Download Operational Amplifiers

電路學(一)
Chapter 5
Operational Amplifiers
Operational Amplifiers Chapter 5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
Operational Amplifiers
Ideal Op Amp
Inverting Amplifier
Noninverting Amplifier
Summing Amplifier
Difference Amplifier
Cascaded Op Amp Circuits
Applications
5.1 Operational Amplifiers (1)
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 (2)
The op amp is an electronic unit that behaves
like a voltage-controlled voltage source.
1.
2.
3.
4.
5.
The
The
The
The
The
inverting input, pin 2
noninverting input, pin 3
output, pin 6
positive power supply V+, pin 7
negative power supply V–, pin 4
5.1 Operational Amplifiers (3)
vo  Avd  A(v2  v1 )
A is called the open-loop voltage gain.
5.1 Operational Amplifiers (4)
parameter
Typical range
Open-loop gain, 105 to 108
A
Input resistance, 105 to 1013 
Ri
Output
resistance, Ro
10 to 100 
Supply voltage,
Vcc
5 to 24 V
Ideal values
∞
∞
0
5.1 Operational Amplifiers (5)
Example 1 A 741 op amp has an open-loop voltage gain of 2105,
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)
An ideal op amp is an amplifier with
1.Infinite open-loop gain, A≈∞
2.Infinite input resistance, Ri ≈∞
3.Zero output resistance, Ro≈0.
Two important characteristics
of ideal op amp
i1  0, i2  0
v1  v2
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)
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。
vi  v1 v1  vo
i1  i2 

R1
Rf
v1  v2  0
vo  
Rf
R1
vi
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)
Example 4. Determine vo in the op amp circuit .
(p.183)
5.3 Inverting Amplifier (4)
Example 5. (a) Show that for converter in the figure (a)
vo
 R
is
(b) Show that for converter in the figure (a)
(p.183)
 R3 R3 
vo
 R1  1 
 
is
R1 R2 

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。
i1  i2
0  v1 v1  vo


R1
Rf
but
v1  v2  vi
Rf

vo   1 
R1



 vi

vi vi  vo

R1
Rf
5.4 Noninverting Amplifier (2)
R f  0 and/or R1  
vo  vi
voltage follower 電壓追隨器
buffer 緩衝器
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)
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。
i  i1  i2  i3
v1  va
v2  va
i1 
, i2 
R1
R2
v3  va
va  vo
i3 
, i
R3
Rf
Rf
Rf 
 Rf
vo   
v1 
v2 
v3 
R2
R3 
 R1
5.5 Summing Amplifier (2)
Example 7. Calculate vo and io in the op amp circuit.
(p.186)
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。
Applying KCL to node a
v1  va va  vo

R1
R2
Applying KCL to node b
v 2  v a vb  0

R3
R4
va  vb
 R2
 R4
R2
 vo    1 
v2  v1
R1
 R1
 R3  R4
5.6 Difference Amplifier (2)
(1  R2 / R1 )
R2
vo 
v2 
v1
(1  R3 / R4 )
R1
vo = 0 when v1 = v2
R1 R3

R2 R4
R2
vo 
( v2  v1 )
R1
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)
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 singlepackage units. Show that
(p.189)
R2  2 R3 
vo 
1
 ( v2  v1 )
R1 
R4 
5.6 Difference Amplifier (5)
Example 10. Obtain io in the instrumentation amplifier
(p.190)
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
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。
A=A1A2A3
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)
Example 12. If v1 = 1 V and v2 = 2 V, find vo the op amp circuit.
(p.192)
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。
Vo 
Rf
R1
V1 
Rf
R2
V2 
Rf
R3
V3 
MSB most significant bit
最大有效位元
LSB least significant bit
最小有效位元
Rf
R4
V4
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)
Vo 
Rf
V1 
Rf
V2 
Rf
V3 
Rf
V4
R1
R2
R3
R4
 V1  0.5V2  0.25V3  0.125V4
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。