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Active Filter OpAmp를 사용하고 이득이 있는 filter Passive filter Active filter LPF HPF

Active Filter 실제 필터 Highpass Filter Lowpass Filter pass band stop band Transmit band Bandpass Filter Bandstop Filter(Notch Filter)

i V Active Filter + V(s)=R(s) i V - 0 + , - 0 ,

Active Filter H Vi(t) Vo(t) H(S) = Transfer function =

Pole – Zero Diagram Pole zero diagram을 그렸을때 나타나는 특성을 통해 전달함수의 특성을 알 수 있다. *보통 통신에 사용 되는 전달함수는 가 0이다 Right half Plame Left half Plame

Active Filter CASE 1 근) Diverge Die out * BIBO(Bounded Input Bounded Output) Stability

Active Filter CASE 2 Diverge Osillation : 모든pole이 LHP에 있음 • Natural Response “die out” • Transient Response “homogeneous” • Steady-stata Frequency Response • S=jw인 H(s) , w축에서의 변화만 분석 Die out

R2 C 4 R1 V- 2 1 Vi - OS1 6 OUT Vo 3 5 + OS2 7 V+ 0 Transfer Function Vo(jw) Vi(jw) H Vi(t) Vo(t) Lowpass filter 3dB

Transfer Function Highpass filter 3dB Bandpass filter

First order Active Filter Lowpass filter Dc gain(low frequency gain) 일때 3dB -20dB/dec 3dB cut off frequency

First order Active Filter Highpass filter High frequency gain 3dB cut off frequency 3dB 일때 20db/dec

First order Active Filter Bandpass filter 일때

First order Active Filter Phase - Shifter H

Second order Active Filter 다항식(m<=2) : undamped natural frequency damping ratio 로 다른 실근 2개) • Over damped • Natural response는 2개의 지수함수로 이루어짐 0 • Natural response : damped sine

Second order Active Filter : undamped • Natural response stable Diverge (unstable) >1 >1

Second order Active Filter osilation Damping Q 1. LPF 소자값에 따라 결정 :dc gain (low freq gain) Q값에 따라서 overshoot, undershoot 발생 1. 3. -40dB/dec 2. [dB]

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