Electronic Devices for anolog signal processing pdf

Thus, the input resistance, current, and offset voltage are determined by the input stage, while the output resistance and the maximal values of the output voltage and current are determ

on all the topics relevant for the design, processing, and manufacturing of electronic devices The books, each prepared by leading researchers or engineers

micro-in their fields, cover the basic and advanced aspects of topics such as waferprocessing, materials, device design, device technologies, circuit design, VLSIimplementation, and subsystem technology The series forms a bridge betweenphysics and engineering and the volumes will appeal to practicing engineers as well

as research scientists

Series Editors:

Dr Kiyoo Itoh

Hitachi Ltd., Central Research Laboratory, 1-280 Higashi-Koigakubo

Kokubunji-shi, Tokyo 185-8601, Japan

Professor Thomas Lee

Department of Electrical Engineering, Stanford University, 420 Via Palou Mall,CIS-205 Stanford, CA 94305-4070, USA

Professor Takayasu Sakurai

Center for Collaborative Research, University of Tokyo, 7-22-1 Roppongi

Minato-ku, Tokyo 106-8558, Japan

Professor Willy M.C Sansen

ESAT-MICAS, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10

3001 Leuven, Belgium

Professor Doris Schmitt-Landsiedel

Lehrstuhl f¨ur Technische Elektronik, Technische Universit¨at M¨unchen

Theresienstrasse 90, Geb¨aude N3, 80290 Mu¨anchen, Germany

For further volumes:

http://www.springer.com/series/4076

Electronic Devices for

Analog Signal Processing

123

Tomsk Polytechnic University

Electro Physical Department

Springer Dordrecht Heidelberg London New York

Library of Congress Control Number: 2011940132

© Springer Science+Business Media B.V 2012

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose

of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

This book deals with modern devices for analog signal processing A particularattention is paid to the main element of such devices: integral operational amplifiers(op-amps) and electronic devices based on them, including scaling, summing,integrating, and filtering linear devices The principles of construction of nonlineardevices in op-amps are presented along with various circuit solutions for limiting,rectification, and piecewise linear conversion of input signals Sine wave and pulseoscillators are analyzed Some examples of applying these devices to processing ofsignals from resistance, inductive, optical, and temperature sensors are presented.This book is intended for engineers and post graduated students, learning thecourse “Instrument Making” and for advanced learning of the courses “Electronicspart III” and “Electronics and Microprocessor Hardware,” but is can be also used

by other students and engineers dealing with the design of electronic devices andsystems

This book has been prepared at the Chair “Computer Measuring Systems andMetrology” of the Tomsk Polytechnic University

v

This book considers electronic devices applied to process analog signals in strument making, automation, measurements, and other branches of technology.They perform various transformations of electrical signals: scaling, integration,logarithming, etc Such devices are considered in tutorials on electronics The need

in-in their deeper study is caused, on the one hand, by the great demands of extendin-ingthe range of input signals, as well as increasing the accuracy and speed of suchdevices, which usually receive insufficient attention On the other hand, new devicesarise permanently, which are not considered in electronic tutorials yet, but alreadywidely applied in practice

Chapter 1 concerns the principles of design of modern operational amplifiers(op-amps) This choice is caused by the fact that an op-amp is now one of themost popular and versatile semiconductor components of almost any electronicdevice Since the advent of operational amplifiers, their circuits and fabricationtechnology have been permanently improved The efforts of developers were aimed

at the design and fabrication of different op-amp types with various characteristics

As a result, the parameters of amplifiers with the traditional structure controlled amplifiers) have been improved and new current-controlled op-amps,rail-to-rail amplifiers, clamping amplifiers, and specialized amplifiers of sensorsignals appeared The information about these amplifiers is mostly concentrated

(voltage-in scientific journals and manufacturers’ materials, but is almost lack(voltage-ing (voltage-in theeducational literature

Chapter 2 is devoted to the consideration of features of linear and nonlinearoperations with signals The experience in teaching the electronics shows that readernot always are able to determine correctly the function performed by an electronicdevice, fail to select the method for its analysis, and, as a consequence, obtainmistaken results Therefore, this chapter considers the principal differences of linearand nonlinear transformations by invoking the concepts of the spectrum of input andconverted signals

Chapter 3 presents linear functional devices based on op-amps: inverting,noninverting, summing, and instrumental amplifiers with the normalized gain Thesedevices are now widely used for the primary processing of measuring, acoustic,

vii

and video information, where they execute the functions of matching, precisionamplification, coupling with information transmission lines, etc.

Chapter4is devoted to nonlinear devices It concerns the general issues of thetheory of nonlinear devices in op-amps and the practical circuits of such devices:comparators, logarithmators, rectifiers, limiters, functional signal converters.Chapters 5 and 6 consider sine wave and pulse oscillators The range ofapplicability of such oscillators is extremely wide They are used in devices forexciting sensors of physical parameters, in meters of frequency characteristics ofamplifiers and filters, in devices for transformation of signal spectra, in clockingand synchronization devices, etc As was mentioned in book (Horowitz P., Hill W.The Art of Electronics Second Edition Cambridge University Press, England,1998), a device without generator either is capable of nothing or is designed to

be connected to other device (which, most probably, includes a generator) Despitethis, such devices receive insufficient attention in the educational literature Theirconsideration is often fragmentary and does not favor the understanding of processesoccurring in them Chapter5considers sine wave oscillators and the main knownapproaches to the analysis of the processes of self-oscillation excitation and settling

in them In particular, the analysis by the method of complex amplitudes, the method

of differential equations, the method of phase plane, and the two port method isdiscussed The preferable areas of application of these methods are demonstrated.The well-known amplitude and phase balance conditions are criticized Chapter6isdevoted to pulse oscillators It is well-known that pulsed signals and their derivativeshave some features: parts with fast and slow change, wide spectrum Pulsed signalsare generated by specific oscillating systems, for which the general conditions ofself-oscillation excitation are obtained

Chapter7is devoted to the consideration of practical circuits for processing ofsignals from sensors of physical parameters: resistance, inductive, semiconductorsensors and coupling of sensors with electronic devices

