Chapter 5Chapter 5

Operational AmplifiersOperational Amplifiers

電路學電路學 (( 一一 ))

Operational Amplifiers - Operational Amplifiers - Chapter 5Chapter 5

5.1 Operational Amplifiers5.2 Ideal Op Amp5.3 Inverting Amplifier5.4 Noninverting Amplifier5.5 Summing Amplifier5.6 Difference Amplifier5.7 Cascaded Op Amp Circuits5.8 Applications

Operational amplifier, op amp, 運算放大器

An op amp is an active circuit element designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation, and integration.

5.1 Operational Amplifiers (1)5.1 Operational Amplifiers (1)

5.1 Operational Amplifiers (2)5.1 Operational Amplifiers (2)

The op amp is an electronic unit that behaves like a voltage-controlled voltage source.

1. The inverting input, pin 22. The noninverting input, pin 33. The output, pin 64. The positive power supply V+, pin 75. The negative power supply V–, pin 4

5.1 Operational Amplifiers (3)5.1 Operational Amplifiers (3)

2 1( )o dv Av A v v

A is called the open-loop voltage gain.

parameter Typical range Ideal values

Open-loop gain, A

105 to 108 ∞

Input resistance, Ri

105 to 1013 ∞

Output resistance, Ro

10 to 100 0

Supply voltage, Vc

c

5 to 24 V

5.1 Operational Amplifiers (4)5.1 Operational Amplifiers (4)

5.1 Operational Amplifiers (5)5.1 Operational Amplifiers (5)

Example 1 A 741 op amp has an open-loop voltage gain of 2105, input resistance of 2 M, and output resistance of 50 . The op amp is used in the circuit, find the closed-loop gain vo/vs. Determine current I when vs = 2 V.

(p.178)

5.2 Ideal Op Amp (1)5.2 Ideal Op Amp (1)

An ideal op amp is an amplifier with1. Infinite open-loop gain, A≈∞2. Infinite input resistance, Ri ≈∞3.Zero output resistance, Ro≈0.Two important characteristics of ideal op amp

1 20, 0i i

1 2v v

5.2 Ideal Op Amp (2)5.2 Ideal Op Amp (2)

Example 2. Using ideal op amp model, find the closed-loop gain vo/vs in the circuit. Determine current I when vs = 2 V.

(p.181)

5.3 Inverting Amplifier (1)5.3 Inverting Amplifier (1)

1 11 2

1

1 2 0

i o

f

v v v vi i

R R

v v

1

fo i

Rv v

R

Inverting amplifier 反相放大器，其重要特徵是其輸入信號及迴授信號皆接到反相輸入端。

5.3 Inverting Amplifier (2)5.3 Inverting Amplifier (2)

Example 3. If vi = 0.5 V, calculate: (a) the output voltage vo, and (b) the current in the 10-k resistance.

(p.182)

5.3 Inverting Amplifier (3)5.3 Inverting Amplifier (3)

Example 4. Determine vo in the op amp circuit .(p.183)

5.3 Inverting Amplifier (4)5.3 Inverting Amplifier (4)

Example 5. (a) Show that for converter in the figure (a)

(b) Show that for converter in the figure (a)

(p.183)

o

s

vR

i

3 31

1 2

1o

s

v R RR

i R R

5.4 Noninverting Amplifier (1)5.4 Noninverting Amplifier (1)Noninverting amplifier 非反相放大器，是將其輸入信號接到非反相輸入端。

111 2

1

0 o

f

v vvi i

R R

1 21

i i oi

f

v v vv v v

R R

but

1

1 fo i

Rv v

R

5.4 Noninverting Amplifier (2)5.4 Noninverting Amplifier (2)

10 and/orfR R

o iv v

voltage follower 電壓追隨器buffer 緩衝器

5.4 Noninverting Amplifier (3)5.4 Noninverting Amplifier (3)

Example 6. For the op amp circuit, calculate the output voltage vo.

