1. Operational Amplifiers
電路學(一)
Chapter 5
Operational Amplifiers

2. Operational Amplifiers - Chapter 5
5.2 Ideal Op Amp
5.3 Inverting Amplifier
5.4 Noninverting Amplifier
5.5 Summing Amplifier
5.6 Difference Amplifier
5.7 Cascaded Op Amp Circuits
5.8 Applications

3. 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.

4. 5.1 Operational Amplifiers (2)
The op amp is an electronic unit that behaves like a voltage-controlled voltage source.
The inverting input, pin 2
The noninverting input, pin 3
The output, pin 6
The positive power supply V+, pin 7
The negative power supply V–, pin 4

5. 5.1 Operational Amplifiers (3)
A is called the open-loop voltage gain.

6. 5.1 Operational Amplifiers (4)
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, Vcc
5 to 24 V

7. 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)

8. 5.2 Ideal Op Amp (1) An ideal op amp is an amplifier with
Infinite open-loop gain, A≈∞
Infinite input resistance, Ri ≈∞
Zero output resistance, Ro≈0.
Two important characteristics of ideal op amp

9. 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)

10. 5.3 Inverting Amplifier (1)

11. 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)

12. 5.3 Inverting Amplifier (3)
Example 4. Determine vo in the op amp circuit . (p.183)

13. 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)

14. 5.4 Noninverting Amplifier (1)
but

15. 5.4 Noninverting Amplifier (2)
voltage follower 電壓追隨器
buffer 緩衝器

16. 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

17. 5.4 Noninverting Amplifier (4)
Practice Calculate vo in the circuit
(p.185)

18. 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。
此相當於幾個inverting amplifier疊加的結果

19. 5.5 Summing Amplifier (2)
Example 7. Calculate vo and io in the op amp circuit.
(p.186)

20. 5.6 Difference Amplifier (1)
Applying KCL to node a
Applying KCL to node b
亦可由重疊原理得上式

21. 5.6 Difference Amplifier (2)
vo = 0 when v1 = v2

22. 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

23. 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)

24. 5.6 Difference Amplifier (5)
Example 10. Obtain io in the instrumentation amplifier
(p.190)

25. 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

26. 5.7 Cascaded Op Amp Circuits (2)
Example 11. Obtain vo and io in the instrumentation amplifier
(p.191)
兩個noninverting amplifier串接

27. 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)

28. 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。
MSB most significant bit
最大有效位元
LSB least significant bit
最小有效位元

29. 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)

30. 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。