This book is organized nontraditionally Its main goal is not only to give someknowledge on modern electronic devices, but also to inspire students to the moredetailed study of these devices, understanding of their operation, ability to analyzecircuits, synthesize new devices, and assess the possibilities of their application forsolution of particular practical problems

As was already mentioned, the course is divided into seven chapters Eachchapter includes the theoretical material, questions, and tests to check how thestudents have learned the theoretical material in the process of independent cognitivework, as well as how ready he or she is to practical and laboratory works The mostdifficult questions are marked by asteriskand can be given to advanced readers.Paragraphs way of writing by italics are very important for the understanding ofthe studied material and together they can serve a brief summary of a section Thetext marked by italic indicates new or non-traditional concepts Calculated examplesare indicated by

1 Modern Operational Amplifiers 1

1.1 Introduction 1

1.2 Application of Operational Amplifiers 2

1.3 Amplifiers with Potential Input 3

1.4 Electrical Models of Operational Amplifiers 8

1.5 Analysis of the Effect of Signal Source and Load 13

1.6 Amplifiers with Current Input 14

1.7 Amplifiers with Current Output 19

1.8 Current-Differencing Amplifiers 24

1.9 Rail-to-Rail Amplifiers 26

1.10 Instrumental Amplifiers 27

1.11 Clamping Amplifiers 27

1.12 Isolation Amplifiers 28

1.13 Conclusions 29

References 33

2 Functional Transformations of Signals 35

2.1 Introduction 35

2.2 Linear Transformations of Signals 36

2.3 Nonlinear Transformations of Signals 40

2.4 Conclusions 42

References 44

3 Linear Functional Units in Operational Amplifiers 45

3.1 Introduction 45

3.2 General Circuit Designs of Linear Devices 45

3.3 Scalers 49

3.3.1 Inverting Amplifiers 49

3.3.2 Noninverting Amplifier 53

3.3.3 Amplifiers Based on Inverting and Noninverting Amplifiers 54 3.4 Integrating Amplifiers 60

3.4.1 Inverting Integrating Amplifiers 60

ix

3.4.2 Noninverting Integrating Amplifier 64

3.4.3 Integrating Amplifier with Two Inputs 65

3.4.4 Double Integrating Amplifier 66

3.5 Differentiating Amplifier 67

3.6 Active Filters Constructed in Op-amps 69

3.7 Conclusions 77

References 80

4 Nonlinear Devices in Op-amps 81

4.1 Introduction 81

4.2 Voltage Comparator 83

4.3 Logarithmic Amplifier 84

4.4 Operational Rectifiers 90

4.5 Full-Wave Operational Rectifiers 92

4.6 Voltage Limiters and Overload Protection Circuits 99

4.7 Op-amp Function Generators 103

4.8 Conclusions 108

References 110

5 Sine Wave Oscillators 111

5.1 Introduction 111

5.2 Oscillatory Processes 118

5.2.1 Analysis by the Method of Phase Plane 118

5.2.2 Analysis by the Method of Complex Amplitudes 123

5.2.3 Analysis by the Method of Differential Equations 126

5.2.4 Analysis by the Two-Port Network Method 130

5.3 Features of Oscillating Systems 133

5.4 RC Sine-Wave Oscillators 134

5.4.1 Principles of the Theory of RC Oscillators 134

5.4.2 The Oscillation Amplitude Stabilization and Nonlinear Distortions 141

5.5 LC Sine Wave Oscillators 148

5.5.1 Transformer-Coupled LC Oscillators 148

5.5.2 Three-Point Oscillators 152

5.6 Quartz Oscillators 154

5.7 Negative Resistance Oscillators 155

5.8 Synthesis of Oscillating Systems of RC Oscillators 160

5.9 Conclusions 167

References 172

6 Pulse Oscillators 173

6.1 Introduction 173

6.2 Selected Issues of Theory of Pulse Oscillators 174

6.2.1 The Conditions for Excitation of Pulsed Oscillations 176

6.3 Op-amp Pulse Oscillators 184

6.4 Possible Circuits of Op-amp Oscillators 194

7 Signal Conditioners 211

7.1 Introduction 211

7.2 Resistive Sensor Signal Conditioners 212

7.3 Inductive Sensor Signal Conditioner 219

7.4 Optical Sensor Signal Conditioners 223

7.5 Thermocouple Signal Conditioners 225

7.6 Voltage and Current Sensor Signal Conditioners 227

7.7 Conclusions 228

References 229

Appendix 231

Abbreviations 243

Parameters 245

Conclusions 247

Glossary 249

Index 255

Abstract The purpose of this chapter is to introduce specific features of circuit

design of modern op-amps, their parameters, characteristics and macromodels toensure effective use and proper design of electronic devices based on these op-amps The necessary prerequisite is the knowledge of theory of amplifiers withinthe course “Electronics” or “Electronics in Instrument Making.”

Having studied this Chapter, one will be able to determine the structure of anoperational amplifier, analyze circuits, basic parameters and characteristics, andknow their structural differences

An operational amplifier is a direct current (DC) amplifier intended for executing (together with external elements) various operations on (above) input signals and capable of working with the large feedback.

This term arose in the 1930s [1],1and initially it applied to DC amplifiers used

in telephony and analog computers

First operational amplifiers (op-amps) were based on electronic tubes; theyexecuted linear mathematical operations with input voltages: multiplication by

a constant, differentiation, and integration, and allowed electronic modeling ofdifferential equations These op-amps had large size and several supply voltagesand consumed power up to several watts

With further development of semiconductor industry, hybrid op-amps (assembled

of separate elements: transistors and resistors) were designed, and later on op-ampswere manufactured on a single piece of silicon crystal (chip) Specifications andcharacteristics of these op-amps are persistently improved Now such op-amps are

1Appearance of operational amplifiers is associated with Harold S Black, who, working in Bell Labs, proposed op-amps for telephony in 1934 [2].

Y.K Rybin, Electronic Devices for Analog Signal Processing, Springer Series

in Advanced Microelectronics 33, DOI 10.1007/978-94-007-2205-7 1,

© Springer Science CBusiness Media B.V 2012

1

called integral operational amplifiers Though their basic application has changedsince appearance of digital computers, these amplifiers are still referred to asoperational and widely used in various electronic devices This term no longercarries the meaning that had at the beginning The word “operational” assumes someoperation on signal, but an operational amplifier itself performs no other operationswithout external elements, but only signal amplification, which is its main and,perhaps, sole function Modern op-amps perfectly carried out this function.

