응용전자회로 제출일 : 2014. 3. 31 (월) 생체의공학과 2006200077 김 준 성.

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응용전자회로 제출일 : 2014. 3. 31 (월) 생체의공학과 2006200077 김 준 성

Op amp Op Amp circuits 해석 Negative Feedback이 있으면 선형동작하는 회로 1) 𝑣 𝑃 = 𝑣 𝑁 2) 𝑖 𝑃 = 𝑖 𝑁 =0 ( 𝑟 𝐷 가 매우 크기 때문에 전류가 흐르지 않는다) 3) 𝑉 𝐸𝐸 ≤ 𝑉 𝑂𝐿 ≤ 𝑣 𝑜 ≤ 𝑉 𝑂𝐻 ≤ 𝑉 𝐶𝐶 𝑉 𝐶𝐶 𝑉 𝐸𝐸 𝑣 𝑃 𝑣 𝑁 𝑟 𝐷 𝑣 𝑜

Amplifier 종류 𝐴 𝑣 = 𝑣 𝑜 𝑣 𝑖 𝑅 1 𝑅 2 𝑣 𝑜 𝑣 𝑖 𝑣 𝑖 𝑣 𝑜 𝑣 𝑖 = 𝑅 1 𝑅 1 + 𝑅 2 𝑣 𝑜 ⇒ 𝑣 𝑜 =( 1+ 𝑅 2 𝑅 1 ) 𝑣 𝑖 𝑅 𝑖 = ∞, 𝑅 𝑜 =0 모든 신호원 무시(전압원 short, 전류원 open) 1. Noninverting Amp 𝐴 𝑣 = 𝑣 𝑜 𝑣 𝑖 𝑅 1 𝑅 2 𝑣 𝑖 𝑣 𝑜 등가회로 𝑅 𝑖 𝑣 𝑖 𝑣 𝑜 𝑅 𝑜 + + − ( 1+ 𝑅 2 𝑅 1 ) 𝑣 𝑖 − 입력, 출력 모두 Loading effect가 발생하지 않는다.

Amplifier 종류 𝑣 𝑖 𝑅 1 + 𝑣 𝑜 𝑅 2 =0 ⇒ 𝑣 𝑜 = − 𝑅 2 𝑅 1 𝑣 𝑖 𝑅 1 𝑅 2 𝑣 𝑖 𝑣 𝑖 𝑅 1 + 𝑣 𝑜 𝑅 2 =0 ⇒ 𝑣 𝑜 = − 𝑅 2 𝑅 1 𝑣 𝑖 𝑅 𝑖 = 𝑅 1 , 𝑅 𝑜 =0 2. Inverting Amp 𝑣 𝑖 𝑣 𝑜 𝑅 1 𝑅 2 0 V 𝑖 2 = 𝑣 𝑜 𝑅 2 𝑅 𝑖 𝑖 1 = 𝑣 𝑖 𝑅 1 𝑅 𝑜 등가회로 𝑣 𝑖 + − + − 𝑅 2 𝑅 1 𝑣 𝑖 𝑣 𝑜 − Loading effect가발생한다. −

Amplifier 종류 𝑣 𝑜 = 𝑣 𝑖 의 결과가 나온다. 𝑣 𝑖 𝑣 𝑜 = 𝑣 𝑖 𝑣 𝑜 𝑣 𝑖 𝑣 𝑜 = 𝑣 𝑖 의 결과가 나온다. 입력 전원의 저항이 큰 경우 사용한다. 𝑅 𝑖 = ∞, 𝑅 𝑜 =0 3. Uniting gain buffer (voltage follower) 𝑣 𝑖 𝑣 𝑜 = 𝑣 𝑖 𝑅 𝑜 𝑅 𝑖 + - 등가회로 𝑣 𝑖 𝑣 𝑜 − +

(전류가 흐르지 않기 때문에 전압강하가 일어나지 않고 buffer의 입력 전압이 𝑣 𝑆 인 것이다. ) Amplifier 종류 3. Uniting gain buffer (voltage follower) 𝑅 𝑆 값이 큰 경우 buffer를 사용하여 𝑣 𝑜 = 𝑣 𝑆 의 결과를 얻을 수 있다. (전류가 흐르지 않기 때문에 전압강하가 일어나지 않고 buffer의 입력 전압이 𝑣 𝑆 인 것이다. ) 𝑣 𝑜 = 𝑣 𝑆 𝑣 𝑆 𝑅 𝑆 + - 𝑣 𝑆 𝑖=0 등가회로 𝑣 𝑆 𝑣 𝑜

