electronic devices and amplifier circuits with matlab applications

Electronic Devicesand Amplifier Circuits

with MATLAB / Simulink / SimElectronics Examples

Third EditionSteven T. Karris

Orchard Publicationswww.orchardpublications.com

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition

Copyright 2012 Orchard Publications. All rights reserved. Printed in the United States of America. No part of thispublication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system,without the prior written permission of the publisher.

Direct all inquiries to Orchard Publications, [email protected]

Product and corporate names are trademarks or registered trademarks of The MathWorks, Inc. They are used only foridentification and explanation, without intent to infringe.

Library of Congress CataloginginPublication Data

Library of Congress Control Number (LCCN) : 2012943157

TXu1254-969

ISBN-13: 9781934404256

ISBN-10: 193440425X

Disclaimer

The author has made every effort to make this text as complete and accurate as possible, but no warranty is implied.The author and publisher shall have neither liability nor responsibility to any person or entity with respect to any loss ordamages arising from the information contained in this text.

are well illustrated.

* These are Circuit Analysis I with MATLAB Computing and Simulink/SimPowerSystems Modeling, ISBN9781934404171, Circuit Analysis II with MATLAB Computing and Simulink/SimPowerSystemsPreface

This text is an undergraduate level textbook presenting a thorough discussion of stateofthe artelectronic devices. It is selfcontained; it begins with an introduction to solid state semiconductordevices. The prerequisites for this text are first year calculus and physics, and a twosemester coursein circuit analysis including the fundamental theorems and the Laplace transformation. Noprevious knowledge of MATLAB is required; the material in Appendix A and the inexpensiveMATLAB Student Version is all the reader needs to get going. The discussions are based on a PCwith the Windows 7 platform but if you have another platform such as Macintosh, please refer tothe appropriate sections of the MATLABs User Guide which also contains instructions forinstallation. Additional information including purchasing may be obtained from The MathWorks,Inc., 3 Apple Hill Drive, Natick, MA 01760-2098. Phone: 508 6477000, Fax: 508 6477001, email: [email protected] and web site http://www.mathworks.com. Even though this text canalso be used without MATLAB, it is highly recommended to be used with the inexpensiveMATLAB Student Version. The MATLAB scripts in this text are available free of charge uponrequest. Contact us at [email protected].

This is our fourth electrical and computer engineering-based text with MATLAB applications. Myassociates, contributors, and I have a mission to produce substance and yet inexpensive texts for the

average reader. Our first three texts* are very popular with students and working professionalsseeking to enhance their knowledge and prepare for the professional engineering examination.

The author and contributors make no claim to originality of content or of treatment, but havetaken care to present definitions, statements of physical laws, theorems, and problems.

Chapter 1 is an introduction to the nature of small signals used in electronic devices, amplifiers,definitions of decibels, bandwidth, poles and zeros, stability, transfer functions, and Bode plots.Chapter 2 is an introduction to solid state electronics beginning with simple explanations ofelectron and hole movement. This chapter provides a thorough discussion on the junction diodeand its volt-ampere characteristics. In most cases, the nonlinear characteristics are plotted withsimple MATLAB scripts. The discussion concludes with diode applications, the Zener, Schottky,tunnel, and varactor diodes, and optoelectronics devices. Chapters 3 and 4 are devoted to bipolarjunction transistors and FETs respectively, and many examples with detailed solutions are provided.Chapter 5 is a long chapter on op amps. Many op amp circuits are presented and their applicationsModeling, ISBN 9781934404195, and Signals and Systems with MATLAB Computing and SimulinkModeling, ISBN 9781934404232.

The highlight of this text is Chapter 6 on integrated devices used in logic circuits. The internalconstruction and operation of the TTL, NMOS, PMOS, CMOS, ECL, and the biCMOS familiesof those devices are fully discussed. Moreover, the interpretation of the most important parameterslisted in the manufacturers data sheets are explained in detail. Chapter 7 is an introduction to pulsecircuits and waveform generators. There, the 555 Timer, the astable, monostable, and bistablemultivibrators, and the Schmitt trigger are discussed

Chapter 8 discusses to the frequency characteristic of single-stage and cascade amplifiers, andChapter 9 is devoted to tuned amplifiers. Sinusoidal oscillators are introduced in Chapter 10.

This is the third edition of this title, and includes several Simulink, SimPowerSystems, andSimElectronics models. Appendix A, is an introduction to MATLAB. Appendix B is anintroduction to Simulink, Appendix C is an introduction to Simscape toolbox that includesSimPowerSystems and SimElectronics libraries, Appendix D is an introduction to Proportional-Integral-Derivative (PID) controllers, Appendix E describes uncompensated and compensatednetworks, and Appendix F discusses the substitution, reduction, and Millers theorems.

The author wishes to express his gratitude to the staff of The MathWorks, the developers ofMATLAB and Simulink for the encouragement and unlimited support they have provided mewith during the production of this text.

A companion to this text, Digital Circuit Analysis and Design with Simulink Modeling and Introductionto CPLDs and FPGAs, ISBN 9781934404058 is recommended as a companion. This text isdevoted strictly on Boolean logic, combinational and sequential circuits as interconnected logicgates and flipflops, an introduction to static and dynamic memory devices. and other relatedtopics.

Although every effort was made to correct possible typographical errors and erroneous references tofigures and tables, some may have been overlooked. Our experience is that the best proofreader isthe reader. Accordingly, the author will appreciate it very much if any such errors are brought to hisattention so that corrections can be made for the next edition. We will be grateful to readers whodirect these to our attention at [email protected]. Thank you.

Orchard PublicationsFremont, California 945384741United States of [email protected]

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition iCopyright Orchard Publications

Table of Contents

1 Basic Electronic Concepts and Signals1.1 Signals and Signal Classifications ........................................................................... 111.2 Amplifiers ................................................................................................................ 131.3 Decibels ................................................................................................................... 131.4 Bandwidth and Frequency Response...................................................................... 151.5 Bode Plots............................................................................................................... 171.6 Transfer Function ................................................................................................... 191.7 Poles and Zeros...................................................................................................... 1101.8 Stability.................................................................................................................. 1111.9 Voltage Amplifier Equivalent Circuit................................................................... 1151.10 Current Amplifier Equivalent Circuit .................................................................. 1171.11 Summary................................................................................................................ 1191.12 Exercises ................................................................................................................ 1221.13 Solutions to EndofChapter Exercises ............................................................... 124

MATLAB Scripts Pages 17, 113, 114, 116, 125, 126, 127, 129, 130

Simulink/SimPowerSystems/SimElectronics Models Pages 132, 133

2 Introduction to Semiconductor Electronics Diodes2.1 Electrons and Holes ..................................................................................................212.2 Junction Diode.........................................................................................................242.3 Graphical Analysis of Circuits with NonLinear Devices ........................................282.4 Piecewise Linear Approximations ..........................................................................2122.5 Low Frequency AC Circuits with Junction Diodes...............................................2152.6 Junction Diode Applications in AC Circuits ........................................................2182.7 Peak Rectifier Circuits ...........................................................................................2302.8 Clipper Circuits......................................................................................................2312.9 DC Restorer Circuits .............................................................................................2342.10 Voltage Doubler Circuits .......................................................................................2352.11 Diode Applications in Amplitude Modulation (AM) Detection Circuits ............2352.12 Diode Applications in Frequency Modulation (FM) Detection Circuits..............2362.13 Zener Diodes ..........................................................................................................2372.14 Schottky Diode.......................................................................................................2432.15 Tunnel Diode.........................................................................................................2442.16 Varactor ................................................................................................................. 2462.17 Optoelectronic Devices ......................................................................................... 2462.18 Summary................................................................................................................ 250

ii Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publications

2.19 Exercises.................................................................................................................2542.20 Solutions to EndofChapter Exercises ...............................................................259

MATLAB Scripts Pages 26, 227, 228, 259, 267

Simulink/SimPowerSystems/SimElectronics Models Pages 214, 218, 223, 224, 229, 243, 261

3 Bipolar Junction Transistors3.1 Introduction ..........................................................................................................313.2 NPN Transistor Operation....................................................................................333.3 Bipolar Junction Transistor as an Amplifier .........................................................33

3.3.1 Equivalent Circuit Models NPN Transistors...........................................363.3.2 Equivalent Circuit Models PNP Transistors ...........................................373.3.3 Effect of Temperature on the Characteristics...........................39

