introduction to electronic hardware operational amplifiers ...jke1/intro_to_elec_hardware... ·...

Introduction to Electronic Hardware

Operational AmplifiersELE00001C

Jeremy Everard

1©2015 University of York

Syllabus• The properties of an ideal operational amplifier

– infinite input impedance, zero output impedance and infinite voltage gain and

– these properties in real (non-ideal) operational amplifiers • Ideal model of an operational amplifier using:

– virtual voltage sources and – the Virtual Earth Model

• Analysis and design of:– Inverting and non-inverting amplifier configurations– Differential Amplifiers– Summing Amplifiers applicable to audio mixer desks and Digital

to Analogue convertors• Gain Bandwidth Product• General model for feedback and in particular negative

feedback and how this applies in operational amplifier circuits

• Comparators and active rectifiers2©2015 University of York

On completion of this course you are expected to be able to:• Understand the main characteristics of an ideal

op amp– Understand the key limitations

• Analyse and design fundamental op amp circuits– Use equivalent circuit models to analyse op amp

circuits• Brief introduction to the gain bandwith product• Understand the principles of feedback in relation

to op amp circuits• Appreciate the practical issues around op amp

circuits


Timetable: 7 lectures, 2 workshops & Labs

• Lectures: Wk 6 & 7– Monday 14:00 P/L/001– Friday 14:00 P/L/001

• Lectures: Wks 8, 9 & 10– Monday: 14:00 P/L/001

• Workshops: Weeks 8 & 10– Group B, Monday: 09:00 D/L047– Group A, Thursday 09:00 D/L047

• Labs: Wks: 8 & 9 in mornings on 4th floor - D Pearce– Group A: Monday/Tuesday– Group B: Wednesday/Thursday


Operational Amplifier

5

• High gain directly coupled building block

• Two Voltage inputs– Non-inverting (+)– Inverting (−)– Amplifier with very high

open loop voltage gain (without feedback)

– voltage gain 105 to 106 at lower frequencies

• Output– low output impedance– ≈75Ω

=©2015 University of York

Operational AmplifiersSometimes a different notation

6

Note: =

©2015 University of York

Operational Amplifiers: key uses• Inverting Amplifier

• The output (red) is a larger copy of the input (green). The multiplying factor is called Voltage Gain

• The output is inverted with respect to the input, ie 180 degrees out of phase

• Use resistors (R1 and RF) to set the final (closed loop) gain

©2015 University of York 7

Time/uSecs 50uSecs/div

250 300 350 400 450 500 550

mV

-200

-100

0

100

200

300

Guess Voltage Gain ??

Operational Amplifiers: key uses• Non Inverting Amplifier

• The output (red) is a larger copy of the input (green). The multiplying factor is called Voltage Gain

• The output is in phase with the input©2015 University of York 8

Time/mSecs 200uSecs/div

0 0.2 0.4 0.6 0.8 1 1.2

V

-1.5

-1

-0.5

0

0.5

1

1.5

2

Guess Voltage Gain ??

Look at the different resistor topologies• Inverting Amplifier

• Non inverting Amplifier

9

Time/uSecs 50uSecs/div

250 300 350 400 450 500 550

mV

-200

-100

0

100

200

300

Time/mSecs 200uSecs/div

0 0.2 0.4 0.6 0.8 1 1.2

V

-1.5

-1

-0.5

0

0.5

1

1.5

2


Operational Amplifiers: key uses

• Differential Amplifier


Operational Amplifiers:

• Summing Amp– Mixer desk

• D to A


Inverting amp with extra resistors on the input

Switch in resistors ofdifferent values for

different bits

Operational Amplifiers:

• Active Rectifier


Operational Amplifiers(not covered in this course)

• Integrator

• Differentiator


Operational Amplifiers• Course Materials available from web link at module information

– Set of lecture slides– Tutorials and indicative answers

• Recommended texts:• Fundamentals of Electric Circuits (chapter 5 on Operational Amplifiers)

– By Charles K Alexander and Mathew N.O Sadiku, – Published by McGraw-Hill– Fourth Edition, – ISBN 978–0–07–352955–4

• Additional Texts– Stanley, W.D., Operational Amplifiers with Linear Integrated Circuits (3rd ed)

