Automation in high-performance negative feedback amplifier design

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J. Stoffels

TR diss

1604

AUTOMATION IN HIGH-PERFORMANCE

NEGATIVE FEEDBACK AMPLIFIER DESIGN

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof.dr. J.M. Dirken, in het openbaar te verdedigen ten overstaan van een commissie aangewezen door het College van Dekanen, op dinsdag 19 januari 1988, te 16.00 uur

door Johannes Stoffels elektrotechnische ingenieur geboren te Amsterdam

TR diss

1604

Leden van de promotiecommissie:

Wnd Rector Magnificus Prof.dr.ir. J. Davidse Prof.dr.ir. R. Boute

Prof.dr.ir. W.M.G. van Bokhoven Prof.dr.ir. N.F. Benschop

Dr.ir. E.H. Nordholt Prof.dr.ir. R. Otten Ir. E. Kleihorst

Delft University of Technology Delft University of Technology-University of Nijmegen

Eindhoven University of Technology Philips Research Laboratories Delft University of Technology Delft University of Technology Philips Research Laboratories

1 Cor.13 vers 2.

Aan mijn neefjes Martijn en Jeroen

1.1 DESCRIPTION OF SOME ESSENTIAL

CONCEPTS 3 1.2 AMPLIFIER DESIGN AUTOMATION 12

2. THE DESIGN PROCEDURE 15 2.1 THE BASIC CONFIGURATION 22

2.2 THE FIRST STAGE OF THE ACTIVE CIRCUIT 37 2.3 THE LAST STAGE OF THE ACTIVE CIRCUIT 47 2.4 THE MIDDLE STAGES OF THE ACTIVE

CIRCUIT 54 2.5 CONCLUSION 67 3. NOISE OPTIMIZATION 70

Introduction 70 3.2 BJT NOISE MODEL 72

3.3 JFET NOISE MODEL 75 3.4 NOISE CONTRIBUTION FOR THE FIRST ACTIVE CIRCUIT

STAGE 77 3.5 NOISE CONTRIBUTION IN AN AMPLIFIER DUE TO THE

ACTIVE CIRCUIT 78 3.6 AMPLIFIER OUTPUT NOISE TO BE

MINIMIZED 79 3.7 CONCLUSION 94 4. COMPENSATION 96

INTRODUCTION 96 4.2 FINDING THE REALIZED TRANSFER FROM THE SYM­

BOLIC TRANSFER 107 4.3 FINDING THE TRANSFER DEVIATION 108

4.4 ESTIMATING THE ORDER OF THE TRANSFER

DEVIATION 110 4.5 CALCULATION OF STARTING VALUES 113

-4.8 CONCLUSION 124

ABSTRACT 126 SAMENVATTING 129 APPENDIX 1. FUN SYNTAX 133

An overview of FUN 133 The syntax of FUN 133 Functional forms, F' 135 Definitions, D 136 Functions 136 APPENDIX 2. ROOT EXTRAPOLATION 140

APPENDIX.3 EXAMPLE 145 ACKNOWLEDGEMENTS 151

BIOGRAPHY 152 References 154

-Figure 2. Single-loop configurations 27 Figure 3. The basic two-loop configurations 31

Figure 4. Simplified circuit for output noise

calculation 39 Figure 5. Loading of the last stage 51

Figure 6. Introducing phantom zeros 62

Figure 7. BJT noise model 72 Figure 8. Equivalent noise sources in a BJT 74

Figure 9. JFET noise model 75 Figure 10. Equivalent noise sources in a JFET 76

Figure 11. Sub-integrands for the noise spectrum

integral 84 Figure 12. Multipliers for sub-integrands in noise spectrum

integral 85 Figure 13. Sub-integrands for a JFET input stage 93

Figure 14. Multipliers for JFET sub-integrands 93

Figure 15. Selecting dominant poles 112 Figure 16. Operations on oneports 137 Figure 17. Operations on twoports 138 Figure 18. Transistor operator 139

-Figure 2 1 . Transfer function modulus before and after

compensation 150

-TABLE 2. Mapping table for a two-loop configuration 30

TABLE 3. BJT noise model parameters 73 TABLE 4. JFET noise model parameters 76 TABLE 5. Table of devices to select from 146 TABLE 6. Results of noise optimization 147 TABLE 7. Compensation component values 149

-1. INTRODUCTION

The title of this thesis, "Automation in the design of negative feedback amplifiers", may give rise to a feeling of discontent in many an electronic circuit designer. He may very well get the idea that an attempt is being made to render his creativity and work superfluous. In the following we will show not only that this concern is unfounded, but that automation totally depends on his creativity.