3.3.4 Collector Output Resistance Early Voltage ..........................................3103.4 Transistor Amplifier Circuit Biasing...................................................................3183.5 Fixed Bias.............................................................................................................3203.6 SelfBias ..............................................................................................................3253.7 Amplifier Classes and Operation........................................................................327

3.7.1 Class A Amplifier Operation ...................................................................3303.7.2 Class B Amplifier Operation....................................................................3333.7.3 Class AB Amplifier Operation.................................................................3353.7.4 Class C Amplifier Operation ...................................................................337

3.8 Graphical Analysis...............................................................................................3383.9 Power Relations in the Basic Transistor Amplifier .............................................3423.10 PiecewiseLinear Analysis of the Transistor Amplifier.......................................3433.11 Incremental Linear Models .................................................................................3483.12 Transconductance ...............................................................................................3533.13 HighFrequency Models for Transistors .............................................................3543.14 The Darlington Connection ...............................................................................3583.15 Transistor Networks.............................................................................................359

3.15.1 hEquivalent Circuit for the CommonBase Transistor.......................3593.15.2 TEquivalent Circuit for the CommonBase Transistor.......................3633.15.3 hEquivalent Circuit for the CommonEmitter Transistor..................3643.15.4 TEquivalent Circuit for the CommonEmitter Transistor..................3683.15.5 hEquivalent Circuit for the CommonCollector Transistor ...............3693.15.6 TEquivalent Circuit for the CommonCollector Transistor...............375

3.16 Transistor Cutoff and Saturation Regions .......................................................... 3763.16.1 Cutoff Region ........................................................................................3763.16.2 Active Region .........................................................................................3763.16.3 Saturation Region ..................................................................................377

iC vBE

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition iiiCopyright Orchard Publications

3.17 The EbersMoll Transistor Model......................................................................3793.18 Schottky Diode Clamp........................................................................................3833.19 Transistor Specifications .................................................................................... 3833.20 Summary ............................................................................................................ 3853.21 Exercises ............................................................................................................. 3893.22 Solutions to EndofChapter Exercises .............................................................395

MATLAB ScriptsPages 312, 338, 3111

Simulink/SimPowerSystems/SimElectronics ModelPage 399

4 Field Effect Transistors and PNPN Devices4.1 Junction Field Effect Transistor (JFET) ................................................................414.2 Metal Oxide Semiconductor Field Effect Transistor (MOSFET) ..................... 46

4.2.1 NChannel MOSFET in the Enhancement Mode................................... 474.2.2 NChannel MOSFET in the Depletion Mode ...................................... 4124.2.3 PChannel MOSFET in the Enhancement Mode ................................. 4154.2.4 PChannel MOSFET in the Depletion Mode ....................................... 4184.2.5 Voltage Gain ......................................................................................... 418

4.3 Complementary MOS (CMOS)....................................................................... 4204.3.1 CMOS CommonSource Amplifier ..................................................... 4204.3.2 CMOS CommonGate Amplifier......................................................... 4214.3.3 CMOS CommonDrain (Source Follower) Amplifier ......................... 421

4.4 Metal Semiconductor FET (MESFET)............................................................ 4224.5 Unijunction Transistor ..................................................................................... 4234.6 Diac.................................................................................................................. 4244.7 Silicon Controlled Rectifier (SCR).................................................................. 424

4.7.1 SCR as an Electronic Switch ................................................................ 4274.7.2 SCR in the Generation of Sawtooth Waveforms .................................. 428

4.8 Triac ............................................................................................................... 4394.9 Shockley Diode.............................................................................................. 4404.10 Other PNPN Devices...................................................................................... 4414.11 The Future of Transistors ............................................................................... 4424.12 Summary........................................................................................................ 4444.13 Exercises ........................................................................................................ 4474.14 Solutions to EndofChapter Exercises ........................................................ 449

MATLAB ScriptsPages 45, 49

Simulink/SimPowerSystems/SimElectronics ModelsPages 411, 417, 437, 438

iv Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publications

5 Operational Amplifiers5.1 Operational Amplifier ........................................................................................ 515.2 An Overview of the Op Amp ............................................................................. 515.3 Op Amp in the Inverting Mode ......................................................................... 525.4 Op Amp in the NonInverting Mode................................................................ 555.5 Active Filters........................................................................................................ 585.6 Analysis of Op Amp Circuits............................................................................5115.7 Input and Output Resistances ..........................................................................5215.8 Op Amp Open Loop Gain ...............................................................................5245.9 Op Amp Closed Loop Gain .............................................................................5265.10 Transresistance Amplifier .................................................................................5285.11 Closed Loop Transfer Function .......................................................................5295.12 Op Amp Integrator ...........................................................................................5305.13 Op Amp Differentiator .....................................................................................5345.14 Summing and Averaging Op Amp Circuits5375.15 Differential Input Op Amp...............................................................................5385.16 Instrumentation Amplifiers...............................................................................5415.17 Offset Nulling ....................................................................................................5435.18 External Frequency Compensation...................................................................5435.19 Slew Rate ...........................................................................................................5445.20 Circuits with Op Amps and Non-Linear Devices .............................................5455.21 Comparator .......................................................................................................5485.22 Wien Bridge Oscillator......................................................................................5495.23 DigitaltoAnalog Converters ..........................................................................5515.24 AnalogtoDigital Converters ..........................................................................556

5.24.1 Flash AnalogtoDigital Converter ......................................................5555.24.2 Successive Approximation AnalogtoDigital Converter ....................5575.24.3 DualSlope AnalogtoDigital Converter............................................558

5.25 Quantization, Quantization Error, Accuracy, and Resolution ........................5605.26 Op Amps in Analog Computers .....................................................................5625.27 Gyrator ..............................................................................................................5655.28 Summary ...........................................................................................................5695.29 Exercises ............................................................................................................5735.30 Solutions to EndofChapter Exercises...........................................................580

MATLAB Scripts Pages 582, 590Simulink/SimPowerSystems/SimElectronics Models Pages 55, 534, 568

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition vCopyright Orchard Publications

6 Integrated Circuits6.1 Basic Logic Gates................................................................................................. 616.2 Positive and Negative Logic ................................................................................ 616.3 Inverter................................................................................................................ 626.4 AND Gate ........................................................................................................... 666.5 OR Gate.............................................................................................................. 686.6 NAND Gate ........................................................................................................ 696.7 NOR Gate......................................................................................................... 6136.8 Exclusive OR (XOR) and Exclusive NOR (XNOR) Gates............................... 6156.9 FanIn, FanOut, TTL Unit Load, Sourcing Current, and Sinking Current 6176.10 Data Sheets ....................................................................................................... 6206.11 Emitter Coupled Logic (ECL) .......................................................................... 6246.12 NMOS Logic Gates........................................................................................... 628

6.12.1 NMOS Inverter..................................................................................... 6306.12.2 NMOS NAND Gate ............................................................................. 6316.12.3 NMOS NOR Gate................................................................................ 632

6.13 CMOS Logic Gates .......................................................................................... 6326.13.1 CMOS Inverter ..................................................................................... 6336.13.2 CMOS NAND Gate ............................................................................. 6346.13.3 CMOS NOR Gate..................................................................................634

6.14 Buffers, Tri-State Devices, and Data Buses .......................................................6356.15 Present and Future Technologies......................................................................6396.16 Summary............................................................................................................6436.17 Exercises.............................................................................................................6466.18 Solutions to EndofChapter Exercises ...........................................................649

7 Pulse Circuits and Waveform Generators7.1 Astable (Free-Running) Multivibrators.................................................................717.2 555 Timer .............................................................................................................727.3 Astable Multivibrator with 555 Timer .................................................................737.4 Monostable Multivibrators .................................................................................7157.5 Bistable Multivibrators (FlipFlops) ...................................................................721

7.5.1 FixedBias Flip-Flop...............................................................................7217.5.2 SelfBias FlipFlop ................................................................................7247.5.3 Triggering Signals for FlipFlops ...........................................................7297.5.4 Present Technology Bistable Multivibrators ..........................................731

7.6 Schmitt Trigger ..................................................................................................7327.7 Summary............................................................................................................7357.8 Exercises.............................................................................................................7367.9 Solutions to EndofChapter Exercises ...........................................................739

