Filters Filter frequency selective circuits Input signal Filter

Filters Filter : frequency - selective circuits Input signal Filter Output signal 원하는 영역 밖 주파수의 입력 신호를 소멸 시킨다. 예) Equalizer of audio system Key word - pass band a) low-pass b) high-pass c) bandpass d) bandreject - stop band - frequency response plot - phase angle plot - cut off frequency - passive filters, active filters Circuit Theory II Lecture 16 -4

Denominators of Butterworth Low-Pass Filter - Butterworth low-pass transfer functions Circuit Theory II Lecture 16 -5

Butterworth LPF – Fourth and Eighth Order - 고차로 갈수록 이상적인 필터의 주파수 응답 을 갖게 되지만, 필터 회로가 복잡하게 된다. - 4차에서 8차로 설계를 하면 성능은 좋아지 지만, 부품 수, 소비 전력, 조립 비용, 회로 차지 면적이 두 배가 되는 것을 고려해야 한 다. Circuit Theory II A comparison of the frequency responses of fourth-order and eighth-order Butterworth low-pass filters with c = 1 rad/s. Lecture 16 -6

Second-Order Filters - 2차 필터는 이상적인 필터를 값싸게 구현할 수 있다는 점과 고차 필터의 단위 모듈로서 활용될 수 있다는 점에서 중요하게 다루어진다. - 2차 필터의 중요한 세 가지 요소: A second-order low-pass filter’s transfer function (1) 이득 (gain) : k (2) 모서리 주파수 (corner frequency) : w 0 (3) Q 값 (quality factor) : Q A second-order low-pass filter’s network function Q = 0. 707 이면 버터워쓰 low pass 필터에 해당. Circuit Theory II Frequency responses of second-order low-pass filters with four values of Q ( c = 1 rad/s). Lecture 16 -8

Second-Order RLC Filters – Low-Pass Filter Circuit Theory II Lecture 16 -9

Second-Order RLC Filters High-pass Band-stop (notch) Circuit Theory II Lecture 16 -10

Sallen-Key Filters – Low-Pass Filter Circuit Theory II Lecture 16 -11

Sallen-Key Filters – High-Pass Filter Circuit Theory II Lecture 16 -12

Sallen-Key Filters – Band-Pass Filter Circuit Theory II Lecture 16 -13

Sallen-Key Filters – Band-Stop Filter Circuit Theory II Lecture 16 -14

Sallen-Key Filters – Band-Pass Filter : Example - center frequency : f 0 =500 Hz, bandwidth = 100 Hz. Circuit Theory II Lecture 16 -15

Tow-Thomas Band-Pass or Low-Pass Filter - v 1(t) : 저주파통과 필터, v 2(t) : 대역통과 필터. Band-pass filter Low-pass filter The Tow-Thomas filter. Band-pass filter Circuit Theory II Low-pass filter Lecture 16 -16

Butterworth Tow-Thomas Low-Pass Filter - 버터워쓰 토우토마스 저주파통과 필터를 설계하라. dc 이득 : 5, 차단주파수 1, 250 Hz. - dc 이득 : 5 - 버터워쓰 저주파통과 필터가 되려 면 Q = 0. 707 이어야 한다. Lowpass filter Band-pass filter Butterworth Tow-Thomas low-pass filter. Circuit Theory II Lecture 16 -17

Butterworth Tow-Thomas High-Pass Filter (I) - 버터워쓰 토우토마스 고주파통과 필터를 설계하라. dc 이득 : 5, 차단주파수 1, 250 Hz. Constant gain High-pass filter Low-pass filter Band-pass filter Circuit Theory II Lecture 16 -18

Butterworth Tow-Thomas High-Pass Filter (II) - 버터워쓰 저주파통과 필터와 대역 필터로 고주파통과 필터를 구현한다. Constant gain Band-pass filter Low-pass filter Highpass filter Butterworth Tow-Thomas high-pass filter. Circuit Theory II Lecture 16 -19

Butterworth Tow-Thomas High-Pass Filter (III) R 7 10 k. W R 8 R 6 C 2 5 R 1 2546 W R 2 50 k. W 12732 W 0. 01 m. F 4 9003 W R 3 3 12732 W R 7 C 1 2 0. 01 m. F R 4 1 12732 W R 5 6 12732 W 7 R 9 50 k. W R 10 8 50 k. W 9 V 1 1 V 1 k. Hz 0 Deg U 4 U 1 U 2 U 3 OPAMP_3 T_VIRTUAL 0 - Multisim simulation. 1250 Hz Circuit Theory II Lecture 16 -20

Measuring Parameters of Filter Stage Circuit Theory II Lecture 16 -23

Output Impedance of Sallen-Key Band-Pass Filter Circuit Theory II Lecture 16 -24

Third-Order Butterworth Low-Pass Filter (I) - 3차 버터워쓰 저주파통과 필터를 설계하라. - 차단주파수= 500 rad/s, 직류이득=1. - 2차 필터와 1차 필터를 연이어 연결하여 구 성. Sallen-Key low-pass filter First-order low-pass filter Circuit Theory II Sallen-Key high-pass filter Lecture 16 -25

Third-Order Butterworth Low-Pass Filter (II) (b) a first-order filter stage (a) A Sallen-Key filter stage (c) a third-order Butterworth low-pass filter Circuit Theory II Lecture 16 -26

Anti-Aliasing Filter (II) - 4차 버터워쓰(Butterworth) 저주파통 과 0. 1 m. F 3183 W 0. 1 m. F 3931 W 3183 W - C = 0. 1 m. F 를 선택. Circuit Theory II Lecture 16 -28

Anti-Aliasing Filter (III) - 4차 버터워쓰(Butterworth) 저주파통 과 0. 1 m. F 3183 W 0. 1 m. F 484 W 3183 W - C = 0. 1 m. F 를 선택. Circuit Theory II Lecture 16 -29

Anti-Aliasing Filter (IV) - 여러 설계가 가능. 20 k. W 7. 76 k. W Circuit Theory II 10 k. W 3. 88 k. W 2 k. W 0. 776 k. W Lecture 16 -30

Anti-Aliasing Filter (VI) - 저항은 7. 5 k. W 사용. - 표준 저항을 사용. 3183 W => 3. 3 k. W 사용. f 0= 482. 5 Hz. 0. 1 m. F 3183 W 3. 3 k. W 3183 W 20 k. W 7. 76 k. W 7. 5 k. W 0. 1 m. F 3931 W 15 k. W 3183 W 12 k. W 0. 1 m. F 484 W 3183 W 51 k. W - 연산증폭기 입력단자에서 바라본 저항이 같도록 설계. - 양의 입력단자 : 6. 6 k. W 저항. Circuit Theory II 7. 5 k. W 5. 6 k. W - 저항은 2 k. W ~ 500 k. W 을 사용한다. Lecture 16 -32

Anti-Aliasing Filter (VII) 0. 1 m. F 3. 3 k. W 15 k. W 3. 3 k. W 0. 1 m. F 12 k. W 20 k. W 7. 5 k. W 51 k. W 5. 6 k. W Circuit of the anti-aliasing filter. 477 Hz Frequency response of the antialiasing filter. Circuit Theory II Lecture 16 -33

Standard Resistors Standard values of commercially available resistors. Boylestad 책 80쪽 표 3. 8 • Standard values and their tolerances. Boylestad 책 80쪽 표 3. 9 10 씩 증가하지 않는 이유? - 회로이론 1의 강의록 2 -19 참조 Circuit Theory II Lecture 16 -34