Ch.5 Operational Amplifiers
Introduction
3
• OP Amp : an active circuit element designed to perform
mathematical operations of addition, subtraction,
multiplication, division, differentiation, and integration
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DIP package Pin Configuration
Circuit Symbol
Introduction
4
• Powering of op amp
op amp의 𝑉+ 및 𝑉− 양단자에 ±15V, ±12V 또는 +5V, 0V
전압 인가
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Introduction
5
• op amp의 등가회로
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입력단 : 𝑣𝑑 = 𝑣+ − 𝑣−
출력단 : ሻ𝑣o = 𝐴𝑣𝑑 = 𝐴(𝑣+ − 𝑣− ,
단 A : open-loop voltage gain
op amp 일반적인 파라미터
Introduction
6
• 출력의 포화특성 : 𝑣𝑜는 𝑉𝐶𝐶 보다 큰 값을 가질 수 없음
(과목에서는 non-saturation 영역, 즉 선형영역만 취급)
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1. Positive saturation: 𝑣o = 𝑉𝐶𝐶
2. Linear region : −𝑉𝐶𝐶 ≤ 𝑣o(= 𝐴𝑣𝑑ሻ ≤ 𝑉𝐶𝐶
3. Negative saturation: 𝑣𝑜 = −𝑉𝐶𝐶
Introduction
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Example 5.1
The op-amp in the following figure has an open-loop V-gain of 2x105, input resistance of 2𝑀𝛺 and output resistance of 50𝛺. Find the closed-loop gain Τ𝑣o 𝑣𝑠. Determine current 𝑖 when 𝑣𝑠=2V.
Ideal Op-Amp
8
• Ideal Op-Amp의 정의
- open-loop gain : 𝐴 = ∞
- input resistance : 𝑅𝑖𝑛 = ∞
- output resistance : 𝑅𝑜𝑢𝑡 = 0
• Ideal op amp의 특성
- 입력단자에 유입되는 전류는 0 : 𝑖1 = 0, 𝑖2 = 0
- 두 입력단자의 전압차는 0 : 𝑣𝑑 = 𝑣2 − 𝑣1 ≈ 0 or 𝑣1 = 𝑣2• 대부분의 경우 Ideal op amp의 가정하에 문제를 풀어도
현실적으로 문제가 없음
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Ideal Op-Amp
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Example 5.2
Calculate the closed-loop gain Τ𝑣o 𝑣𝑠 and find 𝑖0 when 𝑣𝑠 = 1V using ideal op amp model.
Inverting Amplifier
10
• op amp의 (-)단자에 입력된 신호를 증폭하는 회로
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1
f
o i
Rv v
R
inverting amplifier
등가회로
Inverting Amplifier
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Example 5.3
If 𝑣𝑖 = 0.5V, calculate: (a) the output voltage 𝑣o, and (b) the current in the 10𝑘𝛺 resistor.
Inverting Amplifier
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Example 5.4
Determine 𝑣𝑜 in the following op amp circuit
Inverting Amplifier
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Practice Problem 5.4 (Current-to-Voltage Converter)
(a) Show that for the converter in Fig. (a) is Τ𝑣o 𝑖𝑠 = −𝑅
(b) Show that for the converter in Fig. (b) is 3 31
1 2
1o
s
v R RR
i R R
Noninverting Amplifier
14
• op amp의 (+)단자에 입력된 신호를 증폭하는 회로
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1 2
1 2
1
0
1
i
i i o
f
o i
v v v
v v v
R R
Rv v
R
noninverting amplifier
Noninverting Amplifier
15
• Voltage follower (𝑅𝑓 = 0 and/or 𝑅1 = ∞)
- 매우 높은 입력임피던스를 가지고 있어, 회로간의 간섭
을 차단하는 용도로 사용
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Voltage follower(𝑉𝑜 = 𝑉𝑖)
Typical application of voltage follower
Noninverting Amplifier
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Example 5.5
For the following op amp circuit, calculate the output voltage 𝑣𝑜 by superposition method and KCL:
Summing Amplifier
17
• Inverting amp의 변형회로를 이용하여 Addition 기능구현
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Summing amplifier
1 2
1 2
By superposition
f f f
o n
n
R R Rv v v v
R R R
Summing Amplifier
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Example 5.6
Calculate 𝑣𝑜 and 𝑖𝑜 in the following op amp circuit
Difference Amplifier
19
• op amp의 양단의 전압차이를 계산하는 회로
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Difference amplifier
22 1 1
1
2 41 2 2
1 3 4
1 2
2 4 22 1
1 3 4 1
2 1 2 22 1
1 3 4 1
32 12 1
1 2 4
By superposition
: off
: off 1
1
1 /
1 /
( ) if
o
o
o o o
Rv v v
R
R Rv v v
R R R
v v v
R R Rv v
R R R R
R R R Rv v
R R R R
RR Rv v
R R R
Difference Amplifier
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Example 5.7
Design an op amp circuit with input 𝑣1 and 𝑣2 such that
𝑣𝑜 = −5𝑣1 + 3𝑣2.
Method 1 : Use difference amplifier
Method 2 : Use two op amps : summer and inverting amplifier
Difference Amplifier
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Example 5.8
Find the relationship between input and output of the following circuit :
Cascade Op Amp Circuits
22
• 여러 개의 op amp를 직병렬로 연결하여 복잡한 식 구현
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Cascade Op Amp Circuits
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Example 5.9
Find 𝑣𝑜 and 𝑖𝑜 in the following circuit:
Cascade Op Amp Circuits
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Example 5.10
If 𝑣1 = 1V and 𝑣2 = 2V, find 𝑣𝑜 in the following op amp circuit:
Digital-to-Analog Converter
25
• Digital input을 Analog output으로 변환하는 회로
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1 2 3 4
1 2 3 4
1 2 3
1 2 3 4
By superposition,
( 2 2 2 )
f f f f
o
R R R Rv v v v v
R R R R
v v v v
4-bit DAC (Vi는 0 또는 1)
2 3
1 2 1 3 1 4 1, 2 , 2 , 2fR R R R R R R R
Digital-to-Analog Converter
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Example 5.12
Let 𝑅𝑓 = 𝑅1 = 10𝑘𝛺, 𝑅2 = 20𝑘𝛺, 𝑅3 = 40𝑘𝛺 and 𝑅4 = 80𝑘𝛺. Obtain
the analog output for binary inputs [0000], [0001], [0010], … , [1111].
Assignment
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Chapter 5
5.10, 5.13, 5.18, 5.23, 5.29, 5.41, 5.46, 5.48, 5.63, 5.71
Due date :