In other sectors of electronic design, automation has made considerable progress. In the design of digital circuits, for instance, larger circuits per­ forming more complex functions are becoming available as design automa­ tion proceeds and better software tools come into being.

In the sector of analog circuit design the development of software design tools has lagged considerably. This is not only due to the fact that the theory required to practice in this branch of electronic design is remarkably more complex, but also because the habits of the analog designer do not particularly encourage the development of further, more advanced software. Often, an analog designer can get along remarkably well using existing analysis and synthesis methods suitable for calculation by hand. If he combines these methods with intuition and a thorough understanding of his field of design, he may not even feel the need for design aids in the form of soft ware-tools.

In this introduction we try to indicate why design automation can nevertheless lead to the improvement of analog electronic circuit design. To this end, first the concepts "automation" and "design" are described, since they may easily be misunderstood due to the lack of a precise, commonly-accepted definition.

As amplifiers are a class of circuits, for which a highly developed sys­ tematic design procedure exists "1, the automation activity discussed in this thesis is focused on the design of this type of circuit. However, the term "amplifier" is also prone to be misunderstood and, therefore, requires an explanation.

U DESCRIPTION OF SOME ESSENTIAL CONCEPTS

In the description of the essential concepts embodied in the words "automa­ tion" and "designing", the computer on which the design or automation pro­ cess is performed and the designer will be considered to be a single closed system. In this system, the designer performs the role of an automating human being. The system is occupied with manipulation of the knowledge it contains. Design automation is a useful activity, if the system of designer and computer achieves a design quality better than the design quality obtained by the designer alone. In order to assert how tasks are to be divided in a sensible way between the designer and the computer, atten­ tion is paid to the nature of the knowledge exchanged between the human and the computer, and the representation of this knowledge. Subse­ quently, the subject on which the automation activity is focused here, the design of high-performance, negative-feedback amplifiers, is dealt with.

1.1.1 Automation

Automation can be considered to be a knowledge transfer process, where knowledge is being transferred from the automating human to a computer system. Not all knowledge is equally suitable for such transferral.

A human being, roughly speaking, manipulates two types of knowledge. First, he uses vague, not well-reasoned out knowledge. This knowledge has an improvized, ad-hoc character. Its origin is spontaneous and creative. An important factor when using this type of knowledge is experience. Still, it is remarkable that man can take decisions without formal reasoning and without a guarantee of correctness. A property of vague knowledge is that it is difficult to communicate and to teach. Creativity can only be encouraged in others, not transferred from one person to another.

The second type of knowledge is concrete knowledge. This knowledge applies to well-described data and procedures. Since no undefined ideas or procedures are used in concrete knowledge it is suitable for teaching. Also, it can be satisfactorily transferred into a computer system and hence automated. An interesting demonstration of this is given by the develop­ ment of calculus. It took centuries, before calculus had reached its present, strict form. During this time, creative steps had been continuously made.

Thus has vague knowledge been continuously transformed into concrete knowledge in an ongoing process of posing questions and of seeking appropriate definitions and procedures. Also, continuous attention had to be paid to notational problems as these problems hampered the proper for­ mulation of questions and the answers found to these questions. This pro­ cess of developing theory and notation to express the theory has cul­ minated in the automation of the knowledge involved in calculus, in the form of a mathematical software packages such as MACSYMA or REDUCE, which are capable of performing operations defined in calculus such as integration and differentiation, in a symbolic fashion.

For those not familiar with symbolic computation, we give two examples of the capabilities of such a system, which are equivalent to or even better than our own ability to manipulate formulas. If one enters the following expressions into a REDUCE system:

int (log(x ),x );

and

dif/(logixlx);

then the following responses are obtained: x * ( l o g ( x ) - l )

which is the integral of log(x), and

Ux

being the derivative of log(x ). Because the complexity of the expressions is not one of the principal problems in symbolic evaluation, the capabilities of a human being using a symbolic expression manipulator are greatly enhanced. This is a good example of a successful automation activity.

