전자 회로 1Lecture 2 (Op-Amp I)

2009. 03.임한조

아주대학교 전자공학부hanjolim@ajou.ac.kr

이 강의 노트는 전자공학부 곽노준 교수께서 08.03 에 작성한 것으로 노트제공에 감사드림 .

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Overview

Reading: Sedra & Smith Chapter 2.1~2.4 Chap. 2.4.2 is omitted in this lecture. (Self study needed)

Outline Ideal Op-Amp Inverting/non-inverting configuration Difference Amp.

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OP AMP

OP AMP = Operational Amplifier ( 연산증폭기 ) + / - / 미분 / 적분 등의 연산이 가능

Symbols

최소한 3 개의 터미널이 있음 (2 input / 1 output) DC power 도 필요 (1 개 혹은 2 개 : V+ / V-)

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Ideal Op-Amp

TABLE 2.1 Characteristic of the ideal Op Amp

1. Infinite input impedance

2. Zero output impedance

3. Zero common-mode gain or, equivalently, infinite common-mode rejection

4. Infinite open-loop gain A

5. Infinite bandwidth

6. Ideal voltage controlled voltage source

• OP-AMP 는 input signal 의 차이 (v2-v1)를 증폭해서 output 에 나타낸다 .

• 즉 v0 = A (v2-v1): voltage amplifier

• A: differential gain open-loop gain

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Common & differential mode signals

2 1 (2.1)Id

1 2

1( ) (2.2)

2Icm

1 /2 (2.3)Icm Id

2 /2 (2.4)Icm Id

• Common-mode input signal:

• Differential input signal:

• Infinite Common-mode rejection: v1 과 v2 에 공통으로 있는 성분을 전혀 증폭하지 않는다 .

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Inverting configuration (1)

Closed-loop gain G=Vo/Vi A 가 무한대라고 가정하면 , V1-V2 = Vo/A = 0

Virtual short circuit V2 = 0 V1 = 0 이므로 V1 을 virtual ground 라고도

함 .

Negative feedback

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Inverting configuration (2)

11

1 1 1

0I I IiR R R

0 1 1 2 20 I

I

i R RR

0 2

1I

R

R

R1 과 R2 의 비율을 변화시킴으로써 closed-loop gain G 를 변화시킬 수 있다 . (G 는 A 와 independent; if A is infinite)

G =

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Finite open-loop gain

A 를 무한대로 만드는 것은 물리적으로 불가능

What if A is finite? Virtual ground 대신 terminal

의 전압이 – Vo/A 라고 가정

Ainfinity G-R2/R1

V10 Virtual ground 성립 Open loop gain A 의 영향을

줄이기 위해

0 01

1 1

( / A) / AI IiR R

0 0 00 1 2 2

1

/ A

A AIi R RR

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Input resistance (closed-loop)

Ideal op-amp 를 가정하면 (A= infinity) input resistance:

What if A = finite? solve

11 1/I I

iI

R Ri R

High gain G 를 얻기 위해서는 R1 이 작아져야 한다 . (R2 를 크게 할 수는 없기 때문에 )

small input resistance problem (solution in Example 2.2)

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Output resistance

Output resistance 를 구하기 위해서는 Input voltage 를 0 으로 하고 강제로 output 에

전압을 준 후 Vo/Io 를 구한다 .

그림 2.6(a) 에서는 Roa = 0 작은 output resistance (Good!)

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Model of inverting configuration

Closed-loop inverting configuration 은 다음과 같은 voltage controlled voltage source (voltage amplifier) 로 모델이 가능

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Inverting config. with general impedance

R1, R2 Z1, Z2 로 대체

Z1, Z2 를 바꿔가면서 다음을 만들 수 있다 . Integrator (Chap. 2.8) Differentiator (Chap. 2.8) Summer (Chap. 2.2.4) …

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Examples: The Weighted Summer

1 2 3 41 2 3 4

(2.8)a c a c c c

b b

R R R R R R

R R R R R R

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Non-inverting configuration

No inversion ! Inverting conf: G = - R2/R1

Virtual short circuit (v2 = v1)

0 0 for A = AId

0 21

II R

R

0 2

1

1 (2.9)I

R

R

11 0

1 2

(2.10)R

R R

Gain

Q1. Input Resistance?Q2. Output Resistance?

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Finite open loop gain

If A >> 1+R2/R1 G = 1+R2/R1

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Voltage follower (unity buffer)

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Difference Amplifier (two sources)

0 A A (2.13)d Id cm Icm

ACMRR = 20log (2.14)

Ad

cm

• Common mode rejection ratio:

Analysis either by • Brute force ( 힘으로 ~)• Superposition ( 머리로 ~)

Solution:

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Example (Superposition): Single Diff. Amp.

= +

21 1

1O I

R

R 4 2 2

2 2 23 4 1 1

1O I I

R R R

R R R R

By superposition: 2 22 1

1 1

(2.16)O I I Id

R R

R R

2

1

A (2.17)d

R

RDifferential gain:

3 1 4 2 and R R R R Usual selection:

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41

1 4 3

3

4 3 1

1

1 (2.18)

Icm Icm

Icm

Ri

R R R

R

R R R

42 2

4 3O Icm

Ri R

R R

34 2

4 3 1 4 3

34 2

4 3 1 4

= 1

O Icm Icm

Icm

RR R

R R R R R

RR R

R R R R

A 0cm

34 2

4 3 1 4

A 1 (2.19)Ocm

Icm

RR R

R R R R

12 (2.20)idR RProblem: Low input resistance (see 2.4.2)Good!

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Summary

Characteristic of the ideal Op Amp (Open loop)

1. Infinite input impedance

2. Zero output impedance

3. Zero common-mode gain or, equivalently, infinite common-mode rejection

4. Infinite open-loop gain A

5. Infinite bandwidth

6. Ideal voltage controlled voltage source

Characteristic of the ideal Op Amp

(Closed loop – feedback)

1. Inverting configuration

G = -R2/R1, Rin = R1, Ro = 0

Applications: summer, integrator,

differentiator, …

2. Non-inverting configuration

G = 1+R2/R1, Rin = inf., Ro = 0

Applications: unity buffer …

3. Difference amp. (R2/R1 = R4/R3)

G = R2/R1, CMRR=inf.

Rin = 2*R1 (if R1=R3, R2=R4), Ro = 0

* Finite open loop gain (A) should also be noted. But in most cases, infinite gain model is enough.