MATLAB Scripts Pages 710, 728, 740, 741

vi Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publications

Simulink/SimPowerSystems/SimElectronics Models Pages 714, 720

8 Frequency Characteristics of SingleStage and Cascaded Amplifiers8.1 Properties of Signal Waveforms............................................................................ 818.2 Transistor Amplifier at Low Frequencies ............................................................. 858.3 Transistor Amplifier at High Frequencies ............................................................ 898.4 Combined Low- and HighFrequency Characteristics ......................................8148.5 Frequency Characteristics of Cascaded Amplifiers ............................................8148.6 Overall Characteristics of Multistage Amplifiers................................................8258.7 Amplification and Power Gain in Three or More Cascaded Amplifiers ...........8308.8 Summary .............................................................................................................8328.9 Exercises ..............................................................................................................8348.10 Solutions to EndofChapter Exercises.............................................................837

MATLAB Scripts Pages 88, 823, 843

9 Tuned Amplifiers9.1 Introduction to Tuned Circuits ............................................................................ 919.2 Single-tuned Transistor Amplifier......................................................................... 989.3 Cascaded Tuned Amplifiers ................................................................................ 913

9.3.1 Synchronously Tuned Amplifiers............................................................. 9149.3.2 StaggerTuned Amplifiers ....................................................................... 9179.3.3 Three or More Tuned Amplifiers Connected in Cascade....................... 926

9.4 Summary .............................................................................................................. 9279.5 Exercises ............................................................................................................... 9299.6 Solutions to EndofChapter Exercises.............................................................. 930

MATLAB ScriptPage 917

10 Sinusoidal Oscillators10.1 Oscillators Defined.............................................................................................10110.2 Sinusoidal Oscillators.........................................................................................10110.3 RC Oscillator......................................................................................................10410.4 LC Oscillator ......................................................................................................10510.5 Armstrong Oscillator..........................................................................................10610.6 Hartley Oscillator ...............................................................................................10710.7 Colpitts Oscillator ..............................................................................................10710.8 Crystal Oscillators ..............................................................................................10810.9 Pierce Oscillator ...............................................................................................101010.10 Summary...........................................................................................................1012

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition viiCopyright Orchard Publications

10.11 Exercises ........................................................................................................... 101410.12 Solutions to EndofChapter Exercises ......................................................... 1015

A Introduction to MATLABA.1 MATLAB and Simulink................................................................................A1A.2 Command Window.............................................................................................A1A.3 Roots of Polynomials ...........................................................................................A3A.4 Polynomial Construction from Known Roots....................................................A4A.5 Evaluation of a Polynomial at Specified Values..................................................A6A.6 Rational Polynomials...........................................................................................A8A.7 Using MATLAB to Make Plots .........................................................................A10A.8 Subplots .............................................................................................................A18A.9 Multiplication, Division and Exponentiation...................................................A18A.10 Script and Function Files ..................................................................................A26A.11 Display Formats .................................................................................................A31

MATLAB Scripts Pages A3 through A9, A11 through A13, A16, A17 through A21, A23, A24, A26, A27

B Introduction to SimulinkB.1 Simulink and its Relation to MATLAB................................................................B1B.2 Simulink Demos .................................................................................................B20

MATLAB Script Page B4

Simulink/SimPowerSystems/SimElectronics Models Pages B12, B17, B19

C Introduction to SimscapeC.1 Simscape Libraries................................................................................................ C1

C.1.1 Foundation Library ....................................................................................C1C.1.2 Utilities Library ..........................................................................................C3C.1.3 SimElectronics Library ...............................................................................C4C.1.4 SimPowerSystems Library ..........................................................................C7

Simulink/SimPowerSystems/SimElectronics Model Page C4

D ProportionalIntegralDerivative (PID) ControllerD.1 Description and Components of a Typical PID.................................................. D1D.2 The Simulink PID Blocks .................................................................................... D2

Simulink/SimPowerSystems/SimElectronics Models Pages D3, D4

viii Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publications

E Compensated AttenuatorsE.1 Uncompensated Attenuator .................................................................................E1E.2 Compensated Attenuator......................................................................................E2

F Substitution, Reduction, and Millers TheoremsF.1 Substitution Theorem............................................................................................ F1F.2 Reduction Theorem............................................................................................... F6F.3 Millers Theorem................................................................................................. F10

References R1

Index IN1

Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 15Copyright Orchard Publications

Bandwidth and Frequency Response

1.4 Bandwidth and Frequency Response

Like electric filters, amplifiers exhibit a band of frequencies over which the output remains nearlyconstant. Consider, for example, the magnitude of the output voltage of an electric or elec-

tronic circuit as a function of radian frequency as shown in Figure 1.5.

As shown in Figure 1.5, the bandwidth is where and are the cutoff frequencies.

At these frequencies, and these two points are known as the 3dB down or

halfpower points. They derive their name from the fact that since power , for

and for or the power is , that is, it is halved.

Figure 1.5. Definition of bandwidth

Alternately, we can define the bandwidth as the frequency band between halfpower points. Werecall from the characteristics of electric filters, the lowpass and highpass filters have only one cut-off frequency whereas bandpass and bandelimination (bandstop) filters have two. We may thinkthat lowpass and highpass filters have also two cutoff frequencies where in the case of the lowpass filter the second cutoff frequency is at while in a highpass filter it is at .

We also recall also that the output of circuit is dependent upon the frequency when the input is asinusoidal voltage. In general form, the output voltage is expressed as

(1.12)

where is known as the magnitude response and is known as the phase response. These

two responses together constitute the frequency response of a circuit.

Example 1.1

Derive and sketch the magnitude and phase responses of the lowpass filter shown in Figure1.6.

Figure 1.6. RC lowpass filter

Vout

BW 2 1= 1 2

Vout 2 2 0.707= =

p v2 R i2 R= =R 1= v i 2 2 0.707= = 1 2

1

0.707

1 2

Bandwidth

Vout

0= =

Vout ( ) Vout ( ) ej ( )=

Vout ( ) e j ( )

RC

RCvin vout

Chapter 1 Basic Electronic Concepts and Signals

114 Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publicationss

From Figure 1.16 we observe that all poles, denoted as , lie on the lefthand halfplane andthus the system is stable. The location of the zeros, denoted as , is immaterial.

b. We use the MATLAB expand(s) symbolic function to express the numerator and denominatorof in polynomial form

syms s; n=expand((s1)*(s^2+2*s+5)), d=expand((s+2)*(s^2+6*s+25))n = s^3+s^2+3*s-5d = s^3+s^2+3*s-5and thus

For this example we are interested in the magnitude only so we will use the script

num=3*[1 1 3 5]; den=[1 8 37 50]; sys=tf(num,den);...w=logspace(0,2,100); bodemag(sys,w); grid

The magnitude plot is shown in Figure 1.17.

Figure 1.17. Bode plot for Example 1.3

Example 1.4

It is known that a voltage amplifier has a frequency response of a lowpass filter, a DC gain of, attenuation of per decade, and the cutoff frequency occurs at .

Determine the gain (in ) at the frequencies , , , , , and.

Solution:

Using the given data we construct the asymptotic magnitude response shown in Figure 1.18 fromwhich we obtain the data shown on the table below.

G s( )

G s( ) 3 s3 s2 3s 5+ +( )

s3 8s2 37s 50+ + +( )---------------------------------------------------=

Frequency (rad/sec, log scale)

80 dB 20 dB 3 dB 10 KHzdB 1 KHz 10 KHz 100KHz 1 MHz 10 MHz

100 MHz



1.12 Exercises

1. Following the procedure of Example 1.1, derive and sketch the magnitude and phase responsesfor an highpass filter.

2. Derive the transfer function for the network shown below.

3. A system has poles at , , , and zeros at , , and . Derive thetransfer function of this system given that .

4. The circuit model shown below is known as a transresistance amplifier and the ideal characteristicsfor this amplifier are and .

With a voltage source in series with resistance connected on the input side and a load

resistance connected to the output, the circuit is as shown below.

Find the overall voltage gain if . Then, use MATLAB to plot the

magnitude of for the range . From the plot, estimate the cutoff fre-

quency.