CREATIVE ROUTINE teadher AUTOMATIC knowl. knowl. knowl. coding educ ition knowl.

pupil ? «messages «- computer

Figure 1. Knowledge manipulation

An attempt to describe knowledge transfer and storage between human beings and computers in a somewhat more general way is shown in Fig. 1. In this figure, different types of knowledge are represented. Human knowledge is divided into two types. On the left, vague knowledge is present, which has a creative nature. It usually is not controlled cons­ ciously, but it results in concrete thoughts, the second type of knowledge, entering the consciousness. The act of rendering creative knowledge con­ crete is essential in science. Once vague knowledge has been described in the form of data and procedures, it can become a basis for routine action. Also it becomes communicable. Concrete knowledge can be taught to other human beings in the form of procedures and data. In the process, one hopes to encourage the creative thinking of the pupil, but this cannot be forced.

The concrete knowledge can also be modified into a form suitable for use by a computer. The procedures usually need some adjustment, and a large amount of programming activity is involved. Procedures that are experi­ enced by a human as being difficult to perform, often are carried out with ease by a computer. We have focused on such tasks which are of a numeri­ cal nature in the amplifier design problem. The results obtained if such a task is performed by a computer will obviously need to be interpreted by a human. If errors occur during the execution of a task by a computer, or if the procedure carried out does not guarantee optimal results, the messages generated by the computer need interpretation as well. We have avoided the problem of automating the activity of interpreting results and error messages. The procedures described in Chs.3 and 4 have been constructed for interactive use and their results must be judged by a human being. They do perform tedious calculations, however, and therefore are believed to be of great use to the designer.

After this explanation of Fig. 1, we will indicate the parallel between the automation of calculus and the process of design automation.

In design automation, both vague and concrete knowledge are currently being automated. Attempts are being made to automate vague knowledge by means of expert-systems. However, it can be doubted whether this will lead to success, since this kind of automation is essentially an attempt to model our manner of dealing with vague knowledge. Since we don't know how we treat vague knowledge, setting up an expert-system may be con­ sidered a speculative activity as far as the reliability of its reasoning mechanism is concerned.

Instead, our activities will be directed to the discovery and formulation of concrete procedures in the design practice, and the description of the data used in these procedures. If the description is sufficient the procedure can be automated. As a by-product, it will become useful as an educational tool, due to its well-defined nature. In automation, a proper representation for procedure and data description must be chosen. This representation must be useful to both the computer and the human being. Further, all information concerning the design activity must be capable of being represented clearly. We will limit ourselves to the description of

manipulations performed on electronic circuits and the description of these circuits. A distinction may be made in the representation used between human beings, and the representation used between a computer and a human.

Humans tend to be inaccurate in transferring information. They represent their knowledge in an incomplete fashion and assume that the receiving human will complete the message to make a well-defined description. The use that electronic engineers make of circuit diagrams can be used as an example. Often, they do not realize that they call upon vague knowledge present in the receiver of the message when providing him with a circuit diagram. An engineer does not notice, for example, that a hierarchy is not or is only partly represented in the diagram, but that this hierarchy has to be recognized and constructed in the mind of the reader. Still, engineers silently identify the representation of the circuit with the circuit itself. This is an error due to mixing up modes of representation which is cleverly illustrated in a painting by the Belgium impressionist Magritte, who dep­ icts a pipe and adds the annotation "Ceci n'est pas une pipe" on the painting.(Cover)

The information transfer from one human being to another differs funda­ mentally from the information transfer from a human to a computer. A computer is not very effective in recognizing hierarchy, nor does it have access to vague knowledge, for instance in guessing the function of a circuit part. However, designers use a graphic representation to enter a circuit description into a computer in what is called "schematic entry". Commonly, a nctlist is generated from the graphic input which contains only primitive components, such as resistors and capacitors, which are equally present in the graphic description. A description in terms of functionality of circuit blocks cannot be derived from graphic input description in the form of a circuit diagram. Such a higher-level description is essential in a design pro­ cedure which acts through step-wise refinement of the network structure to design. Also, in design the network structure must be easy to modify. Schematic entry is not very useful for this purpose. A more powerful

description method must be used in the representation of procedures and data used in design. To this end, two classes of design problems must be distinguished, each requiring a different approach.

The first problem class is characterized by a rigid structure. The data and the procedures required to solve the problem are defined in all their detail. In the automation of concrete knowledge, procedures belonging to this first class are adapted for execution by a computer. In execution by computer, a complete definition of procedures and data is mandatory. In principle, error conditions during computation should not occur. If they do, this signals that knowledge is lacking, and needs to be added to the solving procedure of the design problem. It is the automating human who has to provide the knowledge, either immediately by direct specification or by specification preceded by a research step which modifies vague knowledge based on creative thinking into concrete knowledge.