Op-amps are characterized by the high gain (1,000,000 and more), low input offset voltage (from 0,1 V), wide frequency band (up to 2,000 MHz), and high slew rate (up to 3,000 V/ s) [3] These op-amp parameters are continuously improving.

Nowadays the industry produces a large number (several hundreds) of various amps; therefore, even simple enumeration of their parameters and characteristics,

op-in particular, those that earlier believed atypical for op-amps (for example, lowinput or output resistance) is a certain problem It is difficult to orient oneself inthis abundance of types and parameters without the necessary structured knowledgeabout them

Thus, consideration of op-amps starts with their electrical models, rather thanparameters and features of circuitry and production technologies (these issues aresufficiently addressed in the literature) It is assumed that the students already havethe basic knowledge about the input and output parameters of op-amps (parametersand characteristics of some of them are presented in Appendix 1)

Op-amps are now used in the systems for data acquisition and signal processing of measurement information, entering of the analog signals into the computer, in audio and medical systems, etc [4–7]

They are characterized by small size, wide range of power supply voltages, lowconsumed power, and others Besides, they are suitable for any operating conditions.However, the main reason for wide application of op-amps is that the parameters andcharacteristics of a device are independent of the parameters and characteristics ofthe op-amp itself, because, as known, the op-amp parameters are usually instable

in time and vary with temperature and frequency, and so developers of electrondevices try all ways to minimize their effect A large feedback allows reaching it.The needed functions of a device are rather readily achieved in this case using ofexternal elements

The relative easiness of designing various circuits with op-amps caused asimplified attitude to them Now the knowledge of parameters and characteristics ofoperational amplifiers sometimes substitutes for the recognition of their structure.The common opinion is that for application of op-amps it is not needed (rather,not necessarily needed) to know their circuit, but it is sufficient to be aware of the

more complex internal structure Moreover, the wide usage of software for eling electronic devices on personal computers (Multisim, Electronics Workbench,DesignLab, Orcad, Protel, and others) approves this approach, because op-amps

mod-in such a case are selected from a library, as any other element Nevertheless,the system modeling assuming the knowledge of the structure, structural relations,and principles of construction of various operational amplifiers allows one to morecompetently design and operate electron devices based on them This concept can

be supported by the following

First, any op-amp model is certainly more simple than the principle circuit and,even more so, its physical prototype

Second, from the system point of view, the amplifier scheme corresponds to ahigher level of modeling, including any model of a black box with all its parameters.Third, the knowledge of the internal structure allows one to more efficiently applyop-amps and to use methods for correction of their characteristics, in particular,those not documented by the manufacturer

Finally, alphanumeric indexes of operational amplifiers give no informationabout their structure (for example, 140UD1 and 1401UD1 (Russian) amplifiers haveabsolutely different structures and different applications)

Op-amps have widely different designs, parameters, and characteristics, and themain problem for developer is to find the best op-amp for some device or anotherone, because the correct and reasonable choice of an op-amp determines the cost,reliability, and quality of the device under development

All amplifiers can be divided into two groups: amplifiers with potential (highresistance) input and amplifiers with current (low resistance) input Let us considerthese two types

The circuit of the K157UD4 op-amp with potential input made using the bipolar technology

is shown on Fig.1.1 The circuit [3] includes three amplifier stages.

The first (input) stage is a symmetric differential one; it is constructed in VT1 — VT4 transistors The input signal is given to one of the bases of the VT1 and VT2

transistors or to the both bases simultaneously The signal amplified by the first stage

comes to the second (intermediate) stage constructed in VT5 and VT6 transistors,

and after amplification by the second stage it comes to the third (output) stage

designed in VT7 — VT10 transistors The output stage is connected in the circuit

of a push-pull compound emitter follower constructed in VT8, VT9 and VT7, VT10

complementary transistors, respectively Note that each arm of the stage includes

Fig 1.1 Circuit of K157UD4-type op-amp with the VCVS structure

Fig 1.2 Drawing of

K157UD4-type op-amps in

figures (a) and simplified

representation (b)

the current sources I3 and I4 Current sources are usually represented by transistors,

and for their normal operation the voltage drop no less than 1–1.5 V is needed.Consequently, the output voltage of the amplifier is always lower than the supplyvoltage by 1.5–2 V

The basic amplifier parameters are determined by the parameters of the stages Thus, the input resistance, current, and offset voltage are determined by the input stage, while the output resistance and the maximal values of the output voltage and current are determined

by the output stage.

The op-amp gain is equal to the product of the stage gains But, as known, theemitter follower does not amplify the signal voltage Therefore, the whole gain ofthe amplifier is determined by the product of the gains of the input and intermediatestages only

The circuit symbols for it are shown on Fig.1.2

One of the basic characteristics of op-amps is the frequency dependence of the gain, which

is called the gain-frequency characteristic (GFC) or the open-loop-gain characteristic.

Fig 1.3 GFC of op-amp without (0) and with feedback (1–3)

The GFC shape in the general case depends on the number of amplifier stages,type of the transistors, circuit of their connection, operating mode, etc

It is a specific of the op-amp GFC that frequency of the input signal increases, andthe gain varies widely: from several tens or even hundreds thousands to 1 and evensmaller In addition, in many circuits the op-amp is to operate with a large feedback,and the gain-frequency and the phase-response (PRC) characteristics should have acertain form, providing for some marginal stability Therefore, the op-amp GFC

is corrected For example, for correction of the K157UD2 amplifier, the circuit

includes the capacitor Cfcconnected to frequency correction (FC) terminals In thiscase, the gain of the intermediate stage and consequently, of the op-amp as a whole

depends on the signal frequency With accordance Cfc, the overall op-amp gain is

where Pk1, Pk2, and Pk3 are the complex gains of the input, intermediate, and output

stages; K0is the gain at f D 0; fcutD f2is the cutoff frequency of the op-amp GFC.The cutoff frequency depends on many factors, first of all, on the collectorcurrents of the transistors: the higher the currents, the higher the cutoff frequency.But the input resistance in this case decreases, because the emitter current increases

