# CS代考 ENGN1218 Electronic Systems and Design – cscodehelp代写

ENGN1218 Electronic Systems and Design

Topic 7 Operational Amplifiers

Video 1 Introducing The Amplifier

• Compared to transformers

• Non-inverted and inverted outputs

ENGN1218 Electronic Systems and Design

• The amplifier circuit

• Increases the amplitude of the input signal • Isasystembuildingblock

• Oneofthemostcommonlyusedcircuits

Amplifiers

• Varietyoffunctions

• Stereo systems contain audio amplifiers to amplify the sound

• Radio and TV receivers contains amplifiers to amplifier the signals • Key building block for robotics

ENGN1218 Electronic Systems and Design

• Amplifiers are linear circuits

– Output shape is same as that of the input

Non-inverting

Non-inverting amplifiers • Positivegain

𝑣 ⁄ 𝑣 𝐴

Amplifiers

𝑣 ⁄ 𝑣 𝐴

• theoutputwaveformis identical in shape to the input waveform

Inverting amplifiers • Negativegain

• theoutputwaveformis an inversion of the input waveform

ENGN1218 Electronic Systems and Design

Amplifier vs Transformer

ENGN1218 Electronic Systems and Design

Amplifiers: Example ECG Machine

• An ECG machine

– Contains amplifiers that amplify the weak signals picked up from the human body

ENGN1218 Electronic Systems and Design

Amplifiers: Telecommunications Vocoder

• A voice coder (Vocoder) inside every mobile phone consists of:

– Speech analyser

• Converts analogue into digital speech

– Speech synthesizer

• Converts digital signals into analogue speech

ENGN1218 Electronic Systems and Design

In our next video…

I will formally introduce you to the op-amp

ENGN1218 Electronic Systems and Design

Overview • Background

Video 2 Introduction to the Op-Amp

• The integrated circuit • The LM741 op-amp

ENGN1218 Electronic Systems and Design

The Operational Amplifier

The op-amp is last of the five circuit elements we are covering in this course • 8-terminals, active (can supply power), needs V DC power

5. The op-amp:

• Previous: 2-terminal and passive circuit elements

1. Resistance:

2. Capacitance:

3. Inductance:

4. The diode:

dissipates energy

stores energy

stores energy

dissipates energy heat/light

ENGN1218 Electronic Systems and Design

Operational Amplifier Circuits

• The operational amplifier (op-amp)

– One of the wonders of the electronics engineering world – Low cost

– Easy to use and versatile

• Broad range of practical applications • Building block of analogue computers

• Early operational amplifiers were primarily used to perform mathematical operations

– such as addition, subtraction, integration and differentiation – thus the term operational amplifier.

ENGN1218 Electronic Systems and Design

Integrated Circuits

• An Integrated Circuit (IC)

– an electronic circuit

– constructed entirely on a single small chip of silicon.

• All the components that make up the circuit – transistors, diodes, resistors, capacitors

– are an integral part of that single chip.

ENGN1218 Electronic Systems and Design

The LM741 Operational Amplifier

• The LM741 operational amplifier

– The single most important integrated circuit for analogue circuit design.

– Released by in 1968

– Designed by

– Most popular op-amp of all time

– Two opposite input terminals

– One output terminal

– Requires DC power supply

Symbol with DC supply 𝑉

Internal Block Diagram

PSPICE Symbol

ENGN1218 Electronic Systems and Design

Operational Amplifier Circuits

• An LM741 operational amplifier – an example of an analogue IC:

– 22 BJTs, 12 resistors, 1 capacitor.

See op-amp datasheet on Course Resources webpage.

In ENGN2218, after we study BJT, we will have look at the internal structure of the amplifier and its currents and voltages.