Procedures fixed in advance are suitable for non-interactive use due to their rigid structure and complete definition. It may be expected that few changes should be made in the description of the procedure which is coded for the computer. An example of the description of a solution to the prob­ lem of analyzing the electrical properties of electronic circuits is the pro­ gram ANP3 '2^ the behavior of which is completely describable and predict­ able. Moreover, it functions without the need for human intervention d u r ­ ing execution. This is a property of all well-defined implementations for automated problem solving. As long as interactivity is required the process of automation is not finished, and the procedure to solve a problem needs better definition.

A second class of problems is requires an interactive solvingprocedure. This means that a series of procedure steps can be distinguished which follow from the judgement of intermediate results by a human observer, usually the designer. He adds vague knowledge, which completes the knowledge required for the complete solution of the design problem. Again, this knowledge consists of data and procedures. Their specification requires a flexible, powerful description system that can be used by both the designer

and the computer. Due to the interactive nature of a dynamic solvingpro-cedure, an interactive environment is the most appropriate to manipulate data and procedures in.

In the automation of design-knowledge, a bipartition can be made. On the one hand, a number of so-called tools is available, which have a completely documented input and output. On the other hand, an interpreter is present that enables the designer to completely define and redefine the designed cir­ cuit. Also, it enables him to influence the design procedure by entering his evaluation of the status of the solution into the design system. Moreover, the tools must be accessible through the interpreter that communicates with the designer. A proposal for such an interpreter is based on the func­ tional language FP. The language interpreted is named FUN, and it defines a symbolic notation that permits a hierarchical description of complex elec­ tronic circuit structures. Also, complex manipulations can be performed on the circuit by means of the procedures described in FUN. In this thesis, use of this language will occasionally be made to indicate its usefulness in the description of the design process of amplifiers. An outline of the language is given in App.1. It can be shown that the set of primitive functions required to describe circuits can never be made complete. An alternative not suffering from this shortcoming is based on /3-calculus. ^ '4\ A func­ tional language for the description of digital circuits has been dealt with in

[5]_

1.1.2 Designing

We will now consider the idea of "designing" in some detail.

In electronics, designing often departs from existing circuit configurations, which are, for instance, taken from handbooks. The values of the components used in the circuit are modified but the structure is left intact. If the designer does not have insight into the concepts that form the basis of the design he takes as a point of departure, he will be incapable of judging optimality of his circuit. In many applications, this may not be a problem. However, we assume that an optimal design is required and, therefore, a more drastic approach to the design problem is desirable.

We will here restrict the notion of "designing". By designing we under­ stand the synthesis of a circuit, so that its quality is optimal for the per­ formance aspects of importance. The topology of the circuit depends on the specification of the problem data, and it should be generated in a hierarchi­ cal manner by step-wise refinement.

A human designer will attempt to realize his circuit design by using all means and knowledge, both vague and concrete, available to him. The quality of the result remains dependent on the amount of vague knowledge possessed by the designer. Even if both an experienced and an inexperi­ enced designer should have the same amount of concrete knowledge, the greater amount of vague knowledge he possesses enables the more experi­ enced designer to locate errors and to judge decisions taken in the process with more success.

Perhaps even more important is the amount of concrete knowledge pos­ sessed by the designer and present in the computer when taken together. As a concrete procedure is fully describable and justifiable, it can often be shown that an optimal result follows for the design step described by the concrete procedure. With vague knowledge only, no certainty about the quality of the result exists. To increase this certainty the amount of vague knowledge involved must be reduced. If the designer has access to automated concrete knowledge, he has to rely less on his store of vague knowledge. Automation can, therefore, offer a significant contribution to the improvement of design quality, as through it more concrete knowledge becomes available to the designer. When using automated knowledge he must still be able to judge the correctness of results obtained by the appli­ cation of software tools. Therefore the greater the amount of knowledge that becomes available in automated form, the more theory the designer will have to be acquainted with. Automation will most likely necessitate that the designer maintains a better control over his design practice, which has been enriched by the knowledge available to him through the design system. The designer's creativity remains a necessity in the design process and it is freed from activities necessitated by standard design practice as

these activities can be performed automatically.

In electronic design practice, work, is being done that forms a basis for the automation of the design of several classes of electronic circuits and sys­ tems, such as oscillators and radio-receivers. Probably the most advanced effort in this direction concerns the design procedure for amplifiers. Avail­ able concrete knowledge for this procedure is described in ***, Although at some points in the procedure vague knowledge plays a role, several steps in the design procedure can be described fully in a concrete algorithmic form. Where vague knowledge is required future research will have to decrease the need for it. In this text the attention is focused on the design of amplifier circuits, since the procedure described for it is the most developed and offers a possibility to acquire experience in the automation of analog design procedures. In the following sections the design steps which are a part of the amplifier synthesis procedure will be briefly described.

