Ch.5 Operational Amplifiers

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Ch.5 Operational Amplifiers

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Introduction

3

• OP Amp : an active circuit element designed to perform mathematical operations of addition, subtraction,

multiplication, division, differentiation, and integration

Pusan National University

DIP package Pin

Configuration Circuit Symbol

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Introduction

• 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

입력단 : 𝑣_𝑑 = 𝑣₊ − 𝑣₋

출력단 : 𝑣_o = 𝐴𝑣_𝑑 = 𝐴(𝑣₊ − 𝑣₋ሻ,

단 A : open-loop voltage gain op amp 일반적인 파라미터

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Introduction

• 출력의 포화특성 : 𝑣

_𝑜

는 𝑉

_𝐶𝐶

보다 큰 값을 가질 수 없음 (과목에서는 non-saturation 영역, 즉 선형영역만 취급)

1. Positive saturation: 𝑣_o = 𝑉_𝐶𝐶 2. Linear region :

−𝑉_𝐶𝐶 ≤ 𝑣_o(= 𝐴𝑣_𝑑ሻ ≤ 𝑉_𝐶𝐶 3. Negative saturation: 𝑣_𝑜 = −𝑉_𝐶𝐶

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Introduction

7 Pusan National University

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 𝑣_oΤ𝑣_𝑠. Determine current 𝑖 when 𝑣_𝑠=2V.

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Ideal Op-Amp

• Ideal Op-Amp의 정의

- open-loop gain : 𝐴 = ∞ - input resistance : 𝑅

_𝑖𝑛

= ∞ - output resistance : 𝑅

_𝑜𝑢𝑡

= 0

• Ideal op amp의 특성

- 입력단자에 유입되는 전류는 0 : 𝑖

₁

= 0, 𝑖

₂

= 0

- 두 입력단자의 전압차는 0 : 𝑣

_𝑑

= 𝑣

₂

− 𝑣

₁

≈ 0 or 𝑣

₁

= 𝑣

₂

• 대부분의 경우 Ideal op amp의 가정하에 문제를 풀어도

현실적으로 문제가 없음

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Ideal Op-Amp

Example 5.2

Calculate the closed-loop gain 𝑣_oΤ𝑣_𝑠 and find 𝑖₀ when 𝑣_𝑠 = 1V using ideal op amp model.

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Inverting Amplifier

• op amp의 (-)단자에 입력된 신호를 증폭하는 회로

1 f

o i

v R v

  R

inverting amplifier

등가회로

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Inverting Amplifier

Example 5.3

If 𝑣_𝑖 = 0.5V, calculate: (a) the output voltage 𝑣_o, and (b) the current in the 10𝑘𝛺 resistor.

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Inverting Amplifier

Example 5.4

Determine 𝑣_𝑜 in the following op amp circuit

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Inverting Amplifier

Practice Problem 5.4 (Current-to-Voltage Converter)

(a) Show that for the converter in Fig. (a) is 𝑣_oΤ𝑖_𝑠 = −𝑅

(b) Show that for the converter in Fig. (b) is ₃ ₃

1

1 2

o 1

s

v R R

i R R R

 

     

 

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Noninverting Amplifier

• op amp의 (+)단자에 입력된 신호를 증폭하는 회로

1 2

1

0

1

i

i i o

f

o i

v v v

R R

v R v

R

 

 

 

 

   

 

noninverting amplifier

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Noninverting Amplifier

15

• Voltage follower (𝑅

_𝑓

= 0 and/or 𝑅

₁

= ∞)

- 매우 높은 입력임피던스를 가지고 있어, 회로간의 간섭 을 차단하는 용도로 사용

Voltage follower

(𝑉_𝑜 = 𝑉_𝑖) Typical application of voltage follower

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Noninverting Amplifier

Example 5.5

For the following op amp circuit, calculate the output voltage 𝑣_𝑜 by superposition method and KCL:

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Summing Amplifier

17

• Inverting amp의 변형회로를 이용하여 Addition 기능구현

Summing amplifier

1 2

By superposition

f f f

o n

n

R R R

v v v v

R R R

 

     

 

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Summing Amplifier

Example 5.6

Calculate 𝑣_𝑜 and 𝑖_𝑜 in the following op amp circuit

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Difference Amplifier

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• op amp의 양단의 전압차이를 계산하는 회로

Difference amplifier

2

2 1 1

1

2 4

1 2 2

1 3 4

1 2

2 4 2

2 1

1 3 4 1

2 1 2 2

2 1

1 3 4 1

3

2 1

1 2 4

By superposition : off

: off 1

1

1 /

( ) if

o

o o o

v v R v

R

R R

v v v

R R R v v v

R R R

v v

R R R R

v v

R R R R

R R R

v v

R R R

  

 

     

  

 

     

  



  

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Difference Amplifier

Example 5.7

Design an op amp circuit with input 𝑣₁ and 𝑣₂ such that 𝑣_𝑜 = −5𝑣₁ + 3𝑣₂.

Method 1 : Use difference amplifier

Method 2 : Use two op amps : summer and inverting amplifier

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Difference Amplifier

Example 5.8

Find the relationship between input and output of the following circuit :

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Cascade Op Amp Circuits

• 여러 개의 op amp를 직병렬로 연결하여 복잡한 식 구현

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Cascade Op Amp Circuits

Example 5.9

Find 𝑣_𝑜 and 𝑖_𝑜 in the following circuit:

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Cascade Op Amp Circuits

Example 5.10

If 𝑣₁ = 1V and 𝑣₂ = 2V, find 𝑣_𝑜 in the following op amp circuit:

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Digital-to-Analog Converter

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• Digital input을 Analog output으로 변환하는 회로

1 2 3 4

1 2 3

1 2 3 4

By superposition,

( 2 2 2 )

f f f f

o

R R R R

v v v v v

R R R R

v

^

v

^

v

^

v

 

      

 

    

4-bit DAC (V_i는 0 또는 1)

2 3

1 _f , 2 2 ,1 3 2 1, 4 2 1

R  R R  R R  R R  R

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Digital-to-Analog Converter

Example 5.12

Let 𝑅_𝑓 = 𝑅₁ = 10𝑘𝛺, 𝑅₂ = 20𝑘𝛺, 𝑅₃ = 40𝑘𝛺 and 𝑅₄ = 80𝑘𝛺. Obtain the analog output for binary inputs [0000], [0001], [0010], … , [1111].

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Assignment

Chapter 5

5.10, 5.13, 5.18, 5.23, 5.29, 5.41, 5.46, 5.48, 5.63, 5.71 Due date :