RC

G s( )L

0.5 H

C 1 F R 1 vin t( )+

vout t( )+

+

4 2 j+ 2 j 1 3 j2+ 3 j2G ( ) 10=

Rin 0 Rout 0

Riniin

iout

voutvin

iin

Rin Rinvoutiin

----------iout 0=

=

Rout

vs RsRload

++

+

0.1 nF

vload

vS

2 t mVcos

RS

1 K +

vinC

10 K

Rin

iin

Rmim

Rout

100 Rload

5 K

Av vload vs= Rm 100 =

Av 103

108 3 dB



4. The equivalent circuit is shown below.

The parallel combination of the resistor and capacitor yields

and by the voltage division expression

Also,

(1)

where

s domain

++

+

+

VS s( ) 103

Iin s( )

104 Vin s( )

+

1010 s

102

100Iin s( ) 5 103

Vload s( )

104 1010 s

Z s( ) 104 1010 s|| 1014 s

104 1010 s+---------------------------------- 10

14

104s 1010+-------------------------------= = =

Vin s( )1014 104s 1010+( )

103 1014 104s 1010+( )+--------------------------------------------------------------VS s( ) 10

14

107s 1.1 10 14+------------------------------------------VS s( )= =

Vload s( )5 103

102 5 103+--------------------------------100Iin s( )

5 1055.1 10 3----------------------Iin s( ) 98Iin s( )= = =

ElectronCopyrig

The Junction Diode

The cutional

across

throug

Whenif the voltag

is

Command ifrevers

The mreferre

The mrecurr

VZ

25 Cic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 27

Figure 2.12. Voltagecurrent characteristics of a forwardbiased junction diode.

rve in Figure 2.12 shows that in a junction diode made with silicon and an impurity, conven- current will flow in the direction of the arrow of the diode as long as the voltage drop

the diode is about volt or greater. We also observe that at , the current

h the diode is .

a junction diode is reversebiased, as shown in Figure 2.13, a very small current will flow andapplied voltage exceeds a certain value the diode will reach its avalanche or Zener region. Theecurrent characteristics of a reverse biased junction diode are shown in Figure 2.13 wherereferred to as the Zener diode voltage. Zener diodes are discussed in the next section.

Figure 2.13. The reverse biased region of a junction diode

ercially available diodes are provided with a given rating (volts, watts) by the manufacturer, these ratings are exceeded, the diode will burnout in either the forwardbiased or theebiased direction.

aximum amount of average current that can be permitted to flow in the forward direction isd to as the maximum average forward current and it is specified at a special temperature, usually. If this rating is exceeded, structure breakdown can occur.

aximum peak current that can be permitted to flow in the forward direction in the form ofing pulses is referred to as the peak forward current.

vD0.65 vD 0.7 V=

iD 0.5 mA

VZ

Avalanche Region

i

v0ht Orchard Publications

Chapter 2 Introduction to Semiconductor Electronics Diodes

214

This vfollow Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition

Figure 2.23. Model for Example 2.4 with SimPowerSystems blocks

Figure 2.24. Piecewise linear equivalent circuit for Example 2.4

alue is not consistent with the value displayed in the model in Figure 2.23, so we perform theing check:

VoutI4

1 K20

I320 20

I2I1

0.3 V 1.3 V 2.3 V

15 50Vout 65 50Vout 115 50Vout Vout+ +1000

-------------------------------------------------------------------------------------------------------------------------- 0=

I1 0.3 1.3( ) 20 50 mA I2 1.3 1.3( ) 20 0

I3 2.3 1.3( ) 20 50 mA=

I4 1.3 1000 1.3 mA= =

I1 I2 I3+ + I4Copyright Orchard Publications

ElectronCopyrig

Low Frequency AC Circuits with Junction Diodes

The minus () sign for the current indicates that this current flows in the opposite direction of

the on

right s

2.5 L

Whenoperatwhere

Figure

Figure

I1ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 215

e shown. Also, the current is zero. Therefore, we must conclude that only the diode on the

ide conducts and by the voltage division expression

ow Frequency AC Circuits with Junction Diodes

used with AC circuits of low frequencies, diodes, usually with are biased toe at some point in the neighborhood of the relatively linear region of the characteristics . A bias point denoted as whose coordinates are is shown in

2.25 for a junction diode with .

Figure 2.25. Junction diode biased at point Q and changes in corresponding to changes in

2.25 shows how changes in result in changes in .

I2

Vout1000

20 1000+------------------------ 2.3 2.3 V=

1.8 n 2.0 i v

0.65 vD 0.8 V Q Q VD ID,( )n 2=

Q

t

t

vD t( )

iD t( )

iD vD

vD t( ) iD t( )ht Orchard Publications

Chapter 2 Introduction to Semiconductor Electronics Diodes

224 Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition

Figure 2.40. Simulation of a fullwave rectifier with SimPower Toolbox

Figure 2.41. Waveforms displayed in the Scope block in Figure 2.40Copyright Orchard Publications

ElectronCopyrig

Solutions to EndofChapter Exercises

2.20 Solutions to EndofChapter Exercises

1. vDxlatitle

We

2. Le

or

Fo

scr

x=xlaic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 259

=0: 0.01: 1; iR=10^(15); n=2; VT=26*10^(3); iD=iR.*(exp(vD./(n.*VT))1); plot(vD,iD);...bel('Diode voltage vD, volts'); ylabel('Diode current iD, amps');...('iDvD characteristics for a forwardbiased junction diode'); grid

observe that when , the diode begins to conduct at approximately .

t and . Then,

r convenience, we let and and we use the following MATLAB

ipt to plot on semilog scale.

1: 10: 10^6; y=2.3.*1.*26.*10.^(3).*log10(x); semilogx(x,y);...bel('x=ID2/ID1'); ylabel('y=VD2VD1')

n 2= 7.8 V

ID1 IreVD1 nVT= ID2 Ire

VD2 nVT=

ID2 ID1 eVD2 nVT eVD1 nVT e VD2 VD1( ) nVT= =

VD2 VD1 nVT ID2 ID1( )ln 2.3nVT ID2 ID1( )10log= =

VD2 VD1 y= ID2 ID1 x=y 2.3nVT x10log=ht Orchard Publications

Chapter 3 Bipolar Junction Transistors

32

Transithese the vo

t

less thoperat

wput of

Like juhas betimes that arit requexpen

NP PNN P

5 V

0 VElectronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition

Copyright Orchard Publications

Figure 3.2. Transistors configured as diodes

stors are used either as amplifiers or more commonly as electronic switches. We will discusstopics on the next section. Briefly, a typical NPN transistor will act as a closed switch whenltage between its base and emitter terminals is greater than but no greater than

o avoid possible damage. The transistor will act as an open switch when the voltage is

an . Figure 3.3 shows an NPN transistor used as an electronic switch to perform theion of inversion, that is, the transistor inverts (changes) an input of to an output ofhen it behaves like a closed switch as in Figure 3.3, and it inverts an input of to an out-

when it behaves like an open switch as in Figure 3.4.

Figure 3.3. NPN transistor as electronic closed switch inverts to

nction diodes, most transistors are made of silicon. Gallium Arsenide (GaAs) technologyen under development for several years and its advantage over silicon is its speed, about sixfaster than silicon, and lower power consumption. The disadvantages of GaAs over silicon issenic, being a deadly poison, requires very special manufacturing processes and, in addition,ires special handling since it is extremely brittle. For these reasons, GaAs is much more

sive than silicon and it is usually used only in superfast computers.

CathodeBE E B

AnodeAnode Cathode

NN P

CBAnode Cathode

NP P

B CCathode Anode

VBE 0.7 VVBE

0.6 V5 V

0 V5 V

E

C

B

VCC 5 V=

RC

Vout VCE 0 V= =

Vin VBE 5 V= =

VCC 5 V=

RC

Vin

5 V 0 V

ElectronCopyrig

The Bipolar Junction Transistor as an Amplifier

The cfor the

3.3.2

Relati

needs

For eators in

The reon an

vBE VT 5 10 6 10

--=

iB =

iB =

iB i=

iB (=ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 37ht Orchard Publications

ollector bias voltage is used for proper transistor operation and its value is not required above calculations.

Equivalent Circuit Models PNP Transistors

ons (3.15), (3.16), and (3.17) apply also to PNP transistor equivalent circuits except that

to be replaced by as shown in Figure 3.8.

Figure 3.8. PNP transistor equivalent circuit model for relations (3.15), (3.16), and (3.17)

sy reference we summarize the currentvoltage relationships for both NPN and PNP transis- the active mode in Table 3.1.

lations in Table 3.1 are very useful in establishing voltage and current levels at various points NPN or PNP transistor.