1.1.3 Amplifier

We will now describe the concept "amplifier". To obtain an accurate reali­ zation of a specified transfer function a feedback amplifier configuration is used.

Feedback amplifiers consist of a feedback network and an active amplifier part that provides the required gain. We will not use an opera­ tional amplifier for the realization of the active circuit. An operational amplifier is intended for use in a wide range of applications. This may be a very useful approach in many cases but, as a consequence, designs for specific purposes will suffer from suboptimal performance if based on a generally applicable operational amplifier. If this is acceptable, a standard-cell approach can well be used. A design system for circuits based on this approach has been described in '6-L In the design procedure described here, loss of transfer quality is deemed unacceptable. To overcome the loss of quality, which results from the requirement of generality imposed on the operational amplifier realization, the amplifier configuration is made to fit optimally for a specific design problem. The design is based on the fact that the function of an amplifier is to enhance the energy level of information

provided by a signal source, minimally affecting the amount of informa­ tion present in the input signal. The signal source often is a transducer transforming a physical quantity into an electrical quantity such as current, voltage, charge or flux. Departing from a complete specification of the signal source, the amplifier load and the desired transfer of the input quantity, an amplifier is synthesized, optimizing the behavior of the amplifier for various quality aspects. Such aspects are its noise contribution and the linear and nonlinear distortion contribution.

In the description of the automation activity given here we will exclude some aspects of amplifier design or treat them superficially. One of these aspects concerns the minimization of nonlinear distortion. We will assume that this can be made sufficiently small, increasing the required bias. Power consumption is left out of the design considerations. By the same token, the common phenomenon of slewing is considered not to interfere with the design procedure, since current limitations can always be solved by adapta­ tion of the bias current. If power consumption does become a problem, the creativity of the designer will be required to find a solution. We are well aware of the fact that the design procedure still needs development at this point. Another important problem that will not be considered is the prob­ lem of realizability. It is very well possible to specify a design problem that has no solution. If no solution can be found by the design procedure here the creativity of the designer will be required to find alternative solu­ tions.

1.2 AMPLIFIER DESIGN AUTOMATION

After the clarification of the concepts "automation", "design" and "amplifier" we will indicate what should be understood under "amplifier design auto­ mation".

In designing amplifiers, the automating designer uses both concrete and vague knowledge. The vague knowledge must be turned into concrete knowledge and then coded into software thereby automating it. This is advantageous for two reasons.

First, a human designer makes errors in his application of concrete knowledge on a design problem, specifically if the problem is of a consider­ able size. This source of error can be eliminated by automation.

As an important advantage, a greater complexity of the designed circuit will turn out to be controllable. The quality of the design will improve.

Second, a human being makes errors in his application of vague knowledge. This is unavoidable because of the very nature of vague knowledge. Vague knowledge must be made explicit and turned into con­ crete knowledge, insofar as possible, and then automated. Again, the qual­

ity of the design will improve.

Because the amount of concrete knowledge available to the designer will increase as automation proceeds the requirements imposed on the designer will increase. A part of his knowledge will no longer be used actively if certain techniques are automated, but a passive knowledge must be called upon in the interpretation of the results yielded by the automated design procedures.

Thus the designer can focus his attention on further improvement and concretization of the design procedures he applies. The automation and design activity will steadily converge. The creativity of the designer is essential here as it is the starting point for the automation activity. The designer will have to continue using his creativity as automation proceeds.

In the following chapter a number of aspects of amplifier design automa­ tion are discussed. First, a survey of the design procedure is made in which attention is paid mostly to the practical side. Where necessary the electronic-theoretical considerations which underly the design procedure will be gone into but most of these considerations will be referred to in ^'. In the overview each of the steps involved in the design procedure will be analyzed. How each step can be performed automatically and what limita­ tions play a role is described. The design steps are assumed to be indepen­ dent unless stated otherwise. If interdependency does exist attention is paid to this problem.

In the following chapters, the theory that is the basis for two software realizations of automated design knowledge is dealt with. In each, a sub­ stantial part of the design procedure is contained so that most of the calcu­ lations to be performed in the design can be performed by the computer, rather than by the designer. The first program (Ch.3) deals with the optim­ ization of the noise properties of the amplifier. The second program (Ch.4), the so-called frequency compensation, performs the calculations required to find the values of components that have been added to the circuit in order to control the amount of linear distortion added by the amplifier.