A way to increase the input resistance is to decrease the emitter currents ofthe input transistors The typical values of the input resistance are from 4 k for the

140UD1 op-amp to 1.5 M for the A725 op-amp However, this decrease in the

currents of the input transistors results in the impossibility of quick recharge ofthe correcting capacitor Therefore, these amplifiers are characterized by the lowfrequency properties and the low slew rate The GFC cutoff frequency for these op-amps usually ranges within 10–100 Hz, and the slew rate does not exceed 10 V/s

Figure1.3 shown GFC of the K157UD4 op-amp in the log scale At the lowfrequencies, the gain is constant, independent of the signal frequency, and equal

Fig 1.4 Circuit of inverter

amplifier with parallel

feedback based on op-amp

with VCVS structure

Fig 1.5 PRC of amplifier without (0) and with feedback (1–3)

to K0 Starting from the cutoff frequency fcutD 20 Hz, the gain monotonically

decreases with the rate of 20 dB/dec because of the decrease in the gain of theintermediate stage caused by the presence of the correcting capacitor with the

capacity CfcD 30 pF At the frequency fTD 1,000 kHz the gain becomes equal to

1, and there is no amplification This frequency is called the threshold amplificationfrequency of op-amp

The gain decreases with the negative feedback (see Fig.1.4) The op-amp gain

with a large feedback is Kfb R2/R1.It is independent of the op-amp parameters,

but determined by external elements The characteristics at Kfbequal to 1,000, –

100, and 10 are shown by lines 1, 2, and 3 on Fig.1.3 As the gain decreases, thefeedback increases and the frequency band becomes wider Amplifiers of this kindare characterized by the roughly constant amplification area, that is the product ofthe gain by the upper threshold frequency (cutoff frequency)

The phase-response characteristic is connected with the GFC and dependent onthis PRC of the K157UD4 without and with feedback is shown on Fig.1.5 It can beseen that at the frequencies higher than the cutoff frequency the op-amp phase is al-most equal to – /2.2If op-amp is enveloped by the negative frequency-independentfeedback, the total phase shift in the feedback loop only slightly exceeds –3 /2, and

the amplifier has the stability margin about 60–70ıat the threshold frequency Theamplified frequency band extends where phase shift is zero

Another important parameter of an amplifier is the gain characteristic (GC), which is the dependence of instant output voltage vs the instant input voltage.

2 It is PRC for the noninverting input For the inverting input, –   should be added at any frequency.

This characteristic is measured as slow variation of the input voltage and haswider variety as compared to GFC However, all GCs are features with limitedoutput values Typical GC is shown on Fig.1.6.

In the general case, it does not pass through the origin, because almost any

amplifier has the input offset voltage Voff As can be seen from Fig.1.6, GC becomesmore linear with feedback; it is a smoothly increasing (for the noninverting input) ordecreasing (for the inverting input) curve limited by the maximum allowable levels

of the output voltage, which, naturally, cannot exceed the supply voltage

For practical calculations accordingly the op-amp nonlinear properties, its GCwithout feedback can be described through the hyperbolic tangent function

Voffis the input offset voltage reduced to the op-amp input;®T is the temperature

voltage (25.6 mV at T D 20ıC); Vmis the maximum allowable voltage at op-amp

output, k2is the gain of the intermediate stage The gain at a small signal in this case

isK D k2Vm ='T

When amplifying pulsed signals and operating in the switching mode, the transient response characteristic (TC) is important.

Remind that TC is the time dependence of the output voltage at a stepwise change

of the input voltage TC for small and large input signals are usually distinguished.

Small signals are the signals, at which the output voltage remains within the linearrange of the gain characteristic and does not achieve the maximum allowable value,

or the signals, variation of whose amplitude does not result in a change of theamplifier parameters Large signals are the signals, at which the output voltage can

Fig 1.7 Typical transient

response characteristics of

A741 amplifier at small (1)

and large (2) signals

take limit values In this case, transistors operate in the cutoff or saturation ranges,that is, high signals force the op-amp into the significantly nonlinear operationmode

TC of theA741 amplifier are shown on Fig.1.7 It can be seen that at small

signals (curve 1) the transient response process is long enough (see the lower scale

of the axis t) At large signals, the op-amp quickly enters the nonlinear mode with

the rate limited only by the rate of increase of the op-amp output voltage

Modern op-amps are made by the integral technology, and so they are chips with scale integration (VLSI).

very-large-The exact analysis of circuits with such op-amps is almost impossible withoutcomputer Even in this case, the circuit including dozens of transistors, resistors, andcapacitors do not analyzed Frequently equivalent circuit is used, whose input andoutput voltages and currents are equal to the input and output voltages and currents

We are considered the known equivalent circuits by the principle “from simple

to complex.”

Fig 1.8 The op-amp linear models in a kind of two-port form

From electrical circuits theory it is well known that any two-port in the linearapproximation can be represented by one of equivalent circuits on Fig 1.8.3Perhaps, it is the simplest electrical models of op-amps They have different inputand output parts depending on the chosen independent input and output electrical

characteristics Parameters of equivalent circuits are denoted as Z, Y, F and H with

the corresponding indexes The meaning and values of these parameters are wellknown.4

The output circuit is represented by a voltage source in Figs.1.8a, c and by

a current source in Figs.1.8b, d, and the both sources are dependent In the first

circuit (1.8a) voltage depends on the input current: E i D Z21Iin, and in the secondone (1.8c) it depends on the input voltage: E V D F21Vin Similarly, the currents ofthe controlled current sources depend on the input voltage in the circuit shown inFig.1.8b (I V D Y21Vin) and on the input current in the circuit shown on Fig.1.8d

(I i D H21Iin) As applied to amplifiers, the parameter Z21D Ztr is transresistance,

F21D K V is voltage gain, Y21D S is transconductance, and H21D K i, is currentgain, that characterized the op-amp amplifying properties

It should be noted that the amplifying parameters are measured in different units:

K V and K i are dimensionless parameters, while Ztr is measured in the units of

resistance, and S is measured in the units of conductance.