(Library catalogue number U 7.534 STA)– Dostal, J., Operational Amplfiers (2nd ed), Butterworth-Heinemann, 1993

(Library catalogue number U7.534 DOS)– Franco, S., Design with Operational Amplifiers and Analog Integrated Circuits

(3rd ed), McGraw-Hill, 2002 (Library catalogue number U 7.534 FRA)– Hambley, Allan R., Electrical Engineering Principles and Applications, Sixth

edition, published by Pearson

• And many, many more in the library


Op Amps - History• 1930’s:origin as differential amplifiers

– (long tailed pair) using pairs of valves • audio amplification, filtering, mixing...

• 1940’s:op amps used in analogue computing– capable of performing mathematical operations:

• origin of name• 1950‘s: transistor op amps using discrete

transistors• 1960s: IC opamps

– 1964, μA702 - the first mass produced IC op amp– 1965, μA709

• Improved gain from a ~3000 up to up to 25,000 to 70,000

• Today: Very important analogue ICs– take a look at RS and Farnell catalogues!


Fairchild μA702 (1964)• First mass produced IC

– Nominal resistor values– Equivalent circuit from

Fairchild data sheet

Pin numbers for metal can only


Fairchild μA709, year after μA702 (1965)

17

• Equivalent circuit from data sheet

• Higher gains– Up to 70,000

• Complementary output stage PNP & NPN


Same structure as previous circuitbut drawn slightly differently

Input stage and block diagram


Difference or differential Amplifier

Amplifies the differenceBetween the I/P voltages

Additionalgain block

Buffer andOutput stage

• Interesting to note that:• In IC design, resistors are rather large• so use transistors as active loads instead !!!!• In fact they have many other advantages as

well


Low cost LM324 Quad Op Amp

AlarmSensor

Differential Amplifer

20

Current Mirrors& Active Loads

O/Pstage

Buffer/emitterfollower &Additional gain

Diff Amp

CurrentMirrors

Diff Amp Active Load


21

Look at Datasheets

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Circuit I developed – can you guess what it is?

©2015 University of YorkEol_1_2_3_2015

Simulation is a very useful tool for checking designs


Simulation: use Simetrix. This can analyse circuits under both small signal and large signal operation. It has a large number of accurate models for devices.

This is a very useful tool for electronics design engineers - use to check design before building it

Described in Dave Pearce’sLabs under module information for second year course on semiconductor Devices.

A number of videos can be found at:

http://www.elec.york.ac.uk/internal_web/meng/yr2/labs/SemiconductorDevices/Simetrix/Simetrix.html

15V2

X1-out

100k

R3

1k

R2

0 AC 1 0 Sine(0 400m 10k 0 0)V1

1KR4X1

uA741

15V3

Definition: A very high gain, direct coupled linear voltage difference amplifier that uses external feedback components to define circuit operation.

Perhaps the most important linear (analogue) integrating circuit

What is an operational amplifier


Inverting input

Non Inverting input

+VCC

−VCC

The ideal linear voltage amplifier

O/P voltage proportional to I/P voltage

Constant of proportionality is

constant (according to application), stable and independent of time/frequency


The op amp: ideal linear voltage difference amplifierOpen loop characteristics (limited by power supply)


+VCC

−VCC

Max I/P beforesaturation

The ideal linear voltage amplifier: VCVSVoltage Controlled Voltage Source


The ideal operational amplifierIdeal operational amplifier: Ideal linear differential voltage amplifier

1. input impedance is infinite2. output impedance is zero3. open loop gain is infinite

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Effect of finite input impedance (potential divider rule)

The ideal linear voltage amplifier: i/p impedance

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Effect of non-zero output impedance (potential divider rule)

The ideal linear voltage amplifier: o/p impedance


Effect of finite input impedance and non-zero output impedance

The ideal linear voltage amplifier: loading


The ideal operational amplifier

Infinite input impedanceNo current into or out of either input terminal

Infinite open loop gainNegative Feedback forces the voltages at the input terminals to become identical!!!Or: Differential voltage to be zero

;