2. THE DESIGN PROCEDURE

In this chapter an overview is given of the procedure for amplifier design as described in [1]. Our main interest is in the rough setup of the procedure insofar as the circuit topology of the amplifier is concerned. For details we refer to the literature. After the overview of the design steps given in this chapter two design steps will be described in more detail. In Ch.3 a pro­ cedure for optimizing the noise performance of an amplifier is discussed and in Ch.4 a procedure for optimization of the linear distortion contribu­ tion of the amplifier is dealt with. These two chapters form the basis for two computer programs that serve as design tools. An application of these programs is shown in App.3.

The aim of the design procedure is limited to the the realization of a com­ plete signal circuit of an amplifier which has a transfer behavior according to specification and which realizes that behavior with optimum quality. The various quality aspects will be dealt with later.

The circuits to be designed are subject to a number of restrictions and assumptions:

— The signal source and the amplifier load have one common terminal in order to avoid disturbance by unwanted signals and parasitic impedances.

— The amplifier has a lowpass filter character. Initially, it must be possi­ ble to realize the amplifier in integrated form.

— Only the signal circuit diagram is here designed. This diagram contains only the components that determine the signal behavior of the amplifier. — Power efficiency is not considered. The bias may be freely chosen. — Slewing is not considered a problem as it can be prevented by increasing

— DC-coupling of the amplifier input is allowed. Therefore, differential input pairs must be permitted in the input stage of the active circuit. Under these restrictions the circuit is realized in a number of steps. Each step adds an amount of concrete and vague knowledge to the initial specification which enables refinement of the basic circuit diagram. A beginning is made with a circuit containing high-level circuit blocks that are not defined at a component level. In a sequence of design stages a full definition of the signal diagram on component level is generated.

Each step is performed in such a way that a particular quality aspect of the amplifier is optimized. In a first approximation, it is assumed that these optimization steps can be performed independently, an assumption which is supported by practical experience. For each step, the following points of importance are analyzed.

First, the procedure step is briefly described in terms of operations on the construction of the amplifier to be carried out. Then a review of the neces­ sary data in taking the decisions involving the construction is given. Further points in the design step where the a designer's judgement may be required are pointed out. Finally, the resulting configuration after finishing the design step is given.

The operations to carry out on the circuit can be roughly divided into two groups.

The first group consists of operations that modify the structure of the network. Such operations refine or expand the network, for instance, by the insertion of an amplifier stage.

The other group consists of calculation operations. Such operations could be, for example, the finding of optimal values for bias currents of transistors and values for components.

The first group - that of the structural operations - can best be described by using a symbolic network description language like FUN. This is an experimental language for the description of analog circuits. It can serve as

an interface between human description and reasoning about circuits and operations on such circuits on the one hand, and their counterpart within a computer system on the other. A description of the syntax and application of FUN can be found in App.1. Operations such as cascading and putting in parallel of circuit parts are readily available in this language, and make possible the description of the modifications the amplifier structure under­ goes possible. Using an experimental implementation of a FUN interpreter, some of the manipulations of the circuit structure have been described by appropriate functions and tested. The data required from the designer are specified as expressions in FUN. An example of this is shown in Sec.2.1, where the basic amplifier configuration is selected from a basic specification. With the present implementation of FUN, however, evalua­ tion of the describing expressions is a time-consuming enterprise.

Many of the operations from the second group, the numerical operations on electronic networks, have been realized in software. Examples of these are the calculation of transfer functions and noise analysis. Such software assumes that a description of a network is input in the form of a netlist and a set of commands requesting the numerical operations to be per­ formed.

A netlist is a set of primitive components, such as capacitors, resistors and transistors, characterized by a number of attributes such as node numbers which indicate the interconnections and component values or types.

If such existing software must be used in an automated design system, in which a network is described by a symbolic language as is used in the first type of software, a conversion of the symbolic description to a netlist is essential. However, evaluation of symbolic expressions describing net­ work structure is extremely time-consuming, mainly due to implementa­ tion problems. It can be expected that fast evaluators will eventually become available. At present the size of the amplifier circuits to be designed is small enough not to demand an excessive amount of time in the manipu­ lation of its symbolic description. Therefore it is not to be expected that practical objections will hamper the application of symbolic network

descriptions in certain stages of amplifier design automation.

After a short overview of the operations that are carried out in a design step, the data involved are inventorized. If data can be derived from exist­ ing data the procedure to follow is indicated.