Depending on the type of the output source and the controlling electrical characteristic, the simple equivalent circuits present, respectively:1.8a – Current controlled voltage source

(CCVS),1.8b – voltage controlled current source (VCCS), 1.8c – VCVS, and 1.8d – CCCS.

Each of these circuits can be described by a system of equations.

3 For simplicity, reverse transfer elements are excluded in Fig 1.8.

4See, for example, A.F Beletskii, Principles of Theory of Linear Electrical Circuits (Svyaz,

Moscow, 1967).

For example, the two-port on Fig.1.8c (VCVS) can be described by the system

The independent variables here are the input voltage (Vin) and the output current

(Iout) The first and second equations describe, respectively, the input and outputop-amp circuits In the first equation, the input circuit is represented by the input

conductance F11D 1/Zin The input resistance serves a load for the signal source

and consumes the corresponding power from it The higher the input resistance, the

lower the input current Iin, so the greater voltage part of the signal source comes tothe op-amp input, and the lower is the power needed from the signal source.Most of modern op-amps are characterized by high input resistance (1–10 M)

Due to this fact, the necessary current from the signal source is low The output

circuit includes the voltage source E V depended on the input voltage Vin and the

output resistance F22D Zout The relation between Zout and Zload determines what

part of voltage E V will be separated at the load resistance

The described equivalent circuits can be used only for approximate calculations of such device parameters as the gain and input and output resistance, because they ignore the following op-amp disadvantages:

– input offset voltage, and input currents;

– limited output voltage;

– rising of the input voltage, etc.

Some of these disadvantages are eliminated in more complex equivalent circuits

The linear one-port equivalent op-amp circuit (macromodel) used in the Electronics Workbench software is shown on Fig.1.9.

It more accurately models the op-amp frequency properties, the input currents

of transistors and the input offset voltage The frequency properties are presented

by two frequency-dependent RC-circuits: (Ri, Ci, Cfc, Rin2) and (Routand Cout), and

one of the capacitors (the frequency correcting capacitor (Cfc)) is connected to theexternal terminals and can be changed The transistor input currents are determined

by the sources of input currents (Ib1, Ib2), and the input offset voltage (Voff) is set bythe voltage source

The circuit includes two (rather than one) depended sources, which are enclosed by the dashed rectangle The disadvantages of this circuit are the impossibility to consider common-mode parameters and the limited output voltage.

In circuit on Fig.1.10these disadvantages are removed Here the input resistance

Zinis represented more specifically by the resistors Rinand input capacitors (C1 and C2) for the symmetric input The elements Rcmand Ccm account for the common-

mode input resistance and common-mode input capacitance The elements Ri, Ci

and R , C model the op-amp frequency properties, while the elements VD1,

Fig 1.9 One-port linear equivalent circuit of op-amp

Fig 1.10 Nonlinear equivalent circuit (macromodel) of op-amp

VD2, V1 and V2 accounts for the effect of the limited output voltage at the level

of V1and V2voltages Diodes in this circuit makes it nonlinear, unlike the previouscircuits

Certainly, now the use of the macromodel is more complicated, and the lations become more complexes Therefore, it suits for computations as a PSpicemacromodel in the Electronics Workbench and DesignLab software Such a modelcan be easily constructed not only for the VCCS structure, but also for any other.The further improvement of the equivalent circuit allows us to take into accountthe input currents and the input offset voltage, to determine more accurately thefrequency properties, limitedness of not only output voltage, but also the outputcurrent, etc

calcu-One of the most perfect op-amp macromodels, namely, the Boyle-Cohn-Pederson model [8]

on Fig.1.11is also used in Electronics Workbench and DesignLab.

Fig 1.11 Boyle–Cohn–Pederson macromodel

This model includes a differential stage consisting of NPN transistors VT1 and VT25 one uncontrolled (I1) and four controlled (I2–I5) current sources, output current limiters assembled in diodes VD1 and VD2, and output voltage limiters assembled in diodes VD3 and VD4 The built-in current sources in their structure

are similar to VCCS The effect of the op-amp input parameters is modeled by the

differential stage, the frequency properties are determined by the capacitors C1 and

Cfc, and the output resistance is modeled by the resistors R7 and R9.

As would be expected, the more exactly is a model, the more complicated one,and it is the nearer to the op-amp circuit But the analyses in this case bring muchtime This is explained by the ancient contradiction between the accuracy and thesimplicity of a model However there are no miracles Hence, it can be concludedthat the op-amp principle circuit serves the most accurate op-amp macromodel, justwhich was stated in the beginning of this Chapter

Thus, for approximate calculations of the gain and the input and output DC resistance, we can use the op-amp models shown on Fig.1.8 If it is necessary to take into account the

op-amp frequency properties, the descriptions of these models should be supplemented with the frequency dependence of their parameters The one-port linear equivalent circuit on Fig.1.9is better suited, when it is needed to more accurately take into consideration the frequency properties in the form of two time constants, as well as the effect of the input currents and the input offset voltage The nonlinear equivalent circuit (macromodel) shown

on Fig.1.10represents better the common-mode parameters and the level of restriction of the output voltage Finally, the Boyle-Cohn-Pederson macromodel on Fig.1.11accounts for all the listed dependences.

5 There are similar models constructed in bipolar (PNP) and field-effect (FET) transistors.

Zs, Zin, Zout, and Zload form voltage dividers.

 In this case, the overall gain with regard for all resistances is

Designers of circuits with amplifiers usually aim to increase the gain K e, but at

the given Zs and Zloadthis can be achieved only by selecting optimal Zin and Zout.From Eq.1.3it is clear that, to increase the gain K e (given K V), it is necessary

to increase Zin and decrease Zout The limit value of the gain K e at ZinD 1 and

ZoutD 0 is equal to K V On the other hand, at the high resistance of the signal

source (Zs > > Zin) or any low input resistance of the amplifier, the gain K e ! 0

according to Eq 1.3 This effect can be explained by following As the internalresistance of the signal source increases, the input voltage and output voltage alsointend to zero However it is not a case In a real amplifier, the input current (base oremitter current) continues to pass through the input circuit Due to the properties ofsemiconductor devices, this current will induce the output voltage Therefore, at the

high resistance Zsit is better using another equivalent circuit with other independentvariables