TABLE 3.1 NPN and PNP transistor currentvoltage characteristics

NPN Transistor PNP Transistor

e10 16

------------------- 5 10= =

vBE VT 5 1010

( )ln=

vBE VT 5ln 10 10ln+( ) 26 10 3 1.61 23.03+( ) 0.64 V= =VCC

vBEvEB

Ir ( )evEB VT vEB

iE

iCiB

iC iB=

CB

E

1+

----------iCiE-----= 1 ------------

iCiB-----= =

iE iB iC+= 1+------------iCiE-----= = 1 ------------

iCiB-----= =

iE iB iC+=

Ir--- e

vBEVT---------

iC Ire

vBEVT---------

= iEIr--- e

vBEVT---------

= iBIr--- e

vEBVT---------

= iC Ire

vEBVT---------

= iEIr--- e

vEBVT---------

=

iC iC iB= iB iC = iB iC = iC iB= iB iC =E 1+( ) iC iE= iE 1+( )iB= iB iE 1+( )= iC iE= iE 1+( )iB=1 ) iE VT 26 mV at T 27 C= = iB 1 ( ) iE= VT 26 mV at T 27 C= =

vBE VT ( )ln Ir( )ln iB( )ln+[ ]= vBE VT ( )ln Ir( )ln iB( )ln+[ ]=

Chapter 3 Bipolar Junction Transistors

352

mode are provided by the transistor manufacturers. Please refer to the last section in this chapter.Table

Exam

For th

SolutiThe in

h=Ac =Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


3.3 lists the hparameter equations for the three bipolar transistor configurations.

ple 3.15

e amplifier circuit in Figure 3.62 it is known that , ,

, and . Find the small signal current amplification

.

Figure 3.62. Transistor amplifier for Example 3.15on:cremental model of this transistor amplifier is shown in Figure 3.63 where

Figure 3.63. The incremental model for the transistor circuit in Figure 3.62

TABLE 3.3 hparameter equations for transistorsParameter CommonBase CommonEmitter CommonCollector

h11 hib hie h11 1 h21+( ) hic h11 1 h21+( )h12 hrb hre h11h22 1 h21+( ) h12 hrc 1h21 hfb hfe h21 1 h21+( ) hfc 1 1 h21+( )h22 hob hoe h22 1 h21+( ) hoc h22 1 h21+( )

rn h11 2 K= = h21 100= =12 5 10

4= go h22 2 10

5 1= =

iload is

is

+

+

2 K

vs

Rs

iload

10 K16 V

2 V

R1

RC

VCC

+

vCE

Req1 go( )Rload

1 go Rload+------------------------------ 50 10

3 2 103

52 103-------------------------------------------- 1.923 K= = =

Req

rnB

ib

isgoib

E

iloadC

RloadR1 vce

Req

Rs 10 K2 K

ElectronCopyrig

Schottky Diode Clamp

(3.185)

or

Using

we can

3.5 S

In thecapacidiode a3.88.

The Sfore, wcarried

3.6 T

TransThe sp

1. Feaand

gIC---------- 1------- I e VB VE( ) VT( )= =ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 383ht Orchard Publications

(3.186)

the relations

(3.187)

also express these smallsignal parameters in terms of one another as

(3.188)

chottky Diode Clamp

saturation region, the collectorbase diode is forwardbiased. Due to the large diffusiontance, it takes a considerably long time to drive the transistor out of saturation. The Schottkylleviates this problem if connected between the base and the collector as shown in Figure

chottky diode has the property that it turns on at a lower voltage than the PN junction. There-hen a transistor is in the saturation region, the current between the base and the collector is by the Schottky diode.

Figure 3.88. NPN and PNP transistors with Schottky diodes

ransistor Specifications

istors are available in a variety of shapes and sizes, each with its own unique characteristics.ecifications usually cover the items listed below, and the values given are typical.

tures, e.g., NPN Silicon Epitaxial Planar Transistor for switching and amplifier applications, mechanical data, e.g., case, weight, and packaging options.

m VB VTS

IC

gmICVT-------=

IC FIB FIE= = IE ICF------ F 1+( )IB= = IBICF-----

IEF 1+---------------= =

rbFgm------ F 1+( )re= = re

Fgm------

rbF 1+---------------= = gm

Frb----- F

re------= =

E

C

B

E

C

B

NPN Transistor PNP Transistor

Schottky diodeSchottky diode

ElectronCopyrig

Exercises

9. For

bia

10. Fo

ac

11. Fo

si

12. Fanab

IC

R

IEic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 391ht Orchard Publications

an NPN transistor circuit , , and with the reverse

sed collectorbase junction set at we want the collector current to be

. What should the values of and be to achieve this value?

r a PNP transistor circuit with , , , , and

, what would the largest value of be so that the transistor operates at thetive mode?

r a PNP transistor circuit with , , , ,

, and , what should the values of and be so that the tran-stor operates at the active mode?

or the circuit below, it is known that for both transistors. Find all indicated voltagesd currents. Are both the transistors operating in the active mode? What is the total powersorbed by this circuit?

E

C

B IB IC

RB VBEVS

VCC

VC

VBRE

3 K

IEVE

5 KRC12 V

100= VCC 11.3 V= VB 3.5 V=VCB 1.8 V=

0.8 mA= RC RE

120= VEE 12 V= VB 0 V= VCC 12 V=E 3 K= RC

150= VEE 12 V= VB 0 V= VCC 12 V=0.8 mA= VCB 3 V= RC RE

120=

E1

C1

B1

IB1

IC1

R2

VBE1

VCC

VC1

VB1RE1

5 K

IE1VE1

8 KRC1R1 60 K

K

C2

E2

B2IB2 IE2

VEB2VE2

RC28 K

IC2VC2

5 KRE2 12 V

10 AVB2

30


Chapter 4

Field Effect Transistors and PNPN Devices

his chapter begins with a discussion of Field Effect Transistors (FETs), characteristics, andapplications. Other PNPN devices, the fourlayer diode, the silicon controlled rectifier(SCR), the silicon controlled switch (SCS), and the triac are introduced with some of their

applications. The chapter includes also a brief discussion on unijunction transistors, and diacs.

4.1 Junction Field Effect Transistor (JFET)

The FieldEffect Transistor (FET) is another semiconductor device. The Junction FET (JFET) is theearlier type and the Metal Oxide Semiconductor FET (MOSFET) is now the most popular type. In thissection we will discuss the JFET and we will discuss the MOSFET in the next section.

Figure 4.1(a) shows the basic JFET amplifier configuration and the output voltampere characteris-tics are shown in Fig. 4.1(b). These characteristics are similar to those for the junction transistorexcept that the parameter for this family is the input voltage rather than the input current. Like theold vacuum triode, the FET is a voltagecontrolled device.

Figure 4.1. Pictorial representation and output voltampere characteristics for a typical JFET

The lower terminal in the N material is called the source, and the upper terminal is called the drain;the two regions of P material, which are usually connected together externally, are called gates. PNjunctions exist between the P and N materials, and in normal operation the voltage applied to thegates biases these junctions in the reverse direction. A potential barrier exists across the junctions,and the electrons carrying the current in the N material are forced to flow through the channel

between the two gates. If the voltage applied to the gates is changed, the width of the transitionregion at the junction changes; thus the width of the channel changes, resulting in a change in theresistance between source and drain. In this way the current in the output circuit is controlled bythe gate voltage. A small potential applied to the gates, 5 to 10 volts, is sufficient to reduce the chan-nel width to zero and to cut off the flow of current in the output circuit.

T

N

PP+

+

vG

RL

VDDRs

vs

vDiG

iD

10 20

iD mA( )15

12

9

6

3

vD V( )a( )

vG 0=

vG 1=

vG 2=

vG 3=vG 4=

b( )

iD

Chapter 4 Field Effect Transistors and PNPN Devices

44 Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third EditionCopyright Orchard Publications

Figure 4.4. NChannel and PChannel JFETs

Like in bipolar transistors, one important parameter in FETs is its transconductance defined as

the ratio of the change in current to the change of voltage which produced it. In other

words,

(4.1)

Example 4.1

Figure 4.5 shows a commonsource Nchannel JFET amplifier circuit and Table 4.1 shows severalvalues of the current corresponding to the voltage .

