1. 응용전자회로#10
강윤실

2. Second order Active filter
-HPF
2. HPF
H jw = 𝐻 𝑂𝐻𝑝 ∗ 𝐻 𝐻𝑝 (𝑗𝑤)
= 𝐻 𝑂𝐻𝑝 −{ 𝑤 𝑤 𝑜 } 2 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄
1. 𝑤 𝑤 𝑜 ≪1 ,
𝐻 𝐻𝑃 →−{ 𝑤 𝑤 𝑜 } 2
𝐻 𝑂𝐻𝑃 =40 log 𝑤 𝑤 𝑜 [dB]
*LPF에서 R과 C를 바꾸면 HPF가 됨
2. 𝑤 𝑤 𝑜 ≫1 ,
𝐻 = 𝐻 𝑂𝐻𝑃
3. 𝑤 𝑤 𝑜 =1 ,
𝐻 𝐻𝑃 =+jQ
𝐻 = 𝐻 𝑂𝐻𝑃 +𝑄

3. Second order Active filter
Band pass filter
𝐻 𝐵𝑃 → 𝑗 𝑤 𝑤 𝑜 𝑄
1. 𝑤 𝑤 𝑜 ≪1 ,
𝐻 𝐵𝑃 =20 log 𝑤 𝑤 𝑜 − 𝑄 𝑑𝐵 [dB]
( 𝑄 𝑑𝐵 =20 log 𝑄 )
2. 𝑤 𝑤 𝑜 ≫1 ,
𝐻 𝐵𝑃 → −𝑗 𝑤 𝑤 𝑜 𝑄
𝐻 𝐵𝑃 =−20 log 𝑤 𝑤 𝑜 − 𝑄 𝑑𝐵 [dB]
H jw = 𝐻 𝑂𝐵𝑃 𝑗 𝑤 𝑤 𝑜 𝑄 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄 = 𝐻 𝑂𝐵𝑝 ∗ 𝐻 𝐵𝑝 (𝑗𝑤)
3. 𝑤 𝑤 𝑜 =1 ,
𝐻 𝐵𝑃 =1
𝐻 = 𝐻 𝐵𝑃
𝐵𝑊= 𝑊 𝐻 − 𝑊 𝐿 or 𝑓 𝐻 − 𝑓 𝐿 [𝐻𝑧]
𝑊 𝑜 = 𝑊 𝐿 𝑊 𝐻
𝑄= 𝑊 𝑜 𝐵𝑊 = 𝑊 𝑜 𝑊 𝐻 − 𝑊 𝐿

4. Second order Active filter
Notch pass filterfilter(Band stop filter)
𝐻 𝑂𝑁 :𝑑𝑐 𝑜𝑟 ℎ𝑖𝑔ℎ−𝑓𝑟𝑒𝑞 𝑔𝑎𝑖𝑛
1. 𝑤 𝑤 𝑜 ≪1 ,
𝐻 = 𝐻 𝑂𝑁
2. 𝑤 𝑤 𝑜 ≫1 ,
𝐻 = 𝐻 𝑂𝑁
H jw = 𝐻 𝑂𝑁 ∗ 𝐻 𝑁 (𝑗𝑤)
𝐻 =0
H jw = 𝐻 𝑂𝑁 1−{ 𝑤 𝑤 𝑜 } 2 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄
3. 𝑤 𝑤 𝑜 =1 ,
𝐻 =−∞(dB)

5. Second order Active filter
-All pass filter
Q증가
H jw =1
∠H jw =−2 tan −1 𝑤 𝑤 𝑜 𝑄 1−{ 𝑤 𝑤 𝑜 } 2 −𝜋
Q증가
−2𝜋

6. KRC filter Low pass filter H jw = 𝐻 𝑂𝐿𝑃 1 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄
𝐻 𝑆 = 𝑉 𝑜 (𝑆) 𝑉 𝑖 (𝑆) = 𝑘 𝑅 1 𝑅 2 𝐶 1 𝐶 2 𝑆 −𝑘 𝑅 1 𝐶 1 + 𝑅 1 𝐶 2 + 𝑅 2 𝐶 1 𝐶 1 +1
H jw = 𝐻 𝑂𝐿𝑃 1 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄
𝐻 𝑂𝐿𝑃 =𝑘
𝑄= 1 1−𝑘 𝑅 1 𝐶 1 𝑅 2 𝐶 𝑅 1 𝐶 2 𝑅 1 𝐶 𝑅 2 𝐶 2 𝑅 1 𝐶 1
𝑉 𝑜 = 1+ 𝑅 𝐵 𝑅 𝐴 𝑉 2
𝑤 𝑜 = 1 𝑅 1 𝑅 2 𝐶 1 𝐶 2
=𝑘 𝑉 2