ENGN1218 Electronic Systems and Design

Op-Amp: Chip Hall of Fame

https://spectrum.ieee.org/static/chip-hall-of-fame

ENGN1218 Electronic Systems and Design

Inverting input 2

Non-inverting input 3

Non-inverting input 3

6 Inverting input 2

Op-Amps: Terminal Behaviour

• The +ve and –ve input terminals

Typical Package

Internal Block Diagram

– can be drawn either with +ve at top or bottom

ENGN1218 Electronic Systems and Design

Op-Amps: Power Supply

• The power supply terminals for 𝑉 and 𝑉

– Sometimes they are not shown in the circuit diagram • But in practice they are always there

– These schematics show the power supply connections and ground locations

– Provide the limits for output voltage

• Use the bubble convention to simplify the circuit diagrams

Single supply

Dual supply

0 𝑣 𝑉

𝑉 𝑣 𝑉

Bubble convention

ENGN1218 Electronic Systems and Design

Op-Amps: Power Supply

• Most op-amps are operated with a dual or split power supply

– From datasheet

» Minimum supply voltage: 5𝑉

» Maximum supply voltages: 22𝑉

» Typical supply voltages: 10𝑉 or 15𝑉

» Typical supply current: 1.7𝐴

» Power rating: 500𝑚𝑊

Dual supply

𝑉 𝑣 𝑉 Bubble convention

ENGN1218 Electronic Systems and Design

• In ENGN1218

Op-Amps: Terminal Behaviour

– Won’t be studying the internal behaviour of the op-amp

– Will take a black-box approach and focus only on the terminal behaviour

• Allows us to use the op-amp as a circuit building block to make an amplifier

ENGN1218 Electronic Systems and Design

In our next video…

We will be introduced to the ideal op-amp model, and the all important summing point constraint

ENGN1218 Electronic Systems and Design

The ideal op-amp model

Topic 7 Operational Amplifiers

Video 3 The Ideal Op-Amp Model

Negative feedback Summing point constraint

ENGN1218 Electronic Systems and Design

Ideal Op-Amp Model

• The voltage controlled voltage source (VCVS)

– Will be used to model the behaviour of the op-amp

– Not a real world device

• Used to theoretically model

– the behaviour of complex real world electronic devices and components

Ideal dependent voltage controlled voltage source (VCVS)

𝑣 𝜇 𝑣

𝜇 is dimensionless

ENGN1218 Electronic Systems and Design

𝑅: input resistance

𝐴: voltage gain due to the device internal circuitry

Ideal Op-Amp Model

The op-amp as represented by an equivalent voltage-amplifier circuit model, with a dependent voltage source

𝑣 and 𝑅: model the driving circuit

𝑅: output resistance 𝑅: load resistance

ENGN1218 Electronic Systems and Design

The ideal op-amp model

• Theinputresistance𝑅 ∞

𝑅 0Ω 𝐴 ∞

Ideal Op-Amp Model

The op-amp can be represented by this equivalent voltage-amplifier circuit model with a dependent voltage source

• Appears in parallel to input terminals, won’t draw any current from the source

• The output resistance 𝑅 0Ω

• Appears in series with load resistance

𝑅: input resistance 𝑅:outputresistance

• Shouldn’tintroduceanyvoltagedrop to the output

𝐴: voltage gain due to the device internal circuitry

• Internal device gain

•𝐴∞

ENGN1218 Electronic Systems and Design

Ideal Op-Amp Model

• The ideal op-amp model

• 𝑅 ∞Ω 𝑣 • 𝑅 0Ω

• 𝐴 ∞

This ideal model leads to Summing Point Constraint

• Practically,fromLM741op-ampdatasheet

• 𝑅 2𝑀Ω

• 𝑅 75Ω

• 𝐴 200,000

ENGN1218 Electronic Systems and Design

Op-Amp Operation: Negative Feedback

• Negative feedback

– A portion of the output voltage of an amplifier is returned to the input

– The two basic op-amp configurations use –ve feedback

• Inverting amplifier

• Non-inverting amplifier

• Non-assessable circuits (will be studied in ENGN2218)

– No feedback e.g. comparators

– Positive feedback e.g. Schmitt trigger comparator

• We can use summing point constraint for design and analysis ENGN1218 Electronic Systems and Design

Op-Amps: Summing Point Constraint • With the ideal op-amp model and negative feedback

• Canmakethefollowingtwoassumptions: • Due to internal circuitry design

1. The input voltages are equal

2. The input currents to the op-amp are negligible

𝑖 𝑖 0𝐴

• Consequences

• Output voltage is independent of the load resistance

• Output is independent of op-amp internal voltage gain

• We do not need to use the ideal op-amp model (containing VCVS) to solve op-amp circuits with –ve feedback

ENGN1218 Electronic Systems and Design

Op-Amps: Summing Point Constraint • Another way of stating the summing point constraint