Figure 4.5. Commonsource Nchannel JFET amplifier for Example 4.1

TABLE 4.1 Current versus voltage for Example 4.1

N

PPG

D

S

+

D

S

G

N

PPG

D

S

+

D

S

G

N Channel JFET P Channel JFET

gmiDS vGS

gmiDSvGS------------

vDS cons ttan=

=

iDS vGS

D

S

G

VDDRD 1 K

vin

vout

+

iDS

+

+

15 V

iDS vGS

vGS V( ) 0 1 2 3 4iDS mA( ) 35 20 8 2 0


Metal Oxide Semiconductor Field Effect Transistor (MOSFET)

Figure 4.13. SimElectronics model with an N-Channel MOSFET

Relation (4.8) which is repeated below for convenience, represents an MOSFET andwe observe that, in saturation, the drain current is independent of the drain voltage

(4.11)

Therefore, we conclude that in the saturation mode the MOSFET behaves as an idealcurrent source whose value is as in (4.11).

In analogy with the transconductance in bipolar junction transistors, the MOSFET transconductanceis defined as

(4.12)

In other words, the transconductance is a measure of the sensitivity of drain current to changes ingatetosource bias.

As indicated in the previous chapter, subscripts in upper case represent the sum of the quiescentand small signal parameters, and subscripts in lower case represent just the small signal parameters.Thus, and (4.11) can be expressed as

n channeliD vDS

iD12--- kn

WL----- vGS VT( )2= for vDS vGS VT

n channel

gmiD

vGS------------

vDS cons ttan=

=

vGS VGS vgs+=

ElectronCopyrig

Op Amp in the Inverting Mode

Note 1: In the inverting mode, the resistor connected between the noninverting (+) input andground serves only as a current limiting device, and thus it does not influence the op

Note 2

As sho

is

minus

that oitive (+op am

put wi

Exam

Comp

shown

of axe

Soluti

This i

and si

the ou

or

R

Rf

180ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 53ht Orchard Publications

amps gain. So its presence or absence in an op amp circuit is immaterial.

: The input voltage and the output voltage as indicated in the circuit of Figure 5.3,

should not be interpreted as open circuits; these designations imply that an input voltageof any waveform may be applied at the input terminals and the corresponding output volt-age appears at the output terminals.

wn in the relation of (5.1), the gain for this op amp configuration is the ratio where

the feedback resistor which allows portion of the output to be fed back to the input. The

() sign in the gain ratio implies that the output signal has opposite polarity from

f the input signal; hence the name inverting amplifier. Therefore, when the input signal is pos-) the output will be negative () and vice versa. For example, if the input is +1 volt DC and thep gain is 100, the output will be 100 volts DC. For AC (sinusoidal) signals, the output will beoutofphase with the input. Thus, if the input is 1 volt AC and the op amp gain is 5, the out-ll be 5 volts AC or 5 volts AC with outofphase with the input.

ple 5.1

ute the voltage gain and then the output voltage for the inverting op amp circuit

in Figure 5.4, given that . Plot and as versus time on the same set

s.

Figure 5.4. Circuit for Example 5.1on:

s an inverting amplifier and thus the voltage gain is

nce

tput voltage is

vin vout

Rf Rin

Rf Rin

180

Gv voutvin 1 mV= vin vout mV

+

RinRf

vin vout

120 K

20 K+

+

Gv

GvRfRin-------- 120 K20 K

-------------------- 6== =

Gv vout vin=

vout Gvvin 6 1= =

vout 6 mV=

ElectronCopyrig

Op Amp Integrator

(5.43)

Since

voltag

Also,

we rew

Exam

The inthe ou

Soluti

From

vC1C---- iC td

0

t V0+=ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 531ht Orchard Publications

Figure 5.53. The Miller integrator

the inverting input is at virtual ground, the output voltage is the negative of the capacitor

e , that is, , and thus

(5.44)

since

(5.45)

rite (5.44) as(5.46)

ple 5.17

put voltage to the amplifier in Figure 5.53(a) is as shown in Figure 5.54(b). Find and sketchtput voltage assuming that the initial condition is zero, that is, .

Figure 5.54. Circuit and input waveform for Example 5.17

on:

relation (5.46)

iC i=

vin vout

i C

R1

voutvC vout vC=

vout1C---- iC td

0

t V0=iC i

vinR1-------= =

vout1

R1C---------- vin td

0

t V0=

V0 0=

vin vout

1 M

vin V( )

t s( )

2

3

a( )

b( )

1 FR1

C

vout1

R1C---------- vin td

0

t V0=

ElectronCopyrig

DigitaltoAnalog Converters

5.23

As weand LnumbDoubleand ze

In Fig

volts) combi

(most

A digitan equ

log deis twicbe dou

* RefISBic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 551ht Orchard Publications

Figure 5.82. Circuit for Example 5.21

DigitaltoAnalog Converters

will see in Chapter 6, digital systems* recognize only two levels of voltage referred to as HIGHOW signals or as logical 1 and logical 0. This twolevel scheme works well with the binaryer system. It is customary to indicate the HIGH (logical 1)and LOW (logical 0) by SinglePoleThrow (SPDT) switches that can be set to a positive nonzero voltage like 5 volts for HIGHro volts or ground for LOW as shown in Figure 5.83.

Figure 5.83. Digital circuit represented by SPDT switches

ure 5.81 , , , and , that is, switches A and C are HIGH (5

and switches B and D are LOW (0 volts). The first 16 binary numbers representing all possiblenations of the four switches with voltage settings (least significant position) through

significant position), and their decimal equivalents are shown in Table 5.1.

altoanalog (D/A or DAC) converter is used to convert a binary output from a digital system toivalent analog voltage. If there are 16 combinations of the voltages through , the ana-

vice should have 16 possible values. For example, since the binary number 1010 (decimal 10)e the value of the binary number 0101 (decimal 5), an analog equivalent voltage of 1010 mustble the analog voltage representing 0101.

er also to Digital Circuit Analysis and Design with Simulink Modeling and Introduction to CPLDs and FPGAs,N 9781934404058.

50 K

D1 D215.9 F 10K

V

Vout

100 K 100 K15.9 F

VN VD VC VAVB

5 V 5 V 5 V 5 V 5 V

VD 0= VC 1= VB 0= VA 1=

VA VD

VD VA

Chapter 5 Operational Amplifiers

562

Example 5.24

How m

Soluti

The in

clock

5.26

Presening thpresen

Exam

Using

where

Soluti

We obconstaa coefcient ias

and thshown

outpu

obtain

obtain

c1 aElectronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


any clock cycles would we need to obtain a 10bit resolution with a dualslope ADC?

on:

tegration time would require clock cycles and also another

cycles for integration time for a maximum conversion of clock cycles.

Op Amps in Analog Computers

t day analog computers are build with op amps. In an analog computer the numbers represent-e variables are voltages. We will not discuss analog computers in this section. We will simplyt two simple examples to illustrate how op amps are used in analog computation.

ple 5.25

two op amps and resistors, design an analog computer that will solve the equations

(5.74)

, , , , , and are constant coefficients.

on:

serve that the arithmetic operations involved in (5.74) are addition and multiplication bynt coefficients. The two additions can be performed by summing op amps. Multiplication byficient greater than unity can be performed with an op amp with feedback, and if the coeffi-s less than unity, we can use a voltage divider. It is convenient to express the given equations

(5.75)

ese equations can be solved using two summing amplifiers as shown in Figure 5.93. As in Figure 5.95, the output of op amp is a voltage representing the unknown and the

t of op amp is a voltage representing the unknown . The fraction of is

ed from the potentiometer and this is summed in op amp with the fraction

obtained from potentiometer and voltage source . A similar summation is

ed by amplifier .

T1 210 1024= 210 1024=

T2 2 210

2048=

a1x b1y+ c1=

a2x b2y+ c2=

a1 a2 b1 b2 c1 c2

xc1a1-----

b1a1-----y=

yc2b2-----

a2b2-----x=

A1 x

A2 y b1 a1 yR adj4 A1

1 R adj1 VS1A2

ElectronCopyrig

Op Amps in Analog Computers

In Figdo noof sim

Beforediscusbeginntime, integr

Initialdenot

neous

Whenoutpu

The inend oset ini

VS1R1 RR adj1ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 563ht Orchard Publications

Figure 5.95. Analog computer for the solution of two simultaneous equations with two unknowns

ure 5.95 the scaling factors chosen must ensure that the voltages representing the unknownst exceed the output capability of the op amps. This procedure can be extended to the solutionultaneous equations with more than two unknowns.

we consider the next example for a circuit to solve a simple differential equation, we need tos a practical integrator circuit that provides some means of setting a desired initial value at theing of the integration cycle. It is also necessary to provide means to stop the integrator at any

and for the integrator output to remain constant at the value it has reached at that time. Anator circuit that provides these means is shown in Figure 5.96.

ly, the integrator sets the initial condition with the switches as shown in Figure 5.94(a), anding the initial condition as . The voltage across the capacitor cannot change instanta-

ly, and thus

(5.76)

switched to the compute mode, the circuit integrates the input voltage and the value of thet voltage is

(5.77)

tegrator is then switched to the hold mode and remains constant at the value reached at thef the compute mode. We observe that the switches in the hold mode are positioned as in thetial condition mode.

