electric circuits (fall 2016) pingqiang zhou...

Electric Circuits (Fall 2016) Pingqiang Zhou

Announcements

• No discussion/lab session on Oct. 8 (SAT) & Oct. 9 (SUN)

Lab3 for week 5 (starting from Oct. 10).

Discussion on circuit theorem in week 5.

• Review solutions to first-order ODEs during holiday

1Lecture 4


请务必遵守学术道德规范！

• 单次作业或者实验抄袭

抄袭与被抄袭者该次作业/实验均计零分，课程总成绩打九折。

• 累计两次作业或者实验抄袭

抄袭与被抄袭者相应作业/实验计零，课程总成绩均打七折。

• 累计三次作业或实验抄袭者，或者考试作弊者

课程总成绩计零，同时上报信息学院学术委员会公开处理。


Lecture 4

- Operational Amplifiers

9/28/2016

Reading: Chapter 5

Lecture 4 3


Outline

• Operational amplifier (op amp) model

• Ideal op amp

• Inverting op amp

• Noninverting op amp

Voltage follower

• Difference amplifier

• Application: DAC

Lecture 4 4


Brief History

• The Operational Amplifier (op amp) was invented in the

40’s.

Bell Labs filed a patent in 1941.

• Many consider the first practical op amp to be the vacuum

tube K2-W invented in 1952 by George Philbrick.

• Bob Widlar at Fairchild invented the uA702 op amp in

1963.

• Until uA741, released in 1968, op amps became relatively

inexpensive and started on the road to ubiquity.

5Lecture 4

https://en.wikipedia.org/wiki/Operational_amplifier

https://en.wikipedia.org/wiki/Operational_amplifier


Where do You Use Op AMP？

• Audio amplifiers

• Low dropout regulators

• Active filters

• Medical sensor interface

• Baseband receivers

• A/D converters

• Oscillators

• Signal generators

• Hearing aids

6Lecture 4[Source: Berkeley]


The Op Amp

• A basic building block used in analog circuits.

• When combined with resistors, capacitors, and inductors,

can perform various functions:amplification/scaling

sign changing

addition/subtraction/multiplication/division

integration

differentiation

analog filtering

nonlinear functions (exponential, log, sqrt)

• Isolate input from output.

Lecture 4 7[Source: Berkeley]


Analog Computer

8Lecture 4[Source: Alexander]


What are Inside an Op Amp?

• Origins at Fairchild Semiconductor in 1968.

9

Source: http://www.ibiblio.org/kuphaldt/electricCircuits/Semi/SEMI_8.html#xtocid109742.

Lecture 4

http://www.ibiblio.org/kuphaldt/electricCircuits/Semi/SEMI_8.html#xtocid109742


Op Amp Terminals

• Five important terminals

The inverting input

The noninverting input

The output

The positive (+) power supply

The negative (-) power supply

• The rest three terminals

2 Offset Null (Balance)

–May used in auxiliary circuit to

compensate for performance

degradation due to aging etc.

1 No Connection (NC)

– Unused, not connected to the

amplifier circuit.

Lecture 4 10


Powering an Op Amp

• As an active element, the op-amp

requires a power source.

Often in circuit diagrams the power

supply terminals are obscured (ignored).

The supply current cannot be

overlooked.

• Most op-amps use two voltage

sources, with a ground reference

between them.

This gives a positive and negative

supply voltage.

𝑖0 = 𝑖1 + 𝑖2 + 𝑖+ + 𝑖−

Lecture 4 11


Output Voltage

• The voltage output of an op-amp is

proportional to the difference between

the noninverting and inverting inputs

Here, A is called the open loop gain.

Ideally A is infinite. In real devices, it is still

high: 105 to 108.

2 1( )o dv Av A v v

Lecture 4 12

𝑣2

𝑣1


Voltage Saturation

• Is the output voltage unlimited?

𝑣0 =

−𝑉𝑐𝑐 𝐴𝑣𝑑 < −𝑉𝑐𝑐𝐴𝑣𝑑 −𝑉𝑐𝑐 ≤ 𝐴𝑣𝑑 ≤ +𝑉𝑐𝑐+𝑉𝑐𝑐 𝐴𝑣𝑑 > +𝑉𝑐𝑐

How do we know the op-amp

is operating in linear region?

Lecture 4 13


Input-Output Transfer Plot

14[Source: Berkeley]


Application

15

𝑅1𝑉𝑟𝑒𝑓

𝑉𝑜𝑢𝑡

Source: http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/the-operational-amplifier/

Lecture 4

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/the-operational-amplifier/


Application

16

Source: http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/the-operational-amplifier/

Lecture 4

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/the-operational-amplifier/


Example



Practice

A 741 op amp has an open-loop voltage gain of 2 × 105, input

resistance of 2𝑀Ω, and output resistance of 50Ω. Find the

closed-loop gain 𝑣𝑜/𝑣𝑠. Determine current 𝑖 when 𝑣𝑠 = 2𝑉.

20Lecture 4


Correct or Not?

