전자 회로 1 lecture 3 (op-amp ii)
DESCRIPTION
전자 회로 1 Lecture 3 (Op-Amp II). 2009. 03. 임한조 아주대학교 전자공학부 hanjolim @ajou.ac.kr. 이 강의 노트는 전자공학부 곽노준 교수께서 08.03 에 작성한 것으로 노트제공에 감사드림. Overview. Reading: Bode plot (frequency response) 에 관한 자료 Sedra & Smith Chapter 2.5~2.8 Outline Non-ideal OP-AMP 성질 Integrator/Differentiator. - PowerPoint PPT PresentationTRANSCRIPT
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전자 회로 1Lecture 3 (Op-Amp II)
2009. 03.임한조
아주대학교 전자공학부[email protected]
이 강의 노트는 전자공학부 곽노준 교수께서 08.03 에 작성한 것으로 노트제공에 감사드림 .
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March, 2008 Nojun Kwak 2
Overview
Reading: Bode plot (frequency response) 에 관한 자료 Sedra & Smith Chapter 2.5~2.8
Outline Non-ideal OP-AMP 성질 Integrator/Differentiator
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March, 2008 Nojun Kwak 3
Frequency response
Transfer function (1st order): T(jw) = 1/(1+jw/w0)
Low pass, 3dB freq (in rad/sec) = w0, f0 = w0/2π T(jw) = 1/(1+w0/jw) = jw/(jw+w0)
High pass, 3dB freq (in rad/sec) = w0, f0 = w0/2π
Freq. response 와 Transfer function 과의 관계 Vin = cos(wt) Vout = Acos(wt+φ), A>0 Re[exp(jwt)] Re[A exp(j(wt+φ))] = Re[A exp(jφ) exp(jwt)] Phasor: 1 A exp(jφ) = T(jw)
A = gain, φ = phase A(w) = |T(jw)|, φ(w) = T(jw)∠ Gain 과 phase 는 frequency w 의 함수
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March, 2008 Nojun Kwak 4
Bode Plot
Transfer function 을 w 에 따라 그린 2 개의 그림 Magnitude: A(w) (in dB), 즉 = 20log(A(w)) = 20log(|T(jw)|) Phase: φ(w) = T(jw) (in degree or radian)∠ x 축 : freq (log scale)
Example1 (LP) T(jw) = 1/(1+jw) w0 = 1 (3dB freq.)
T(jw0) = 1/(1+j)
|T(jw0)| = = -3dB
∠T(jw0) = -45 deg.
-40
-30
-20
-10
0
Mag
nitu
de (
dB)
10-2
10-1
100
101
102
-90
-45
0
Pha
se (
deg)
Bode Diagram
Frequency (rad/sec) = w0
-3dB
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March, 2008 Nojun Kwak 5
Example 2 (HP) T(jw) = jw/(jw+1) w0 = 1 (3dB freq.)
T(jw0) = j/(1+j)
|T(jw0)| = = -3dB
∠T(jw0) = +45 deg.
-60
-50
-40
-30
-20
-10
0
Mag
nitu
de (
dB)
10-2
10-1
100
101
102
0
45
90P
hase
(de
g)
Bode Diagram
Frequency (rad/sec)
= w0
-3dB
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March, 2008 Nojun Kwak 6
Bode plot 손으로 그리기 Magnitude
3dB freq 에서 꺽는다 . freq 가 10 배 될때마다 +-20dB 의 기울기로 마지막으로 분자 / 분모를 합성
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March, 2008 Nojun Kwak 7
Phase
3dB freq. (w0) 에서 +-45 도가 되도록 점을 찍고 0.1w0 와 10w0 를 직선으로 연결한다 . 마지막으로 분자 분모를 합성
jw
1/jw
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March, 2008 Nojun Kwak 8
Non-ideal characteristics of OP-AMP
Finite open-loop gain A Virtual short circuit 이 더 이상 정확하지 않음
Finite bandwidth Frequency response 가 frequency 에 따라 다름 즉 open-loop gain A 가 w 의 함수
Non-zero common mode gain Vout 에 Common mode 의 영향이 있다 . CMRR 이 더 이상 무한대가 아님
Rin ≠inf. / Rout ≠ 0 Output saturation: |Vout| < Vlimit
But …
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March, 2008 Nojun Kwak 9
Finite open loop gain A and BW 지금까지 우리는 open loop bandwidth 가 무한대라고 생각했다 . ( 즉 모든
주파수에서 A 가 일정하다고 가정했다 .) 그러나 실제로는 그렇지 않다 . 일반적으로 high frequency 에서는 A 가
작아지는 다음과 같은 특성을 보인다 .