VS2

R2

R3

R4

f1

R f2R adj2

R adj4

R adj3x

c2 b2y

c1 a1

a2 b2( )x

b1 a1( )y

A1

A2

V0

vout t 0=( )R2R1------ V0=

vout vout t 0=( )1

RinC------------ vin td

0

t=

ElectronCopyrig

Exercises

5.29 Exercises

1. For

2. Fo

3. For

age

souic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 573ht Orchard Publications

the circuit below compute .

r the circuit below compute .

the circuit below, , , and represent the internal resistances of the input volt-

s , , and respectively. Derive an expression for in terms of the input voltage

rces, their internal resistances, and the feedback resistance .

vout2

+

10 mV+

+ +

+vout2

3 K27 K 10 K

90 K

vout1

vin1

i5K

60 mV

+

3 Ki5K

4 K

6 K 5 K+

Rin1 Rin2 Rin3vin1 vin2 vin3 vout

Rf

vin1vin2 vin3

Rin1

Rin2 Rin3

++

++

+

Rf

vout

ElectronCopyrig

Chapter 6

are dis

6.1 B

Electrcuits (these these

Four oare de

6.2 P

Generand w

tion. Tstand Figure

With ter H

* For hexatabl19

Tic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 61ht Orchard PublicationsIntegrated Circuits

his chapter begins with an introduction to electronic logic gates and their function in terms ofBoolean expressions and truth tables. Positive and negative logic are defined, and the transis-tortransistor logic (TTL), emittercoupled logic (ECL), CMOS, and BiCMOS logic familiescussed. Earlier logic families are presented in the exercises section.

asic Logic Gates*

onic logic gates are used extensively in digital systems and are manufactured as integrated cir-ICs). The basic logic gates are the inverter or NOT gate, the AND gate, and the OR gate, andperform the complementation, ANDing, and ORing operations respectively. The symbols forgates are shown in Figure 6.1.

Figure 6.1. The three basic logic gates

ther logic gates, known as NAND, NOR, Exclusive OR (XOR), and Exclusive NOR (XNOR),rivatives of the basic AND and OR gates and will be discussed later in this chapter.

ositive and Negative Logic

ally, an uncomplemented variable represents a logical , also referred to as the true condition,hen that variable is complemented, it represents a logical , also referred to as the false condi-

hus, if (true), it follows that (false). Of course, digital computers do not under-logical , logical , true, or false; they only understand voltage signals such as that shown in 6.2.

Figure 6.2. Typical voltage signal for a digital computer

reference to the voltage waveform of Figure 6.2, integrated circuit manufacturers assign the let-(High) to the level and the letter L (Low) to the ground level as shown in Figure 6.3.

this and the remaining chapters it is assumed that the reader has prior knowledge of the binary, the octal, anddecimal number systems, complements of numbers, binary codes, the fundamentals of Boolean algebra, and truthes. If not, it is strongly recommended that a good book like our Digital Circuit Analysis and Design, ISBN 97834404058 is reviewed.

Inverter AND gate OR gate

10

A 1= A 0=1 0

0 volt ground( ) level

5 volt level

5 volt

ElectronCopyrig

NAND Gate

Figuredescricuit o

6.6 N

The slogic i

1Aic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 69ht Orchard Publications

Figure 6.15. The SN7432 Quad 2input OR gate

6.16 shows the internal details of the TTL SN7432 Quad 2input OR gate. We will notbe the functioning of the SN7432 Quad 2input OR gate at this time. We will defer the cir-peration until we first describe the NOR gate operation in a subsequent section.

Figure 6.16. Circuit for the SN7432 Quad 2input OR gate (Courtesy Texas Instruments)

AND Gate

ymbol for a 3input NAND gate is shown in Figure 6.17, and the truth table with positives shown in Table 6.8.

Figure 6.17. Symbol for 3input NAND gate

1

2

3

4B

Vcc

7

6

4

4A

4Y

3A

3Y

5 3B

1A

2A

1Y

1B

2Y

2B

GND

14

8

9

10

11

12

13

1B1Y

2A

2B2Y

3Y3A

3B

4A4Y

4B

DBC

A

Chapter 6 Integrated Circuits

610

Table cal .

Figure4 NAN

Figurelent toare fabFigure

1 Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition Copyright Orchard Publications

6.8 shows that the output of an NAND gate is logical (false) only when all inputs are logi-

6.18 shows the TTL SN7400 Quad 2input NAND gate where Quad implies that there areD gates within the IC.

Figure 6.18. The SN7400 Quad 2input NAND gate

6.19 shows the internal details of the IC SN7400 NAND gate where transistor is equiva- two identical NPN transistors with their bases and collectors tied together; therefore, theyricated as a single device with 2 emitters but only one collector and one base as shown in 6.19.

TABLE 6.8 Truth table for 3input NAND gate with positive logicInputs Output

A B C D0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 11 0 1 11 1 0 11 1 1 0

0

1Y

3A

1A

1B

2B

2A2Y

3B3Y

4A

4B4Y

1

2

3

4B

Vcc

7

6

4

4A

4Y

3A

3Y

5 3B

1A

2A

1Y

1B

2Y

2B

GND

14

8

9

10

11

12

13

T1

ElectronCopyrig

Exercises

WrWh

5. Fo

6. For

a fa

7. Th

750

0 ic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 647ht Orchard Publications

ite the truth table for the input combinations of and with respect to the ground.ich type of logic gate does this circuit represent?

r the circuit below find and when each of through assumes the values of

and with respect to the ground.

the circuit of Exercise 5, derive an expression for High level when the driving gate has

nout of 2. Hint: Start with an equivalent circuit.

e circuit below is a 3input DiodeTransistor Logic (DTL) gate.

750

750

1 K

T1

5 V

T2

T3

V1

V2

V3

Vout

0 V 5 V

Vout1 Vout2 V1 V4V 5 V

V1

V2

V3750

750

750

750 1 K

T1

T2

T41 K

5 V

5 V

T3

V4

Vout1

Vout2

Vout1

Chapter 7 Pulse Circuits and Waveform Generators

72

F

If in F

where

7.2 5

The 5in Figu

We oband th

plus (+

state o

and ifElectronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


igure 7.3. Waveform showing period T and times ON and OFF for the multivibrator circuit of Figure 7.1

igure 7.3 , the pulse repetition frequency is given by

and are as shown in Figure 7.1.

55 Timer

55 Timer circuit is a widely used IC for generating waveforms. A simplified diagram is shownre 7.4.

Figure 7.4. Simplified circuit for the 555 Timer

serve that this IC includes a resistive voltage divider consisting of three identical resistorsis divider sets the voltage at the plus (+) input of the lower comparator at and at

) input of the upper comparator at . The outputs of the comparators determine the

f the SR flipflop whose output is either or . Thus, if is High (Set state), is Low,

is Low, will be High (Reset state) or vice versa.

Output 1

T

T1 T2

T1 T2= f

f 1T--- 1

T1 T2+------------------ 1

2 RB Cln-------------------------------- 1

0.69 RB C---------------------------------= = = =

RB C

VCC

R

+

+

Disch earg

Trigger

Threshold

Output

S Q

Q

Comparator 2

Comparator 1R

R

R

2 3 VCC

1 3 VCC

1 3 VCC2 3 VCC

Q Q Q QQ Q

ElectronCopyrig

Astable Multivibrator with the 555 Timer

The SR flipflop is Set when a High level is applied to the S input, and it is Reset when a High levelis applied to the R input. Accordingly, the flipflop is Set or Reset depending on the outputs of thetwo coComp

the High,

7.3 A

A usefwe recin Fig

For th

Figurethe du

For this Set.charg

When

resets rated,tors

sistor.

reache

Q

vC =

Ric Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 73ht Orchard Publications

mparators, and these outputs are determined by the inputs Threshold at the plus (+) input ofarator 1, and Trigger at the minus () input of Comparator 2. The output of the 555 Timer is

output of the SR flipflop and when it is Low, will be High, and if the input Discharge isthe transistor will be saturated and it will provide a path to the ground.

stable Multivibrator with the 555 Timer

ul application of the 555 Timer is as an astable multivibrator. From our previous discussion,all that the astable multivibrator is a pulse generator producing waveforms such as that shownure 7.5.