 If we describe the same two-port in Z-parameters (at the independent variables

Iinand Iout), then we obtain the following system of equations:

whose input current and output voltage is the following: VoutD IinZtrD E i at

Fig 1.12 Equivalent circuit of op-amp connection: SS is signal source; Amp is amplifier; L is

load; Es, E V are voltage of the signal source and amplifier; Zs, ZoutD F22 are output resistances

of the signal source and amplifier; Zloadis the load resistance; ZinD 1/F11 is the input amplifier resistance

IoutD 0, where Ztris the transresistance In this case, just transresistance Ztr, rather

than the gain K V, reflects the op-amp amplifying properties Describing the overall

gain with Ztr, we obtain:

Now to increase the gain, it is necessary to decrease the input resistance, but not

increase The maximum value of K e at Z11D 0 and Z22D 0 is equal to Ztr/Zs,that is

a finite nonzero value The minimum value of K e is now achieved at Z11! 1, that

is, the situation is quite opposite to that given by Eq.1.3 What a paradox!

However there is no paradox here It was not by accidentally that we considereddifferent approaches to determination of the amplifying properties of op-amps.These approaches correspond to different physical realizations of op-amps Thefirst of them is characteristic of ordinary (traditional) op-amps with the high inputresistance

Op-amps with the high input resistance are referred to as amplifiers with potential input.

This term describes the fact that the output voltage in them is controlled at low input currents, by the input potential In the electrical circuits theory such two-ports are known

as voltage controlled voltage sources (VCVS).

Another approach is needed when considering op-amps with low inputresistance

Op-amps with the low input resistance are referred to as amplifiers with current input,

because the output voltage in them is depended on the input current, rather than voltage By analogy, they can be classified as Current controlled voltage sources (CCVS).

These amplifiers are known for a long time, but as elements of integratedcircuits they appeared only recently and did not receive wide acceptance yet They

are created as a result of the progress in the complementary bipolar technology.

However, because of their numerous advantages, they can find sufficient place

in electronics To understand the advantages of these new op-amps, considerdifferences in their circuits

Consider now op-amps with the CCVS structure A simplified circuit of AD844 op-amp

is shown on Fig. 1.13 [9] The op-amp has a symmetrical circuit design based on complementary transistors and includes three stages: offset voltage compensation stage, amplification stage and a voltage follower.

Offset voltage compensation stage is assembled using transistors VT1 and VT2 and sources of current IA and IB (see the first dashed rectangle on Fig 1.13)

A voltage equal to the offset voltage, necessary for transistors VT5 and VT6, is

generated on bases of both transistors The first stage does not amplify the signal

Fig 1.13 AD844 op-amp with the CCVS structure

Main amplification is performed by the next stage, assembled using transistors

VT3 – VT12 in accordance with a “current mirror” circuit Output current Iout

on terminal 5 is equal to input current on inverting input –Vin Thus the stagedoes not amplify the signal current but provides significant amplification of signalvoltage Finally, the signal amplified by the intermediate stage follows to the input

of the third (output) stage in VT 13–VT 18 transistors As in the previous circuit

(Fig.1.1) it is designed as the emitter follower circuit and does no provide voltageamplification

Only the intermediate stage has the voltage gain higher than 1 among all thestages, so the overall gain is not high – about 60,000 for the noninverting input

Consider the input stage in more detail At the “CVin” input the transistors areconnected in the circuit with common collector-base (VT1) and common emitter

(CE)(VT5), and at the “–Vin” input the transistors are connected in the circuit withcommon base (CB), so they have different input resistance It is quite natural that

at the “CVin” input the resistance is much higher than at the “–Vin” input, becausethe input resistance of the CE circuit is“ times higher (“ are the current transfer

ratios of the transistor base) than the input resistance of the CB circuit, and thedifference between the resistances may be significant Thus, for the AD844-typeop-amp the resistances are 10 M and 50 , [9] The difference between the inputresistances allows using op-amps with both potential (noninverting) and current(inverting) inputs The maximal output voltage connected with the terminal 6, as

Fig 1.14 Nonlinear equivalent circuit of AD844-type op-amp

in the circuit shown on Fig.1.1, is 1.5–2 V lower than the supply voltage, and at the

current terminal 5 it is almost equal to the supply voltage

Nonlinear equivalent circuit of AD844-type op-amp is shown on Fig.1.14 The

circuit includes two voltage followers OA1 and OA2, a current-controlled current source assembled in accordance with a “current mirror” circuit – CM, RC – a circuit,

which simulates inertial properties, and a double output voltage limiter

One of the inputs of the op-amp (CVin) is a noninverting current input with

high input resistance (voltage input), and another one (Vin) inverting current input

with low input resistance (Rin2) There is a voltage follower OA1 fur the purpose of

reflection of various input resistances It is known that this op-amp has two outputs:

a “current” output (Iout) and “voltage” output (Vout) Conventional voltage output

(Vout) is made on the OA2 follower output after output voltage limiter (VD1 and VD2 with voltage sources E1 and E2) Current output (Iout) has a high output resistance

Ri The main specific feature of this circuit is that it includes a current limiter shown in CM (current mirror) block Output current Ioutis equal to input current oninverting input due to use of “current mirror”, but is limited by maximum allowablevalueI D fIin2ifjIin2j ImaxI ImaxifIin2> ImaxI ImaxifIin2 < Imaxg It is this

feature that distinguishes the circuit design from other known models

Such op-amps in books and articles are often referred to as current-feedback

operational amplifiers – CFOA.6

Figure1.15shows schematic symbols of an op-amp with voltage (3) and current(2) input as well as voltage (6) and current (5) output

The fact that the op-amp has two separate inputs and outputs makes it possible

Fig 1.15 AD844 type op-amp on electric circuits: equivalent circuit – (a) and simplified – (b) with

numerical and corresponding letter identification of outputs (Inverting and non-inverting inputs are

marked with letters x and y or numbers 2 and 3 for AD844CH op-amp, and current and voltage

outputs are marked with letters z and w or numbers 5 and 6, correspondingly)

Fig 1.16 Circuit of inverting

amplifier with the CCVS

 The gain can be calculated by the Fig.1.17 The input (Rin2) and output (Rout)op-amp resistors on Fig 1.17 have low resistance The gain with feedback at

Rin2D RoutD 0 can be determined from the following:

VoutD Iin2ZtrI Iin2D IR1 IR2 Vin=R1 Vout=R2

Substituting Iin2from the second equation into the first one, we obtain Kfb:

Fig 1.17 Equivalent circuit of inverting amplifier with op-amp the CCVS structure

It can be seen that change of the potential input to the current one does notchange the gain of the op-amp with feedback As in the previous case (with the large

feedback F D 1 C Ztr/R2), it is independent of the op-amp amplifying properties, but

determined only by the resistances of the external resistors R1and R2.

