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 :