In general, the data can be divided into the following categories:

1. Data to be specified by the designer. These data depend on the applica­ tion of the amplifier. It is hard to determine whether the data define a solvable design problem. Although this may sometimes be possible at an early stage, it may often not be possible to decide on the solvabil­ ity of the design problem until the design is nearly finished. H o w ­ ever, due to the systematic nature of the procedure and its tendency to produce an optimal design, it will often be possible to decide at some point in the procedure whether the design specification can be met by a proper amplifier design. This usually is very difficult in non-systematic design practice, for in such an approach it is difficult to decide if a design is optimal.

2. Data that can be derived from data previously found. The procedure to obtain the new data from the known data is described.

3. Data describing the structure of the amplifier network in a certain design step. These data are defined in a symbolic network description language. Operations on these data are performed by a special evalua-tor. The evaluation efficiency of such an evaluator needs improve­ ment, but in the near future improved versions of functional descrip­ tion languages will become available. Moreover, the size of the cir­ cuits designed here is limited, keeping the time required for evalua­ tion of a network description within reasonable limits.

4. Data required for numerical procedures. The input data for the pro­ cedures performing calculations, must, for a part, be derived from the symbolic network description. The transformation steps required that must be performed by the symbolic language manipulator are described. During a design step, manipulations on the network struc­ ture are clearly separated from calculations performed thereon. Two

reasons can be given for this. First, such a separation permits calcula­ tions to be performed efficiently by means of software that does not depend on the slow network structure description manipulator. The theory underlying the software that has been implemented for the design procedure calculations is described in separate chapters. Such software has been realized for the design step, where the first stage of the active circuit is designed, and for the realization of the middle-stages of the active circuit. These calculation procedures are described in Ch.3 and 4.

A second reason for the separation of calculations and manipula­ tion on the network structure is that the calculation procedures con­ tain concrete knowledge, which, to a certain extent, is complete. Also, the input data are fully defined. Interaction with the designer is, in principle, not necessary for proper execution of the numerical pro­ cedures. The designer has to intervene, if the results of a calculation step are required, or if a change in the network structure is needed. This can easily be done, since the symbolic network evaluator, which stores calculation results and network structure, is an interpreter, designed to be used by a human being. This interpreter can read lack­ ing information to be provided by the designer, if due to missing knowledge the design process cannot be continued.

The input data for the calculation procedures have now been indicated. After the inventory of the data involved in a design step, the role played by vague information is described for the design step under consideration. In automation, it is extremely important to establish the role of vague information. As the procedure to be automated has previously been in the hands of human beings, it is very likely that a certain amount of vague knowledge is essential in the execution of the design procedure, even though one is not aware of it. In steps where this is the case we will indi­ cate, where concretization of knowledge is still required before full auto­ mation can become possible.

Most certainly, vague knowledge is required in judging the interactions that may exist between design steps. This is one of the most difficult prob­ lems in design. Though such interactions can frequently be avoided in the design procedure a t hand. Complex interactions can only be dealt with by a creative and experienced designer, capable of making sensible trade-offs. The design procedure can be subdivided into the following steps:

1. Selection of a basic amplifier configuration.

At the highest hierarchical level an optimal amplifier structure is selected, containing a so-called nullor and a feedback network. The nullor is to be realized by an active circuit, the design procedure of which is described in the following design steps.

2. The design of the first stage of the active circuit.

Optimization of the noise properties of the amplifier is achieved by making the best choice for the realization of the first stage in the active circuit.

3. The design of the output stage of the active circuit.

On the basis of demands imposed on the range of currents and v o l ­ tages to be handled by the output stage, the configuration and bias of the last stage are determined.

4. Design of the middle-stages of the active circuit.

By inserting a maximum number of optimally configured amplifier stages in the active circuit the linear distortion contribution of the amplifier is minimized. Also, as a side-effect, other quality aspects are improved.

For each of these steps, the following points will be analyzed.

— The available concrete knowledge to solve the partial design problem. — The data to be used in the step.

— Vague information that must be obtained from the designer.

In the description of the design steps it has been assumed that the steps can be performed independently. Although this is true to a large extent, some interaction does exist, which, however, we will not consider.

2.1 THE BASIC CONFIGURATION

It is the function of an amplifier to realize an accurate relationship between its source and load quantity. The source and load quantity can be a voltage or a current, carrying the signal information. A source producing a flux can be treated as a voltage source plus an integration. The integration is realized by adding a pole in the origin of the p-plane to the transfer func­ tion that must be realized. Similarly, a source producing a charge can be treated as a current source plus an integration, which is accounted for in the amplifier transfer function. This information contained in the input quantity can be related to a physical entity. A signal source current can, for instance, be derived from a transducer converting luminance into a current. A load current can serve for the generation of light by means of a Light Emitting Diode. In both cases the electrical quantity has been so chosen that its relationship to the physical entity is optimally linear, and thus represents the signal information in the best way.