Amplifier 종류 𝑅 1 𝑣 1 𝑅 𝐹 𝑅 2 𝑣 2 𝑅 3 𝑣 3 𝑣 𝑜 4. Summing Amp (Adder) 𝑣 1 𝑅 1 + 𝑣 2 𝑅 2 + 𝑣 3 𝑅 3 + 𝑣 𝑜 𝑅 𝐹 =0 𝑣 𝑜 =−( 𝑅 𝐹 𝑅 1 𝑣 1 + 𝑅 𝐹 𝑅 2 𝑣 2 + 𝑅 𝐹 𝑅 3 𝑣 3 ) 예) 𝑅 𝐹 =10𝑘Ω , 𝑅 1 , 𝑅 2 , 𝑅 3 =1𝑘Ω 인 경우 10배 증폭 (위상이 반전된 신호는 디지털신호처리를 통해 처리가능) + - 𝑣 1 𝑣 2 𝑣 3 𝑅 1 𝑅 2 𝑅 3 𝑅 𝐹 𝑣 𝑜 𝑅 𝑖 1 𝑖 1 𝑅 𝑖 2 𝑖 2 0𝑉 𝑖 𝐹 𝑅 𝑖 3 𝑖 3 𝑅 𝑜 𝑅 𝑖 1 = 𝑅 1 𝑅 𝑖 2 = 𝑅 2 𝑅 𝑖 3 = 𝑅 3 𝑅 𝑜 = 0 𝑅 1 , 𝑅 2 , 𝑅 3 를 가변저항으로 사용하면 각각 볼륨조절 가능 𝑉𝑖𝑟𝑡𝑢𝑎𝑙 𝐺𝑟𝑜𝑢𝑛𝑑

Loading effect가 다르게 발생한다. Amplifier 종류 𝑅 1 𝑅 2 = 𝑅 3 𝑅 4 인 경우 𝑣 𝑜 = 𝑅 2 𝑅 1 𝑣 2 − 𝑣 1 5. Difference Amp (subtractor) 𝑣 1 𝑣 2 𝑣 𝑜 𝑅 1 𝑅 2 𝑅 3 𝑅 4 - + 𝑅 𝑖 1 𝑅 𝑖 2 𝑅 𝑖 1 = 𝑅 1 𝑅 𝑖 2 = 𝑅 3 + 𝑅 4 𝑅 𝑜 =0 Op Amp 쪽으로 전류가 흐르지 않는다. Loading effect가 다르게 발생한다.

Amplifier 종류 𝑅 𝑆 1 𝑅 1 𝑅 2 𝑣 1 ’ 𝑣 1 𝑅 𝑆 2 𝑣 2 ’ 𝑣 𝑜 𝑣 2 * 입력에서 부하효과 𝑣 1 ′ = 𝑅 1 𝑅 1 + 𝑅 𝑆 1 𝑣 1 𝑣 2 ′ = 𝑅 1 + 𝑅 2 𝑅 1 + 𝑅 2 + 𝑅 𝑆 2 𝑣 2 𝑣 𝑜 = 𝑅 2 𝑅 1 𝑣 2 ′ − 𝑣 1 ′ 𝑅 𝑆 1 𝑣 1 ’ 𝑣 2 ’ 𝑣 𝑜 𝑅 1 𝑅 2 - + 𝑣 1 𝑅 𝑆 2 𝑣 2 𝑣 2 − 𝑣 1 이 아니다.

Amplifier 종류 𝑣 1 𝑅 1 𝑅 2 𝑣 2 * 계측용 증폭기(Instrumentation Amplifier) - + 𝑣 1 𝑣 2 비를 맞춰주기 위해 가변저항 사용 𝑣 𝑜 = 𝑅 2 𝑅 1 𝑣 2 − 𝑣 1

Amplifier 종류 𝑣 𝑜 =−𝑅𝐶 𝑑 𝑣 𝑖 𝑑𝑡 𝑣 𝑖 𝑣 𝑜 𝐶 𝑅 6. Differentiator (미분기) 𝑖 1 =𝐶 𝑑 𝑣 𝑖 𝑑𝑡 𝑖 2 = 𝑣 𝑜 𝑅 𝑖 1 + 𝑖 2 =0 𝑣 𝑜 =−𝑅𝐶 𝑑 𝑣 𝑖 𝑑𝑡 𝑣 𝑖 𝑣 𝑜 𝑖 1 𝑖 2 𝐶 𝑅 - + 0𝑉

Amplifier 종류 𝐶 𝑅 𝑣 𝑜 =− 1 𝑅𝐶 0 𝑡 𝑣 𝑖 𝑑𝑡 + 𝑣 𝑜 (0) 𝑣 𝑖 𝑣 𝑜 7. Integrator (적분기) 𝑖 1 = 𝑣 𝑖 𝑅 𝑖 2 =𝐶 𝑑 𝑣 𝑜 𝑑𝑡 𝑖 1 + 𝑖 2 =0 𝑣 𝑜 =− 1 𝑅𝐶 0 𝑡 𝑣 𝑖 𝑑𝑡 + 𝑣 𝑜 (0) 𝑣 𝑖 𝑣 𝑜 𝑖 1 𝑖 2 𝐶 𝑅 - + 0𝑉