• Negative feedback imposes constraints on the input voltages and currents

• Due to the complex internal circuitry of the op-amp 1. Voltage drop across the two inputs becomes zero

𝑣 𝑣 𝑣 𝑣 0𝑉

2. Input currents become zero

𝑖 𝑖 0𝐴

ENGN1218 Electronic Systems and Design

Looking Back with Thanks • Black (Engineer in Bell Labs)

• Concept of negative feedback amplifier

• Sketched out on a blank spot of his

Time newspaper

• during his morning commute to Bell Labs in Manhattan in 1927

• Completely revolutionised electronics

• Nine years before the patent office believed it

ENGN1218 Electronic Systems and Design

In our next video…

We will go through the steps for analysis and design of op- amp circuits

ENGN1218 Electronic Systems and Design

Overview Inverting amplifier

Topic 7 Operational Amplifiers

Op-Amp Amplifiers: Analysis

Non-inverting amplifier Buffer amplifier

Steps for analysis and design

ENGN1218 Electronic Systems and Design

Different Op-Amp Configurations

• Over this topic we will study the following op-amp configurations

1. Inverting op-amp amplifier

• Voltage gain with phase reversal

2. Non-inverting op-amp amplifier

• Voltage gain without phase reversal

3. Buffer amplifier

• Have a gain of 1 or less, with the advantage of high input resistance and low

output resistance

• Op-amps that perform arithmetic

4. Summing amplifier

• Output is the inverted scaled sum of the inputs

5. Difference amplifier

• Output is proportional to the difference between the two inputs

6. Op-amp Integrator

• Integrates a signal with respect to time

7. Op-amp Differentiator

• Differentiates a signal with respect to time

ENGN1218 Electronic Systems and Design

Op-Amp Amplifier Circuits

• The basic op-amp circuits studied in ENGN1218 are the non-inverting

and the inverting op-amp amplifier circuits • Both circuits use negative feedback

Non-inverting op-amp

Inverting op-amp

𝐴 𝑣 1 𝑅 𝑣 𝑅

𝐴 𝑣 𝑅 𝑣 𝑅

ENGN1218 Electronic Systems and Design

Non-Inverting Op-Amp Amplifier

• The non-inverting amplifier

– Signal goes into the non-inverting input (+) of the op-amp.

– Voltage gain but not phase reversal

• Input and output signals are said to be in phase

• The voltage gain of the non-inverting amplifier using an op-amp is calculated using the formula

• 𝐴 1

ENGN1218 Electronic Systems and Design

Non-Inverting Op-Amp Amplifier

• Find the voltage gain of the non-inverting amplifier

• when𝑅 1𝑘Ωand𝑅 10𝑘Ω • Ans:

• 𝐴 1 1

• Suppose the input voltage 𝑣 0.5𝑉

• 𝑣𝐴𝑣 110.55.5𝑉

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Amplifier • The inverting amplifier

• has a feedback resistor 𝑅 and an input resistor 𝑅

• The signal is applied to the inverting input (-) of the op-amp • The output signal is both inverted and amplified

• The voltage gain is set by the external resistors 𝑅 and 𝑅

𝐴 𝑣 𝑅 𝑣 𝑅

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Amplifier

• Find the voltage gain of the inverting amplifier

• When𝑅 1𝑘Ωand𝑅 10𝑘Ω • Ans:

• 𝐴 10

• Suppose the input voltage 𝑣 1𝑉

• Then 𝑣 𝐴𝑣 101 10𝑉

ENGN1218 Electronic Systems and Design

The Buffer Amplifier

• Amplifiers have more applications than just providing gain.

• A circuit can be damaged if a load is poorly matched to the circuit it is connected to

– This effect of loading one stage by another can be overcome by using a buffer amplifier between the stages

• Buffer amplifiers are a special case of the non-inverting op-amp amplifier, where 𝑅 Ω open circuit and 𝑅 0 (short circuit)

𝐴 𝑣 1 𝑅 𝐴 𝑣 1

ENGN1218 Electronic Systems and Design

The Buffer Amplifier: Power Gain

• Buffer amplifiers have a power gain

• Example: Assume that the ideal op-amp is operating in the linear region.

• Calculate the power delivered to the 16Ω resistor in both circuits.