0AA( ) = (2.25)
1 + / b
jj
Unity gain bandwidth
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March, 2008 Nojun Kwak 10
Finite open loop gain A and BW
Single time constant LP filter 로 나타낼 수 있음
wb 보다 훨씬 큰 주파수에서 gain 을 다음과 같이 근사화할 수 있음
Unity-gain bandwidth wt
다음 식을 이용하면 어떤 주파수에서라도 gain 을 계산하기가 쉽다 .
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March, 2008 Nojun Kwak 11
Closed-loop OP-AMP 의 주파수 응답 Closed-loop gain (of non-ideal inverting conf.)
만약 A0 >> 1+R2/R1 라면 다음과 같이 근사화가 가능
따라서 , closed-loop gain 의 주파수 응답은 에서 -20dB/dec 의 기울기로 줄어들기 시작함 .
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March, 2008 Nojun Kwak 12
Gain-Bandwidth Tradeoff
w w w
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March, 2008 Nojun Kwak 13
Gain Bandwidth Product (GBP)
OP-AMP 를 사면 주어지는 값
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March, 2008 Nojun Kwak 14
Output Saturation
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March, 2008 Nojun Kwak 15
Slew Rate (BW limited)
Slew = 썰매 , 미끄러지다 , 비틀다 , 회전하다 . Input 이 빨리 변하더라도 output 은 일정 속도 이상으로
변할 수 없는 성질 .
Finite open loop op-amp bandwidth 때문에 발생 자세한 것은 9 장에서 다루어짐
max
SR = (2.38)Od
dx
V 1 (2.39)
V 1 /O
i ts
( ) V(1 ) (2.40)t tO t e
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March, 2008 Nojun Kwak 16
Slew Rate (BW limited)
In the linear region, when the input doubles, the output and the output slope also double. However, when the input is large, the op amp slews so the output slope is fixed by a constant current source charging a capacitor.
This further limits the speed of the op amp.
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March, 2008 Nojun Kwak 17
Slew Rate: Examples
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March, 2008 Nojun Kwak 18
Full-power Bandwidth
iV sinI t
iV cosIdt
dt
maxVM o SR
max
(2.41)2 VM
o
SRf
maxV V (2.42)Mo o
Full-power BW:
Max. undistorted output:
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March, 2008 Nojun Kwak 19
DC offset (Offset voltage)
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March, 2008 Nojun Kwak 20
DC offset (Offset voltage) Modeling & measuring offset voltage
Problems: limited output swing Solution: ac coupling (dc blocking) by capacitor
HPF
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March, 2008 Nojun Kwak 21
Input Bias & Offset Currents
1 2
2B B
B
I II
1 2OS B BI I I
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March, 2008 Nojun Kwak 22
Solution to bias & offset current
2 3 2 1 2 3 1V ( / ) (2.45)O B B BI R R I I R R
2 3 2 1V (1 / )O BI R R R R
2 1 23
2 1 1 2
(2.46)1 /
R R RR
R R R R
• Input bias current 의 효과를 줄이기 위해서 양쪽 dc 저항을 같게 만들어 주어야 한다 . (inverting 이나 non-inverting node 바라본 )
2V (2.47)O OSI R
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March, 2008 Nojun Kwak 23
Inverting Integrator (Miller integrator)
sCRVV
in
out
11
1 dtVCR
V inout
11
1
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March, 2008 Nojun Kwak 24
Inverting Integrator (Miller integrator)
90 (2.53)
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March, 2008 Nojun Kwak 25
DC problems in miller integrator
Voltage offset
Current offset
Ever increasing
Ever increasing
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March, 2008 Nojun Kwak 26
Solution: large resistor RF
V ( ) /
V ( ) 1o F
i F
s R R
s sCR
• @DC (w=0): finite gain
• Tradeoff between - signal performance - DC performance
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March, 2008 Nojun Kwak 27
Differentiator
( )( ) (2.56)I
O
d tt CR
dt
• 일반적으로 잘 안 쓰인다 . why?
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March, 2008 Nojun Kwak 28
Summary
Bode diagram – frequency response Magnitude / phase: 가로축은 log scale
Finite open-loop gain & bandwidth ( 수십 Hz) Low pass 특성 : Gain-bandwidth product = constant (A0wb = const.)
Output saturation Slew rate DC problems: Voltage offset / bias & offset current Integrator (Miller) / Differentiator