Zero output impedanceOutput voltage is independent of the load resistance


The ideal/non ideal operational amplifierMaximum input voltage before saturation

Infinite open loop gainThe voltages at the input terminals are identicalOr: Differential voltage is zero

33

In reality, If A =

= = 1510 = 150Maximum peak input voltage beforesaturation at low frequencies if the supply voltage is + VCC = + 15V:


Analyse the Inverting Amplifier

• Use the virtual earth model

• Use the voltage controlled voltage source model which is more flexible but less simple


The inverting voltage amplifierVirtual earth model

Single op amp circuit that provides voltage amplification with a gain controlled by feedback resistor network

Inverting: 180o phase shift between input and output signalsi.e. output inverted with respect to input


The current intoR1 and RF are the

Same!!

Inverting amplifier: Virtual earth modelIdeal operational amplifier:1. input impedance is infinite: No current flows into inverting input2. open loop gain is infinite:


Inverting amplifier: Virtual earth model

(virtual earth means input voltage dropped across R1)

(current into op amp is zero)

(virtual earth means output voltage is voltage across Rf)


Input impedance of the inverting amplifierInverting amplifier: Virtual earth model

N.B. R1 is the input impedance of the inverting amplifier circuit NOT the input impedance of the op amp which is infinite 38©2015 University of York

Virtual Earth – in words• The I/P impedance of the op amp is infinite in the

ideal case so no current flows into the op amp.• All the current flowing in R1 flows into RF

• The gain of the op amp is infinite in the ideal case.


Virtual Earth (in words)• The output voltage of the amplifier adjusts

itself to force the input voltage to zero (virtual earth) via the feedback network. – If you put a perturbation (of voltage) on the

output (in either direction) away from where it should be, the feedback at the input will try and push it back to the correct position.

40

You can check this bylooking at the model.


Virtual Earth (in words)• As the current into R1 is the same as the

current into Rf (and Ve is zero) then the voltage gain is -Rf/R1.


Test question 1.a & b on the inverting voltage amplifier

Example(a) What is closed loop gain?(b) What is the output voltage when

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(c) Determine the op amp output current with a 2kΩ load and


Test question 1.c on the inverting voltage amplifier

Example(c) Determine the op amp output current with a 2kΩ load and

Remember the current through R1


R1

Operational amplifiers: Summary 1Open loop characteristics

Infinite input impedanceNo current into op amp

Zero output impedanceOutput voltage independent of load

Infinite open loop gainDifferential voltage is zero

Ideal operational amplifier: assumptions


Operational amplifiers: Summary 2Inverting amplifier: virtual earth model

Output 180o out of phase with input (Inverting amplifier)

Closed loop gain: determined by ratio of resistances only45©2015 University of York

Quiz: The inverting amplifiera) Design an inverting amplifier with closed loop gain of -12 and an input impedance of 1kΩ.

b) What is the maximum input voltage allowed for linear operation? (assume saturation voltages of ±13V)

c) For an input voltage of 500mV, calculate the current through a 2kΩ load resistor?

d) what is the actual circuit gain when connected to an input source (e.g. microphone) with an impedance of 50Ω


And now...The VCVS model for circuit analysisClosed loop gain for inverting amplifier using ideal VCVS model

The non-inverting voltage amplifierClosed loop gain and input impedanceSpecial case: the voltage follower

Closed loop op amp circuits: Design considerationsGood practice in the design of operational amplifier circuits

The open loop differential amplifier: CMRR47©2015 University of York

The inverting voltage amplifier: VCVS model

48One method is to use the superposition principle to find νo as a function of νi . Remember it is a linear system ©2015 University of York

Superposition reminderApplies to LINEAR Circuits1. Set all sources, except

one, to zero2. Solve the new circuit for

unknown currents and voltages

3. Repeat 1 and 2 until each source has been allowed to drive the circuit on its own

4. The overall voltages and currents are the sum of voltages and currents due to each source

• Short out νi and work out ν d in terms of νo

• Short out νo and work out ν d in terms of νi

• Add the values of ν dtogether


as

The inverting voltage amplifier: VCVS modelUsing superposition

50

then - 1 =

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Multiply both sides by −A and place vo components on LHS and vi on RHS