7. KRC filter High pass filter 𝑤 𝑜 = 1 𝑅 1 𝑅 2 𝐶 1 𝐶 2
H jw = 𝐻 𝑂𝐻𝑃 −{ 𝑤 𝑤 𝑜 } 2 1−{ 𝑤 𝑤 𝑜 } 2 + 𝑗 𝑤 𝑤 𝑜 𝑄
𝐻 𝑂𝐻𝑃 =𝑘
𝑤 𝑜 = 1 𝑅 1 𝑅 2 𝐶 1 𝐶 2
𝑄= 1 1−𝑘 𝑅 1 𝐶 1 𝑅 2 𝐶 𝑅 1 𝐶 2 𝑅 1 𝐶 𝑅 2 𝐶 2 𝑅 1 𝐶 1
𝑉 𝑜 = 1+ 𝑅 𝐵 𝑅 𝐴 𝑉 2
=𝑘 𝑉 2

8. KRC filter Band pass filter
𝐻 𝑂𝐵𝑃 = 𝑘 1+ 1−𝑘 𝑅 1 𝑅 3 +(1+ 𝐶 1 𝐶 2 ) 𝑅 1 𝑅 2
𝑤 𝑜 = 𝑅 1 𝑅 𝑅 1 𝑅 2 𝐶 1 𝐶 2
𝑄= 𝑅 1 𝑅 −𝑘 𝑅 1 𝑅 𝑅 1 𝐶 1 𝑅 2 𝐶 𝑅 1 𝐶 2 𝑅 1 𝐶 𝑅 2 𝐶 2 𝑅 1 𝐶 1

9. KRC filter Notch pass filter 𝐻 𝑂𝑁 =𝑘= 1+ 𝑅 𝐵 𝑅 𝐴 𝑤 𝑜 = 1 𝑅𝐶 𝑄= 1 4−2𝑘
𝐻 𝑂𝑁 =𝑘= 1+ 𝑅 𝐵 𝑅 𝐴
𝑤 𝑜 = 1 𝑅𝐶
𝑄= 1 4−2𝑘
𝑉 𝑜 𝑅 𝐴 𝑅 𝐴 + 𝑅 𝐵 = 𝑉 3

10. Multiple feedback Filter
Band pass filter
𝐻 𝑗𝑤 = −𝑗𝑤 𝑅 2 𝐶 2 1− 𝑤 2 𝑅 1 𝐶 1 𝑅 2 𝐶 2 +𝑗𝑤 𝑅 1 ( 𝐶 1 + 𝐶 2 )
𝑄= 𝑅 2 𝑅 𝐶 1 𝐶 𝐶 2 𝐶 1
𝑤 𝑜 = 1 𝑅 1 𝑅 2 𝐶 1 𝐶 2
𝐻 𝑂𝐿𝑃 =− 𝑅 2 𝑅 𝐶 1 𝐶 2
𝑄= 𝑊 𝑜 𝐵𝑊 = 𝑊 𝑜 𝑊 𝐻 − 𝑊 𝐿

11. Multiple feedback Filter
Low pass filter
𝐻 𝑗𝑤 = 𝐻(𝑆) 𝑆=𝑗𝑤
𝐻 𝑂𝐿𝑃 =− 𝑅 3 𝑅 1
𝑤 𝑜 = 1 𝑅 2 𝑅 3 𝐶 1 𝐶 2
𝑄= 𝐶 1 𝐶 𝑅 2 𝑅 3 𝑅 𝑅 3 𝑅 𝑅 2 𝑅 3
3. HPF 는 LPF에서 R과 C를 바꿔주면 된다.

12. Multiple feedback Filter
Notch pass filter
All pass에서 BPF를 뺀것
𝑉 𝑜 =− 𝑅 3 𝑅 4 𝑉 𝑖 + 𝑅 5 𝑅 3 𝑉 𝐵𝑃

13. State Variable Filter
적분기
𝑉 𝐻𝑃 =− 𝑅 5 𝑅 3 𝑉 𝑖 − 𝑅 5 𝑅 4 𝑉 𝐿𝑃 + 𝑅 1 𝑅 1 + 𝑅 𝑅 5 𝑅 3 || 𝑅 4 𝑉 𝐵𝑃
𝑉 𝐵𝑃 =− 1 𝑅 6 𝐶 1 𝑆 𝑉 𝐻𝑃
𝑉 𝐿𝑃 =− 1 𝑅 7 𝐶 2 𝑆 𝑉 𝐵𝑃

14. Biguad Filter 𝐻 𝑂𝐵𝑃 =− 𝑅 2 𝑅 1 𝐻 𝑂𝐿𝑃 = 𝑅 5 𝑅 1 𝑤 𝑜 = 1 𝑅 4 𝑅 5 𝐶 1 𝐶 2
𝐻 𝑂𝐵𝑃 =− 𝑅 2 𝑅 1
𝐻 𝑂𝐿𝑃 = 𝑅 5 𝑅 1
𝑤 𝑜 = 1 𝑅 4 𝑅 5 𝐶 1 𝐶 2
𝑄= 𝑅 2 𝐶 𝑅 4 𝑅 5 𝐶 2