Consider now how the amplifier GFC is changed For this purpose, represent the

transresistance Ztrin the complex form:

of feedback However, the difference is following At the same gain, this circuit

can provide for different feedback and different frequency, which depend on the R2 resistance GFC for different values of the transresistance Ztrand the resistance R2 is

shown on Fig.1.18 Curve 0 corresponds to the amplifier without feedback Curves

1, 2, and 3 are for amplifier’s GFC with different feedback.

The analysis of the plots shows that at the same gain K D 100 the GFC cutoff frequency varies upon variation of R2 Thus, the amplifier of this structure ischaracterized by the dependence of the amplification area on the feedback

Note that GFC here is plotted in a wider frequency band comparing to Fig.1.3,and it is not accidentally From Fig.1.13follows that in this structure the frequency

band is determined by the VT5 and VT6 transistors, and the correcting capacitor (not shown on the circuit) is recharged by other transistors: VT10 and VT11, whose

Fig 1.18 GFC of amplifier with the CCVS structure without (0) and with (1, 2, and 3) feedback

collector currents do not affect the input resistance and can be taken high to speed

up recharging In addition, the current input is the input of transistors connected

in the CB circuit As well known, it is characterized by the higher frequency band

of the amplified signals as compared to the CE circuit The low input resistancefor the inverting input neutralizes the effect of the input capacitance, so amplifierswith the CCVS structure also have the wider frequency band That is why thethreshold frequency of the AD844 op-amp is 80 MHz, and the slew rate achieves2,000 V/s [9]

Amplifiers designed in the VS (voltage source) structures have significant disadvantages: low load-carrying capacity, sensitivity to the output short circuit, etc.

The limited allowable load resistance characterizes it, because most of them areintended for operation only with high-resistance load (no less than 2–5 k)

They are unsuitable for operation in matched high-frequency amplification channels with the resistance of 50 and 75  It is better using op-amps with the CS (current source) structure for this purpose.

Consider the circuits of such amplifiers Amplifiers with VCVS structure oftenhave a current output also, therefore the op-amp with the VCVS structure can beeasily transformed into the op-amp with the VCCS structure For this operation thesignal from the intermediate amplification stage should be used On Fig.1.1thisoutput is connected to the terminal 5

Figure1.19shown the amplifier with feedback based on this op-amp The circlewith two arrows near the output terminal indicates the current output

Determine the gain and the frequency properties of this amplifier Since theoutput current is controlled potentially, the op-amp input current can be ignored

by taking the input resistance equal to infinity

Fig 1.19 Inverting amplifier

constructed in op-amp with

VCCS structure

Fig 1.20 Equivalent circuit

of the amplifier with the

 The gain will be calculated for the ideal source of output current, in which

the output resistance is equal to infinity and, consequently, GoutD 0 The system of

depends here only on the transconductance S and the R1resistance At R1D 0 the

denominator is equal to 1 and the feedback is not present Gain is

Fig 1.21 GFC for the VCCS amplifier with (lines 1, 2, and 3) and without (line 0) feedback

The unity in Eq 1.11 determines the direct transmission of the input signal

to the output through the resistors R1 and R2, by-passing the inverting amplifier.

This becomes possible just owing to the output current source In the equation forcircuits with output voltage sources this 1 is not present Certainly, it does not affect

significantly the gain, since it is much smaller than SR2

Consider now the gain-frequency characteristics For this purpose, represent thetransconductance in the complex form:

structures coincide at equal Kfband fcut

Examples of amplifiers with the VCCS structure are NE5517 op-amps fabricated

by Philips, and others

Finally, consider the last op-amp structure based on the current controlled currentsource (CCCS) The circuit of this amplifier can be described, if in the circuit onFig.1.13the signal from the intermediate stage (terminal 5) will be used as output

signal, and the input signal is the input (Vin) (Fig.1.22)

 To calculate the gain and analyze the frequency properties of the amplifier, let

us take the same inverting amplifier (Fig.1.20) The op-amp symbol here representsthe current input and output

Fig 1.22 Inverting amplifier

constructed in op-amp with

CCCS structure

Fig 1.23 Equivalent circuit of the amplifier with the CCCS structure

The equivalent circuit (Fig.1.23) is described by the system of H-parameters for

calculation of the gain

The gain can be found from the following system of equations:

It is notable that in case if KiD1, as for AD844 op-amp, the gain is equal to

From Eq.1.14follows that amplifier with feedback designed in the op-amp with

the CCCS structure, the gain is determined by the resistances of R2and R1, as in the

previous cases only for Ki 1

Consider the amplifier with the series feedback for the current input shown onFig.1.24 From the equivalent circuit, for Ki 1 we have

and the active one (second term including the current gain Ki) The passive part isindependent of the op-amp amplifying properties and at the higher input resistance

H11it is roughly equal to 0, while the active one depends on the current gain Kiand

under the same conditions it is equal to the ratio R2/R1 With no feedback and the

resistor R2 as a load, the gain is K0D R2Ki/H11 SR2.

 Now let us analyze the frequency properties of the amplifier If Ki depends onthe frequency as

Fig 1.25 GFC of amplifier with CCCS structure

Analysis of the equation for Kfb(jf ) and the GFC of this amplifier at different

gain on Fig.1.25show that GFC decreases monotonically with the cutoff frequency

(1 C Ki) times higher than the op-amp cutoff frequency, and the cutoff frequency

is a constant independent of the gain This is a characteristic feature of the op-ampwith the CCCS structure

The distinctive feature of all the amplifiers considered above is the input differential stage.