(p.184)

METHOD 1 Using superposition

METHOD 2 Applying KCL

5.5 Summing Amplifier (1)5.5 Summing Amplifier (1)Summing amplifier 總和放大器，是一個結合多個輸入產生之輸出為輸入之加權總和之放大器線路。

1 2 3

1 21 2

1 2

33

3

,

,

a a

a a o

f

i i i i

v v v vi i

R Rv v v v

i iR R

1 2 31 2 3

ff fo

R R Rv v v v

R R R

5.5 Summing Amplifier (2)5.5 Summing Amplifier (2)

Example 7. Calculate vo and io in the op amp circuit.

(p.186)

5.6 Difference Amplifier (1)5.6 Difference Amplifier (1)Difference amplifier 差分放大器，是一個將兩個輸入信號之差量放大且排拒兩輸入信號共同量之放大器線路。

1

1 2

a a ov v v vR R

Applying KCL to node a

2

3 4

0a bv v vR R

Applying KCL to node b

2 4 22 1

1 3 4 1

1a b o

R R Rv v v v v

R R R R

5.6 Difference Amplifier (2)5.6 Difference Amplifier (2)

2 1 22 1

3 4 1

(1 / )(1 / )o

R R Rv v v

R R R

vo = 0 when v1 = v2

31

2 4

RRR R

22 1

1

( )o

Rv v v

R

5.6 Difference Amplifier (3)5.6 Difference Amplifier (3)

Example 8. Design an op amp circuit with inputs v1 and v2 such that

vo = − 5 v1 + 3 v2

(p.188)Design 1 Design 2

5.6 Difference Amplifier (4)5.6 Difference Amplifier (4)

Example 9. An instrumentation amplifier shown in the figure is an amplifier of low-level signals used in process control or measurement applications and commercially available in single-package units. Show that

(p.189)

322 1

1 4

21 ( )o

RRv v v

R R

5.6 Difference Amplifier (5)5.6 Difference Amplifier (5)

Example 10. Obtain io in the instrumentation amplifier

(p.190)

5.7 Cascaded Op Amp Circuits (1)5.7 Cascaded Op Amp Circuits (1)

A cascade connection 串級接法 is a head-to-tail arrangement of two or more op amp circuits such that the output of one is the input of the next

A=A1A2A3

由於 ideal op amp輸入電阻無窮大，輸出電阻為零，所以串級相接時，不會改變個別輸入 -輸出特性。

5.7 Cascaded Op Amp Circuits (2)5.7 Cascaded Op Amp Circuits (2)

Example 11. Obtain vo and io in the instrumentation amplifier

(p.191)

5.7 Cascaded Op Amp Circuits (3)5.7 Cascaded Op Amp Circuits (3)

Example 12. If v1 = 1 V and v2 = 2 V, find vo the op amp circuit.

(p.192)

5.8 Applications (1)5.8 Applications (1)

Digital-to-Analogy Converter (DAC) 數位 - 類比轉換器

將數位輸入訊號轉成類比輸出。

1 2 3 41 2 3 4

ff ffo

R R R RV V V V V

R R R R

MSB most significant bit 最大有效位元LSB least significant bit 最小有效位元

5.8 Applications (2)5.8 Applications (2)

Example 13. In the op amp circuit, let Rf = 10 k, R1 = 10 k, R2 = 20 k, R3 = 40 k, and R4 = 80 k. Obtain the analog output for binary inputs [0000], [0001], [0010],…,[1111].

(p.196)

1 2 3 41 2 3 4

1 2 3 40.5 0.25 0.125

ff ffo

R R R RV V V V V

R R R R

V V V V

5.8 Applications (3)5.8 Applications (3)Instrumentation Amplifiers 儀表放大器

提供輸入級一個緩衝器機制，降低輸入信號與儀表放大器間之負載效應；輸出級為一個差分放大器，提供將差動訊號放大的機制。