The inverting voltage amplifier: VCVS model

Advantage of VCVS over virtual earth model

Amenable to analysis of non-ideal op amp behaviour

e.g. finite input impedance/ non-zero output impedance

finite open loop gain


An alternative method

Calculate the effect of finite gain on the closed loop gain wherethe I/P impedance is infinite

R1

R2

A.VeVout

Vin

Ve

_

+

i1

i2

dout AVV −=

Assuming no input current

i i1 2 0− =

01

=−+−

f

doutdin

RVV

RVV

νd


i2

+=+

fd

F

outin

RRV

RV

RV 11

11

As AVVd out−=

+−=+

f

out

f

outin

RRAV

RV

RV 11

11

11

1111RV

RRARV in

ffout −=

++

11

111RV

RR

ARV inf

f

out −=

++

++

−=111

1

1

1

RR

ARR

VV

f

f

in

out

For R2 >> R1the error is

approximately

Closed loop gainOp Amp open loop gain

Ideal

Ratio =

Useful to calculate gain in terms of the ideal equation and an error term


Remembering Binomial Series Expansion

......11

1 5432 xxxxxx

−+−+−=+

Check accuracy of this for x = 0.1

For x2 < 1

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Op amp: current controlled voltage source

Current controlled voltage source or

Transimpedance amplifier wheretransimpedance (or transresistance) is

55

This type of amplifier is often usedWith photodiodes

for optical receivers


Photodiode & Amplifier


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Now apply similar technique to virtual earth model to the

Non-inverting amplifier


Amplifier where output voltage is in phase with input voltageNon-inverting voltage amplifier

so


Similar technique to virtual earth model

Example

Example(a) What is closed loop gain?(b) What is the output voltage when

(c) Determine the op amp output current when 59©2015 University of York

Example(c) Determine the op amp output current when


Special case of non-inverting amplifierVoltage follower

Closed loop gain of non-inverting amplifier

61Eol_3_8_11_2013


Design considerationsQuestion: Design an inverting amplifier with a closed loop gain -10.

Design guidelines:

1. Resistor values in range 1kΩ to 100kΩ used typicallyLow R: high current drain and loading of op ampHigh R: input current no longer assumed to be zero

increase noise

Also resistors have tolerances:Example with 5% tolerance resistorsand Rf = 100kΩ; R1 = 10kΩ



Design considerations

2. Input impedanceinverting amplifier: ensure sufficient input impedance to minimise loading of sourcenon-inverting amplifier: input impedance is infinite

5. Frequency response

3. Sufficient dynamic range for desired output voltage rangei.e. Avoid saturation: Many op amps only achieve ～70% of supply voltage

4. Keep closed loop gain much smaller than open loop gain‘ideal’ op amp assumptions breaks down as ACL approaches op amp open loop gain


Frequency response• It has been assumed, so far, that the gain of

the amplifier is constant with increasing frequency– In real life this is not the case

• Many basic components and circuits such as transistors and operational amplifiers have a frequency response which rolls off at higher frequencies.

• This can often be modelled using a simple Resistor Capacitor network (RC network)


RC lowpass network

• An RC network is now shown and the frequency response calculated and simulated.

• The impedance of a capacitor can be shown to be:

• Where f

• The voltage transfer function (using potential divider rule) is therefore:

66

= =

Probe1-NODE

AC 1 0 Sine(0 400m 10k 0 0)V2

1K

R1

C115.915u


Frequency Response of RCnetwork with 10Hz ‘cutoff’