21Lecture 4


Negative Feedback

𝑉𝑖𝑛 ↑ ⟹ voltage differential ↑ ⟹ 𝑉𝑜𝑢𝑡 ↑⟹ voltage differential ↓ ⟹ 𝑉𝑜𝑢𝑡 ↓⟹ ⋯⟹ 𝑉𝑜𝑢𝑡 → 𝑉𝑖𝑛 but small difference exists

Lecture 4 22

Negative feedback


Tradeoff

• Effective input signal

• Circuit gain

• Linear dynamic range

23Lecture 4[Source: Berkeley]

Negative Feedback No Feedback


Negative Feedback

• A self-stabilizing system (also true for any dynamic system

in general), giving the op-amp the capacity to work in its

linear (active) mode.

• Op-amp gain A does not have to be precisely set by the

factory in order for the circuit designer to build an amplifier

circuit with precise gain.

Source: http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/negative-feedback/

Lecture 4 24

Negative feedback

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/negative-feedback/


Ideal Op Amp

• Attributes of ideal op-amp:

infinite open-loop gain, 𝐴 ⋍ ∞– Implies that 𝑣2 = 𝑣1.

infinite resistance of the two

inputs, 𝑅𝑖 ⋍ ∞

–This means it will not affect any

node it is attached to

– Implies that 𝑖1 = 𝑖2 = 0.

zero output impedance, 𝑅𝑜 ⋍ 0–From Thevenin’s theorem one can

see that this means it is load

independent.

Lecture 4 25


Ideal Op-Amp Analysis – Golden Rules

Assumption 1: The potential between the op-amp input terminals, v(+) –

v(-), equals zero.

R2R1

+

V0VIN

EXAMPLE

Assumption 2: The currents flowing into the op-amp’s two input

terminals both equal zero.

No Potential DifferenceNo Currents



27Lecture 4

Inverting Amplifier

[Source: Berkeley]


Example



29Lecture 4

Practice

• Determine 𝑣𝑜 in the circuit shown below


Non-Inverting Amplifier

Lecture 4 30

_

+

vin+-

R2

R1

RL

vo

[Source: Berkeley]


31Lecture 4

Application: Voltage Follower

_

+

vin+- RL

v2

v0

[Source: Berkeley]


Application of Voltage Follower

“Buffer” sections of Circuit



Summing Amplifier

• Aside from amplification, the op-amp can be made to do

addition very readily.

Lecture 4 33


Example

34Lecture 4


Practice

• Find 𝑣𝑜 and 𝑖𝑜 in the circuit shown below

35Lecture 4


Difference Amplifier

Lecture 4 36


Example

• Design an op amp circuit with inputs 𝑣1 and 𝑣2 such that

𝑣𝑜 = −5𝑣1 + 3𝑣2.

37Lecture 4


Common Mode Rejection

• It is important that a difference amplifier rejects any signal

that is common to the two inputs.

Which implies that when 𝑣1 = 𝑣2, 𝑣𝑜 = 0.

2 1 2 2

2 1

1 3 4 1

1

1o

R R R Rv v v

R R R R

Lecture 4 38


Application: Measurement Uncertainty

(T = 21˚C)v2 V0 = V2 ± 1% of V2

21˚C ± 0.21˚CG = 1

± 1%

(T = 21˚C)

Thermistor

Thermistor

Fixed Reference Temp = 20˚C

1˚C ± 0.01˚C

Direct Measurement

G = 11%

v2

v1

V0 = (V2 ‒ V1) ± 1% of (V2 ‒ V1)

Differential Measurement

Much better measurement uncertainty

Lecture 4 39


Cascaded Op Amps

• This head to tail configuration is called “cascading”.

Each amplifier is then called a “stage”.

• The gain of a series of amplifiers is the product of the

individual gains:

𝐴 = 𝐴1 ∙ 𝐴2 ∙ 𝐴3

Lecture 4 40


Digital Input

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16

An

alo

g O

utp

ut

(V)

111110000100

0000 0001

Application - DAC

[Source: Berkeley]


DAC

−𝑉𝑜 =𝑅𝑓

𝑅1𝑉1 +

𝑅𝑓

𝑅2𝑉2 +

𝑅𝑓

𝑅3𝑉3 +

𝑅𝑓

𝑅4𝑉4

Lecture 4 42


A DAC can be used to convert the digital representation

of an audio signal into an analog voltage that is then

used to drive speakers -- so that you can hear it!

0 0 1 0 10 0 1 10 1 0 0

1.52

0 1 0 10 1 1 00 1 1 11 0 0 0

2.53

3.54

1 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1

4.55

5.56

6.57

7.5

Binarynumber

Analogoutput(−𝑉𝑜)

0 0 0 00 0 0 1

0.5

MSB LSB

S1 closed if LSB =1

S2 " if next bit = 1

S3 " if " " = 1

S4 " if MSB = 1

4-Bit D/A

8V

+ V0

5K

80K

40K

20K

10K

S1

+-

S3

S2

S4

+

DAC

“Weighted-adder D/A converter”

(Transistors are used

as electronic switches)

[Source: Berkeley]


Summary

Lecture 4 44


New Content for the Discussion Session

• Positive feedback

• Instrumentation amplifier

• Differentiator

• Integrator

45Lecture 4

Positive feedback

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