Charged particle Free electron and hole ( mobile ) Unbounded ion and molecule ( mobile ) Bounded atom and molecule ( immobile ) Polar molecule ( not charged, immobile )

Coulomb’s law 𝐹 𝑟 2 = 1 4𝜋𝜀 𝑄 ∙ 𝑄 𝑟 𝑟 2 𝑎 𝑟 𝐹 𝑟 2 = 1 4𝜋𝜀 𝑄 ∙ 𝑄 𝑟 𝑟 2 𝑎 𝑟 𝐸 = 𝐹 𝑄 𝑟 = 1 4𝜋𝜀 𝑄 𝑟 2 𝑎 𝑟 ( 𝐸 : 그 위치에서 단위전하가 받는 힘) Q, m, 𝑟 𝑄 𝑟 , 𝑟 2

Coulomb’s law 𝑊=− −∞ 𝑟 𝑄 𝑟 ∙ 𝐸 𝑟 𝑑 𝑟 𝑊=− −∞ 𝑟 𝑄 𝑟 ∙ 𝐸 𝑟 𝑑 𝑟 𝑉= 𝑊 𝑄 𝑟 = −∞ 𝑟 𝐸 𝑑 𝑟 ⇒𝑉 𝑟 1 −𝑉 𝑟 2 =− 𝑟 2 𝑟 1 𝐸 𝑑 𝑟 −𝛻𝑉= 𝐸 ( 𝛻𝑉= 𝜕𝑉 𝜕𝑥 𝑎 𝑥 + 𝜕𝑉 𝜕𝑦 𝑎 𝑦 + 𝜕𝑉 𝜕𝑧 𝑎 𝑧 )

Resister 𝐹 =𝑞 ∙ 𝐸 =𝑞 ∙𝐸 𝑎 𝑥 =𝑚 𝑎 𝑉 𝑑 = 𝜇 𝐸 𝐹 =𝑞 ∙ 𝐸 =𝑞 ∙𝐸 𝑎 𝑥 =𝑚 𝑎 𝑉 𝑑 = 𝜇 𝐸 Volume charge density = 𝜌 𝑟 𝐶 𝑚 3 𝑑𝑄= 𝜌𝑆 𝑉 𝑑 ∆𝑡= 𝜌𝑆𝜇𝐸∆𝑡 𝐼= 𝑑𝑄 𝑑𝑡 = 𝜌𝑆𝜇𝐸 𝐸= 𝑉 𝐿 = 𝜌𝑆𝜇 𝑉 𝐿 = 𝜎 𝑆 𝐿 𝑉 (𝜎= 도전율) 𝑉 𝐼 = 1 𝜎 𝐿 𝑆 =𝑅 𝐸 =𝐸 𝑎 𝑥 S 𝑞 L

Resister + - V R 𝑉=𝑅∙𝑖 𝑣 𝑡 =𝑉 cos 𝑤𝑡 𝑖 𝑡 = 𝑉 𝑅 cos 𝑤𝑡 Drift velocit는 매우 느리지만 저항 속 전하가 동시에 움직이기 때문에 free electro이 빨리 튀어 나온다. => 전류는 빠르게 흐른다. + - V R

capacitor 𝐶= 𝜀𝑆 𝑑 , 𝑄=𝐶𝑉 𝑖 𝑡 = 𝑑𝑄(𝑡) 𝑑𝑡 =𝐶 𝑑𝑣(𝑡) 𝑑𝑡 (Displacement current) 전압의 극성을 바꿔주면 커패시터 주변에 전류가 흐르다. But. DC에서는 전류가 흐르지 않는다.(저항∞) 𝑣 𝑡 =𝑉 cos 𝑤𝑡 𝑖 𝑡 =𝑤𝐶𝑉 sin 𝑤𝑡 =𝑤𝐶𝑉 cos (𝑤𝑡+ 𝜋 2 ) 전류는 전압과 위상차가 𝜋 2

Complex exponential 𝑟 cos 𝑤𝑡 +𝑗𝑟 sin 𝑤𝑡 =𝑟 𝑒 𝑗𝑤𝑡 (오일러 공식) 허수 2𝜋 𝑇 =2𝜋𝑓=𝑤 (각주파수) 𝜃=𝑤𝑡 (단위 rad/s) (𝑟 cos 𝜃, 𝑟 sin 𝜃 ) (𝑟 cos 𝑤𝑡, 𝑟 sin 𝑤𝑡 ) r 𝜃 실수 허수 𝑟 cos 𝑤𝑡 +𝑗𝑟 sin 𝑤𝑡 =𝑟 𝑒 𝑗𝑤𝑡 (오일러 공식) (𝑟 cos 𝑤𝑡, 𝑟 sin 𝑤𝑡 ) 실수