67Frequency / Hertz

10m 100m 1 10 100 1k 10k 100k 1M

Pro

be1-

NO

DE /

V

20u

40u

100u

200u

400u

1m2m

4m

10m

20m

40m

100m

200m400m

1

-291.303m

999.9995m708.6967m

9.945389410.00000m 9.9553894

AREF

Probe1-NODE

AC 1 0 Sine(0 400m 10k 0 0)V2

1K

R1

C115.915u

©2015 University of York 68Time/mSecs 200uSecs/div

8.8 9 9.2 9.4 9.6 9.8 10

IPROBE1 / u

A

Y2

-400

-300

-200

-100

-0

100

200

300

Probe

1-NODE / mV

Y1

-1

0

1

2

3

4

5

6

IPROBE1

C115.915u

1K

R1

AC 1 0 Sine(0 400m 1k 0 0)V2

Probe1-NODE

VoltageCurrentNote 90 phase shift


Time Domain Response

Op Amp Frequency Response

69

Frequency / Hertz

10m 100m 1 10 100 1k 10k 100k 1M

X1-

out /

V

200m400m

124

102040

100200400

1k2k4k

10k20k40k

100k200k400k

1M15V2

X1-out

100k

R3

1k

R2

0 AC 1 0 Sine(0 400m 10k 0 0)V1

1KR4X1

uA741

15V3



• Gain bandwidth product. It can be seen that: G×B is a constant

70

Frequency / Hertz

10m 100m 1 10 100 1k 10k 100k 1M

X1-

out /

V

200m400m

124

102040

100200400

1k2k4k

10k20k40k

100k200k400k

1M

15V2

X1-out

100k

R3

1k

R2

0 AC 1 0 Sine(0 400m 10k 0 0)V1

1KR4X1

uA741

15V3



Frequency / Hertz

10m 100m 1 10 100 1k 10k 100k 1M

X1-

out /

V

200m400m

124

102040

100200400

1k2k4k

10k20k40k

100k200k400k

1M

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Simulator


Closed loop differential amplifierDifferential amplifier: amplifies the difference between the voltages applied to two inputs with controlled weighting

Electrocardiography (ECG)Instrumentation Amplifier

72Eol_4_17_11_2014


Closed loop differential amplifier

73

Same as non inverting amplifier

Use superposition


Using superposition add the terms for vo together

Closed loop differential amplifier

Special case:

N.B Input impedance of inputs differ

Instrumentation amplifier: typically includes voltage follower/ buffer on both inputs 74©2015 University of York

Common mode rejection ratioCommon mode rejection ratio (CMRR): Important measure that quantifies the ability of a differential amplifier to amplify the difference between inputs and reject common mode signals.

N.B. in ideal amplifier75©2015 University of York

Closed loop differential amplifier: CMRR

N.B. Resistor tolerances!


Feedback

Feedback: a process for controlling the state of a system e.g. gain of an amplifier, by transferring a portion of the output signal back to the input

1927 Harold S. Black


Fluid mechanics (toilets!)

Feedback

Mechanical EngineeringFly ball governor Biology

Homoeostasis

ANDControl EngineeringChemistryEconomicsClimate...


FeedbackNegative feedback: Temperature regulation

Negative feedback: Voltage follower Negative feedback: non-inverting amp


Two different examples

With gainHow much?

Fundamental feedbackrelationship

Feedback: Basic definitions


Feedback: Basic definitions

1. Closed loop gain is open loop gain divided by

2. Without feedback (i.e. β=0)

3. if then i.e. independent of A


Feedback: non-inverting amplifier


Operational amplifiers with non-infinite gainFor ideal amplifier

What is the closed loop gain of the amplifier if A= 1000

(ideal case)


Operational amplifiers with non-infinite gain

For ideal amplifier

In reality open loop gain is finite

10 5 1 0.99999 0.001

10 5 100 9.999 0.1

10 5 1,000 990.1 1

10 5 10,000 9091 9.0984©2015 University of York

Feedback: positive and negativeNegative feedback: feedback signal subtracted from input signal

Positive feedback: feedback signal added to input signalNegative feedback Positive feedback

85Eol_5_18_11_2013 ©2015 University of York

For positive feedbackVf is added to vi.

In an oscillator they add in phase andAβ tends to −1 so the gain is initially

infinite. The oscillation builds upuntil it hits the power supply !!!

Positive feedback:tends to cause system instability in amplifierscan be used to create oscillators

Negative feedback:1. reduce gain to a specified level below the open loop gain;2. reduce distortion;3. make the input impedance more ideal (increase);4. make the output impedance more ideal (decrease);5. improve the frequency response.

Feedback in operational amplifiers


Review: feedback

Fundamental feedbackrelationship

Negative feedback: feedback signal subtracted from input signal

Positive feedback: feedback signal added to input signal87Eol5_wk9_24_11_2014 ©2015 University of York

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