Circuit 2 48kΩ

• Circuit 1:

• voltage divider 𝑣 320𝑚 86.8𝑚𝑉

• Power . 0.4μ𝑊

• Circuit 2: Buffer configuration 𝑖 𝑖 0𝐴 • 𝑣 𝑣 320𝑚𝑉

• The power ratio with and without the op-amp:

• Power 6.4μ𝑊

• .μ 16

ENGN1218 Electronic Systems and Design

Analysis/Design of Op-Amp Circuits

• When using the ideal op-amp model and summing point constraint:

• Ifyoutrytousethemesh-currentmethodtoanalyseop-amp circuits, you will not be able to make any progress

ENGN1218 Electronic Systems and Design

Summing point constraints Analysis: Ideal Non-Inverting Op-Amp

• Apply op-amp assumptions • 𝑣 𝑣

• 𝑖 𝑖 0 • Step 2:

• Find voltage at inverting pin • 𝑣 𝑣 𝑣

• Apply KCL at inverting pin node

• 𝑖 0

• Simplify

Find Rin and Rout

• 𝑅 ∞Ω

• 𝐴 1

• 𝑅 0Ω

ENGN1218 Electronic Systems and Design

Summing point constraints Analysis: Ideal Inverting Op-Amp

• Apply op-amp assumptions • 𝑣 𝑣

• 𝑖 𝑖 0 • Step 2:

• Find voltage at inverting pin • 𝑣 𝑣 0𝑉

Virtual Ground Concept Zero voltage at inverting terminal (negative pin) is referred to as virtual ground.

• Apply KCL at inverting pin node

• 𝑖0

• Simplify𝐴

• Find Rin and Rout • 𝑅 𝑅

• 𝑅 0Ω

• 15𝑉𝑣 15𝑉 ENGN1218 Electronic Systems and Design

Output Voltage Range • For linear operation as an amplifier

• Outputvoltagemustliebetweenthetwosupplyvoltages •determinedby𝑉 𝑣 𝑉

For example:

• when the op-amp is powered by dual supply,

with 𝑉 15𝑉 and 𝑉 15𝑉

• Thenas𝑉𝑣𝑉, • The output voltage range is

ENGN1218 Electronic Systems and Design

In our next video…

We will work through inverting op-amp examples

ENGN1218 Electronic Systems and Design

Topic 7 Operational Amplifiers

Video 5 Op-Amp Examples

• Op-amp circuit analysis examples

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Analysis: Example 1 pg. 1/3 • Solve Textbook Assessment problem 5.1

𝑣 5 3.5 17.5𝑉 Op-amp saturates at -15V ENGN1218 Electronic Systems and Design

Inverting Op-Amp Analysis: Example 1 pg. 2/3 • a) Calculate 𝑣 for the following vales of 𝑣:

• 0.4,2.0,3.5,0.6,1.6,2.4

Ans:𝐴 5

𝑣 15 𝑣 10𝑉

𝒗𝒔 (V) -2.4 -1.6 -0.6 0.4 2.0 3.5

𝒗𝐨𝐮𝐭 comment

𝑣 5 2.4 12𝑉 Op-amp saturates at +10V

» 𝑣 5 𝑣

𝑣 5 1.6 8𝑉

𝑣 5 0.6 3𝑉

𝑣 5 0.4 2𝑉 𝑣 5 2.0 10𝑉

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Analysis: Example 1 pg. 3/3

• b) Specify the range of 𝑣 required to avoid amplifier saturation Ans:

• With the dual power supply and 𝑣 5 𝑣 • Then𝑣

15 𝑣 10𝑉

15 𝑣 10

555 3𝑣 2

(multiplying by -1 changes the inequality signs)

2 𝑣 3

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Analysis: Example 2 • Solve Textbook Example 5.1

ENGN1218 Electronic Systems and Design

Inverting Op-Amp Analysis: Example 2

• a) Calculate 𝑣

if𝑣 1𝑉and𝑣 0𝑉

• 𝐴

10𝑉 𝑣 10𝑉

• 𝑣 . 𝑣

•. 1 4𝑉

• b) Calculate 𝑣

if𝑣 1𝑉and𝑣 2𝑉

• Thesummingpointconstraint •𝑣 𝑣 and𝑖 𝑖 0𝐴

𝑣 𝑣 𝑣 𝑣 0 25𝑘 100𝑘

• Then𝑣 𝑣 𝑣

2 1 2 𝑣 25𝑘 100𝑘

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 3 pg. 1/3 • Solve Textbook problem 5.18

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 3 pg. 2/3

• a) What op-amp circuit configuration is this?