Figure 7.5. Typical waveform for an astable multivibrator

e waveform of Figure 7.5,

7.6 shows an astable multivibrator employing a 555 Timer. We will see that with this circuitty cycle will always be greater than 0.5 as shown in Figure 7.7.

e circuit of Figure 7.6 let us first assume that the capacitor is uncharged and the SR flipflop In this case the output is High and the transistor is does not conduct. The capacitor then wille towards through the resistors and . When the capacitor reaches the value

the output of Comparator 2 goes Low and the SR flipflop remains Set.

the capacitor reaches the value , the output of Comparator 1 goes High and

the SR flipflop and thus the output goes Low, goes High, the transistor becomes satu- its collector voltage becomes almost zero, and since it appears at the common node of resis-

and , the capacitor begins to discharge through resistor and the collector of the tran-

The capacitor voltage decreases exponentially with time constant and when it

s the value , the output of Comparator 2 goes High and Sets the SR flipflop.

Q

T

T1 T2

Period T T1 T2+= =

Pulse Repetition Frequency f 1T---= =

Duty CycleT1T-----=

VCC RA RB1 3 VCC

vC 2 3 VCC=

Q Q

A RB RBvC td RBC=

vC 1 3 VCC=


74

The othroug

time cand th

We ar

and th

VCC

T T=Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


Figure 7.6. Implementation of an astable multivibrator with a 555 Timer

Figure 7.7. Input and output waveforms for the astable multivibrator of Figure 7.6

utput goes High, goes Low, the transistor is turned OFF, the capacitor begins to chargeh the series combination of resistors and , and its voltage rises exponentially with

onstant and when it reaches the value it resets the flipflope cycle is repeated.

e interested in the pulse repetition frequency and the duty cycle where

and the desired values are dependent on appropriate values of resistors and

e capacitor . As we know, the capacitor voltage as a function of time is given by

RA

RB

C

vC

R

R

R

2 3 VCC

1 3 VCC

Comparator 1

Comparator 2

OutputR

S Q

Q

+

+

T1 T2

T2T1

vC 2 3 VCC=

vC 1 3 VCC=

Output waveform

Q QRA RB

tr RA RB+( )C= vC 2 3 VCC=

f 1 T= T1 T

1 T2+ RA RBC


722

Soluti

This cThe anconne

7.27(a

as

Let us

are smas shoBy the

and th

cutoff

+12 V

T2Electronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


Figure 7.26. Fixedbias flipflop circuit for Example 7.4.on:

ircuit consists of two crosscoupled inverter circuits such as that of Exercise 8 in Chapter 6.alysis is facilitated by breaking the given circuit into two parts, the first part indicating the

ctions between the base of transistor and the collector of transistor as shown in Figure

), and the second part indicating the connection between the collector of and the base of

shown in Figure 7.27(b).

Figure 7.27. Circuits for the computation of the stable states for Example 7.4

first assume that transistor is OFF and transistor is ON. Since the saturation voltages

all (about ), we will initially neglect them and we let and wn in Figures 7.25(a) and 7.25(b) respectively. voltage division expression

is voltage will certainly keep transistor at cutoff. To verify that with transistor beyond

transistor is in saturation, we calculate by first finding and as follows:

12 V

2.2 K15 K

2.2 K15 K

VC2VC1

K100 100

K

T1 T2

T1 T2T1

+12 V +12 V

12 V 12 V

T1 T2 T1 T2

2.2 K

15 K 15 K

2.2 K

100K K

100

VC2 0 V VC1OFF ON

ON OFF

VB2 0 VVB1IC2

I1I2

IB2

I4

I3

a( ) b( )

T1 T20.2 V VC2 sat( ) 0 V VB2 sat( ) 0 V

VB115 K

100 K 15 K+-------------------------------------------- 12 V( ) 1.57 V= =

T1 T1T2 IC2 I1 I2

ElectronCopyrig

Bistable Multivibrator (FlipFlop)

F

7.5.4

The bwere iwhichamps tion.

The cbrator

+VCCCic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 731ht Orchard Publications

Figure 7.37. A method of triggering unsymmetrically an NPN or a PNP transistor

igure 7.38. Methods of symmetrical triggering through diodes at the collectors or the bases of the transistors

Present Technology Bistable Multivibrators

istable multivibrator (flipflop) circuits weve discussed thus far are the original circuits andn use in the 1960s. We have included them in this text because they are the circuits from present technology bistable multivibrators such as those with CMOS technology and ophave evolved. We will briefly discuss a bistable multivibrator with an op amp in this subsec-

ircuit of Figure 7.39 shows how an op amp can be configured to behave as a bistable multivi-.

a( )V BB

V CC

+VBB

Trigger

b( )

T1

Trigger

input

input

T2

T1T2

OFF

ON

OFF

ON

RC

R1

R2

1

C

RS

RS

C1

R1

RC

R2

C

D1

C

+VCC

V BB

TT

C

a( ) b( )

T1

T2T1

T2

OFF

ONOFF

ON

RC

R2

D2RC

R2

D1

D2

D3

D3


732

The stput is itive feFigure

7.6 S

Anoth

The Svoltag

of the

to its

put is

the in

voltag

age

of the

vin

Vout

VElectronic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition


Figure 7.39. Op amp configured as a bistable multivibrator

able states for the bistable multivibrator of Figure 7.39(a) are the conditions where the out-at positive or negative saturation. It assumes either positive or negative saturation by the pos-edback formed by resistors and . A positive or negative going pulse as that shown in 7.39(b) causes the circuit to switch states.

chmitt Trigger

er bistable multivibrator circuit is the Schmitt trigger shown in Figure 7.40(a).

Figure 7.40. Schmitt trigger circuit and waveforms for increasing and decreasing input signals

chmitt trigger circuit and transfer characteristics are similar to the comparator. It provides ane when its input signal reaches some predetermined value set at the noninverting input

op amp. The output of the op amp changes from the positive saturation voltage

negative saturation voltage and vice versa. As shown in Figure 7.40(b), the out-

positively saturated as long as the input signal is less than the upper threshold . If

put signal rises slightly above this threshold voltage, the output drop abruptly to

and stays there until drops below a lower threshold voltage . The threshold

es and are determined by the resistors and , and the reference volt-

. These threshold voltages can be found by application of KCL at the noninverting input

op amp. Thus,

a( ) b( )

vin

voutvoutR1

C

R3R2

R2 R3

vs

a( )Vref

vout

R2R1

vout

vs

vout

vs

b( ) c( )

V +

V +upper V +lower

vsVout max( )

Vout max( )vs V +upper

vsmax( ) vS V +lower

V +upper V +lower R1 R2

ref

ElectronCopyrig

Solutions to EndofChapter Exercises

7.9 Solutions to EndofChapter Exercises

1.

Th

Fro

Th

Su

an

2.

Th

acmThic Devices and Amplifier Circuits with MATLAB / Simulink / SimElectronics Examples, Third Edition 739ht Orchard Publications

e period is and the duty cycle is

m relation (7.6)

(1)

e duty cycle is and from relations (7.3) and (7.6) we obtain

(2)

btraction of (2) from (1) yields

d from (2)

e period is . The duty cycle is . To

hieve a duty cycle at , we must make and this condition will be satisfied if weultiply relation (7.11) by 3 and equate it to relation (7.14) subject to the constraint of (7.16).en,

0 1 2

5

t s( )

v V( )

3 4

T1

T

T2

T T1 T2+ 3 1+ 4 s= = =

T1 T 3 4 0.75 75 %= = =

T 4 10 6 0.69 RA 2RB+( )C 0.69 10 9 RA 2RB+( )= = =

RA 2RB+4 10 6

0.69 10 9--------------------------- 5.77 K= =

T1 T

Duty cycle 0.75T1T----- 0.69 RA RB+( )C

0.69 RA 2RB+( )C------------------------------------------- RA RB+

RA 2RB+----------------------- RA RB+

5.77 K----------------------= = = = =

RA RB+ 0.75 5.77 4.33 K= =

RB 5.77 4.33 3.44 K= =

RA 4.33 3.44 890 = =

0 1 2

5

t s( )

v V( )

3 4 5

T

T1 T2

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