

2. S-plane

* Case 2. Pole이 켤레복소수를 가질 경우

, oscillation

, Diverge

, Die out

* : 모든 pole이 LHP에 있음

- Natural Response : Die out ( 시간이 지나면 없어진다 = Transient Response)

- Steady State Frequency Response만 따짐

2 s plane3

2. S-plane

- 주파수는 같으나 크기와 위상이 변함

3 active filter

First Order Active Filter

3. Active Filter

* Low Pass Filter

<Bode Plot>

* : w가 10증가할 때마다

-20dB만큼 변화함

3 active filter2

First Order Active Filter

3. Active Filter

* Band Pass Filter(Capacitor와 pole의 수가 같다)

3 active filter3

First Order Active Filter

3. Active Filter

* Phase Shifter(All pass filter)

3 active filter4

First Order Active Filter

3. Active Filter

* Phase Shifter(All pass filter) 이어서

이득 1 : 진폭감쇄가 없다

신호의 Amplitude를 바꾸지 않으면서 위상만을 변화시키고자 할 때 사용

3 active filter5

Second Order Active Filter

* 의값의 범위에 따라 다른 값의 근이 나온다

3. Active Filter

3 active filter6

Second Order Active Filter

3. Active Filter

* ζ > 1 (서로 다른 실근 2개)

- overdamped : 2개의 pole이 LHP

- Natural Response는 2개의 지수함수의 합

* 0 < ζ< 1 (Complex Conjugate)

-

- Natural Response: Damped Sinusoid

* ζ = 0 (Undamped)

- Natural Response: Oscillation

* ζ< 0 (diverge : unstable)

(ζ> 1)

(0 < ζ < 1)

(ζ < 0)

(ζ = 0)

3 active filter7

Second Order Active Filter

3. Active Filter

* 종합

(ζ = 0)

(ζ < 0)

(ζ < 1)

(ζ = 1)

(ζ < 0)

(0 < ζ < 1)

(ζ = 0)

3 active filter8

Second Order Active Filter

3. Active Filter

* LPF

1. << 1 , “ ”

2. >> 1 , “”

3. = 1 , “ ”

Cutoff frequency에서 값은 Q에 따라 변화

소자의 값에 따라 결정된다(R, C)

(1차)

(2차)

2차 Filter가 1차 보다 성능은 좋으나 Q값에 따라 파형이 바뀜