– Lets redraw the circuit in a more standard configuration.

ANS: non-inverting op-amp with input voltage at +ve input terminal

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 3 pg. 3/3

• b) Calculate 𝑣

ANS: The gain of an non-inverting amplifier

• 𝐴 1

•𝑣𝐴.𝑣1 𝑣

• 1 411444𝑉

• Op-amp saturates to +16V so 𝑣 16𝑉

16𝑣 16

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 4 pg. 1/2

• Derive 𝑣 for the circuit shown • Step 1:

• Apply op-amp assumptions • 𝑣 𝑣 0𝑉(given)

• 𝑖 𝑖 0𝐴

• Find voltage at inverting pin • 𝑣 𝑣 0𝑉(given)

• Apply KCL at inverting pin node

• 𝑖

• 0

• 0 → 𝑣𝑣

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 4 pg. 2/2

• Derive 𝑣 for the circuit shown • Step 3 cont.:

• Apply KCL at 𝑣 node

• 0

• 𝑣

• 𝑣 𝑅 𝑣

• 𝑣 𝑅 𝑣

• 𝑣 𝑣

ENGN1218 Electronic Systems and Design

In our next video…

We do more examples of op-amp analysis and design

ENGN1218 Electronic Systems and Design

Topic 7 Operational Amplifiers

More Examples of Op-Amp Circuits

Examples for design and analysis Check solutions with PSPICE

ENGN1218 Electronic Systems and Design

Op-Amp Design: Example 1 pg. 1/6 • Solve Textbook Example problem 5.2

ENGN1218 Electronic Systems and Design

Op-Amp Design: Example 1 pg. 2/6

• a) Design an inverting amplifier • withgainof12

𝐴 12 𝑅

• Choose common resistor value • 𝑅 1𝑘Ω

15𝑉 𝑣 15𝑉

• then 𝑅 12𝑘Ω

ENGN1218 Electronic Systems and Design

Op-Amp Design: Example 1 pg. 3/6

• b)What range of input voltages allows the op-amp to remain in the linear operating range?

• that 15𝑉 𝑣 15𝑉

• And 12

15𝑉 𝑣 15𝑉

𝑣 12𝑣 15𝑉 𝑣 15𝑉

15𝑉 12𝑣 15𝑉

15 𝑉 𝑣 15 𝑉 12 12

1.25𝑉 𝑣 1.25𝑉

ENGN1218 Electronic Systems and Design

Example 1 PSICE Simulation pg. 4/6

• Here is the example circuit drawn in PSPICE

– The circuit looks different because the +ve input pin is at the top of the op-amp symbol

• This is the only way PSPICE will draw this circuit

The input is sinusoidal

We have used the ‘bubble’ to draw the bias voltages

ENGN1218 Electronic Systems and Design

Example 1 PSICE Simulation pg. 5/6

• The red is the input with peak 1V, and the green is the output

• The output voltage peak is very close to 12V

ENGN1218 Electronic Systems and Design

Example 1 PSICE Simulation pg. 6/6 • What happens if we increase the peak input voltage to 2V?

• The output voltage will try to move between 24𝑉 peak

• The circuit reaches ‘saturation’ at 15V (not clipping)

• Saturation occurs if input voltage is outside the linear range

• 1.25𝑉 𝑣 1.25𝑉

• No longer functioning as an amplifier as is now non-linear

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 2 pg. 1/6 • Solve Textbook problem 5.6

• 𝑣 𝑣 0𝑉(given)

ENGN1218 Electronic Systems and Design

Op-Amp Analysis: Example 2 pg. 2/6

• Calculate 𝑖, 𝑣, 𝑣, 𝑖

Op-amp is in inverting configuration

• Applyop-ampassumptions • 𝑣 𝑣 0𝑉(given)

• 𝑖 𝑖 0𝐴

15𝑣 15

• Find voltage at inverting pin

ENGN1218 Electronic Systems and Design

ANS contd:

Op-Amp Analysis: Example 2 pg. 3/6

• Calculate 𝑖, 𝑣, 𝑣, 𝑖

• Apply KCL at in