Owing to this stage, it becomes possible to obtain the minimal input offsetvoltage and to perform various operations with input signals regardless of the op-amp parameters But if the amplifier is supplied from one source, bias circuitsbecome more complex, because input voltage dividers are needed to apply the biasvoltage In practice, op-amps are rarely operated from one power supply (except forthe use with bridge circuits)

Recently, amplifiers with the so-called current mirror in place of the bipolar circuit at the input (current-differencing amplifiers) have come into being, and these amplifiers are just intended for operation from one power supply They turned out to have some advantages,

in particular, the minimal number of external elements to provide for bias and others.

But these advantages turn out to be disadvantages at the same time, becausethese amplifiers can amplify only unipolar or variable signals in the presence of a

blocking capacitor Examples of current-differencing amplifiers are LM2900/3900 op-amp fabricated by National Semiconductor and Russian 1401UD1 and 1435UD1 amplifiers fabricated by Foton, Kvazar, and KMT.

The circuit of the 1401UD1 amplifier on Fig.1.26includes three stages: the input

stage in the VT1 and VT2 transistors, the intermediate stage in the VT3 transistor, and the output stage in the VT4 —VT6 transistors The current sources I1 — I3 serve as loads in all stages The VT1 and VT2 input transistors form the current

Fig 1.26 Circuit of 1401UD1 current-differencing op-amp

mirror The intermediate stage is the ordinary inverting stage connected in the CE

circuit with frequency correction realized with the aid of the capacitor Cfc Theoutput stage is a complex voltage follower The amplifier has two inputs: invertingand noninverting, and the input resistance for the inverting input is about 1 M

As the input current is follows to the noninverting input owing to the currentmirror, the current at the inverting input tends to become equal to the input

current Therefore, the collector currents of the VT1 and VT2 transistors are always

maintained equal in the case of feedback This results in appearance of the outputvoltage proportional to the feedback resistance So it is clear that the output voltage

VoutD IinRfb is independent of the amplifier parameters and determined only bythe parameters of the feedback elements, as in the circuit with the differential stage

at the input

Figure1.27shows the circuit of the inverting alternating-voltage amplifier in thecurrent-differencing op-amp

The direct current (DC) mode in the circuit is set by the R2 and R3 resistors.

If R3D 2R2, then the direct voltage at the output is equal to the halved supply

voltage C Vcc, since when the input direct currents are equal, the voltage drop at

the resistor R2 and, consequently, the output direct voltage are twice as low as

the supply voltage The input alternating voltage, transmitting through the resistor

R1 to the inverting input, tends to violate the balance of the currents Thus, the

current difference appears, which is reflected in the title of this op-amp However,the feedback causes the compensating current from the amplifier output, and itagain balances the currents So the circuit maintains the balance of the alternating

Fig 1.27 Inverting amplifier

in the current-differencing

op-amp

currents through the resistors R1 and R2, that is, the equality Vin/R1D Vout/R2is

true Therefore, the gain is KfbD R2/R1 As in the previous cases, it can be seenthat the gain is independent of the op-amp parameters and determined only by theresistance of the external resistors

It is likely most appropriate to use current-differencing op-amps in cheapalternating-voltage amplifiers for mobile systems with battery power supply

In ordinary op-amps, the amplifying properties keep within some range of the outputvoltage The limits of this range are equal to the maximum and minimum allowablevalues Usually they are 1.5–3 V lower than the corresponding supply voltage That

is, the op-amp output voltage is lower than the supply voltages by the residualvoltage at the output transistors, that is, just by 1.5–3 V

The limits of variation of the output voltage are shown on Fig.1.6 It can be

seen that there is a gap, equal to the residual voltage, between C Vcc1and Vout m, as

well as between –Vcc2and –Vout m Hence, it follows that the supply voltage of theordinary op-amp cannot be lower than the doubled residual voltage equal to 3–6 V

At the same time, on the one hand, now it is necessary to have an amplifier capable

of operating at lower supply voltages, for example, in micro-power medical devices,cell phone tools, portable CD players On the other hand, the residual voltagereduces the efficiency of powerful amplifiers So the decrease of the residual voltage

is an urgent problem of op-amp improvement

Figure1.28shows the possible versions of output voltages for op-amps of various types The dashed line indicates the supply voltage level The ideal amplifier is the amplifier, whose output voltage (Fig.1.28c) is equal to the supply voltage Such amplifiers are called rail- to-rail amplifier7amplifiers.

The residual voltage of bipolar transistors cannot be lower than the voltage dropacross the open diode, that is, 1–1.2 V Consequently, the amplifiers in bipolar

7The term “rail-to-rail” is registered trademark of Nippon Motorola Ltd.

Fig 1.28 Output voltages of ordinary amplifiers with potential and current control (a),

current-differencing amplifiers (b), and amplifier amplifiers (c)

transistors cannot operate at voltages lower than 2–2.4 V Therefore, rail-to-rail amplifier op-amps are most often constructed in field effect transistors (FETs) Examples of such amplifiers are ICL761 fabricated by Intersil, TS912 fabricated by STMicroelectronics, 1423UD1, KR1446UD1-5, and 1447UD1 fabricated by Foton, Angstrem, and Pulsar companies, and some others They are capable of operating

at the supply voltage from 1 to 8 V Another distinctive feature of these amplifiers isthe possibility of programming the supply current

Recently a new type of integral amplifiers has appeared: instrumental amplifiers.

These op-amps are intended for operation in input stages of measuring struments, for amplification of signals from high-resistance sensors of physicalparameters, bridge circuits, thermocouples, etc As a rule, they have the normalized

in-gain multiple of 10 For example, the in-gains of LM163 and LM363 op-amps (National Semiconductor), INA258 op-amp (Burr-Brown), or 140UD27 (Kvazar)

are equal to 10, 100, and 1,000 Some or other value is selected by closing chipterminals with jumpers The gain is determined by the resistances of switchedinternal resistors, and the error is 0.1–1% Adding external resistors, it is possible

to increase the number of the fixed gain values These amplifiers find the utility inprecision electron devices

The so-called clamping amplifiers have arisen quite recently They are amplifiers

with switched (clamping) inputs, for example, AD8036 and AD8037 amplifiers fabricated by Analog Devices Such amplifiers are unique devices, which allow