Not only the most suitable electrical quantity must be selected but also an input and output impedance may have to be defined.

A general representation for the specification of input and output quanti­ ties as well as input and output impedances can be given by the K-matrix. This K-matrix specifies the basic requirements for the transfer to be real­ ized. It is defined by the following expression.

(1)

wherein u, and i, are the input current and voltage and u0 and i0 the out­

put voltage and current of the amplifier.

The transfer specified by the K-matrix is realized in its ideal form by an amplifier circuit consisting of a nullor and a non-energic feedback network. A non-energic feedback network dissipates nor stores energy. A set of

A = «/ it A

C

basic circuits can be defined from this K-matrix. Each of these basic cir­ cuits corresponds to a different set of K-matrix coefficients which are either zero or real. Since four coefficients can be set to zero, sixteen distinct classes of circuits exist in theory. In practice, only a subset of the basic circuits can be realized for the following practical reasons. The non-energic feed­ back. network contained in the basic circuit is constructed using ideal transformers and gyrators. Although transformers may be useful in amplifiers which transfer signals at relatively high frequencies, they are not generally useful. However, a design system must be able to handle transformers in case they might be a useful option. We will not deal expli­ citly with the use of transformers hereafter though. As for gyrators, they must be realized by means of active components. The presence of active components in the feedback network is considered undesirable, as this results in an amplifier having inferior transfer properties compared to an amplifier with a feedback network containing passive components only. For the same reason active feedback techniques are not considered here.

Instead, the non-energic feedback network required for an ideal realiza­ tion of a transfer function is approximated by a passive feedback network containing passive components such as resistors and capacitors. As has been mentioned before, large inductors in the feedback network are excluded. However, small integrated inductances may be very helpful in amplifier design. Design tools therefore must be able to cope with these components. Although we will bear this in mind, we will not make further mention of the use of inductors explicitly.

Due to these limitations, related to the use of an energie feedback network, only six basically different feedback configurations can be realized. Four of these can be constructed with one feedback loop, the other two possess two feedback loops if the amplifier is properly terminated. Therefore, a number of transfer specifications is basically unrealizable if passive impedance networks are used. In such cases the designer will have to determine a suitable alternative realization. In the next section attention will be paid to the selection of the amplifier configurations that are realiz­ able if impedance feedback networks are used. In a following subsection,

some attention will be paid to the design of impedance networks required. 2.1.1 Data required for selection of t h e basic configuration

The data required for the determination of the basic configuration are the following:

— The signal quantity to transfer. This source quantity can be a voltage, or a current. If the signal quantity is a charge it can be described as a current and an integration. If the signal quantity is a flux, the input sig­ nal can be described as a voltage and an integration. The integration can be accounted for in the transfer function. Depending on the linearity of the mechanism that generates the source quantity from a primary p h y ­ sical information carrying quantity, the best representation of the origi­ nal information must be specified. This may be done by including a vol­ tage or current source in the circuit description of the signal source, together with a source impedance description, which must be specified as an equivalent electronic circuit diagram.

— The signal quantity to be generated. An output quantity is chosen on the basis of the quality of the information conversion performed in the load of the amplifier, which is used to produce a physical quantity car­ rying the amplified information. By the inclusion of a voltage or current detector in the circuit diagram representing the load of the amplifier, the desired output quantity is indicated. Further, specification of the load impedance is required. This must be specified by an equivalent elec­ tronic circuit diagram.

— The input impedance Z, of the amplifier. This must be specified by a Laplace transform.

— The output impedance of the amplifier. This as well must be specified by a Laplace transform.

— The desired relationship H(p) between input and output quantities.

With these data, the basic amplifier configuration can be selected. The feedback network, can be dimensioned. For the generation of the feedback network, the intervention of the designer is still required.

2.1.2 Mapping of the transfer type to t h e basic circuit structure In the realization of the basic configuration we limit ourselves to applica­ tion of impedance feedback networks. Because of this only four basically different configurations containing a single feedback loop can be realized, and only two configurations containing two feedback loops can be con­ structed if certain requirements for source and load impedance are fulfilled. The single-loop configurations can be used if the input data answer the following requirements.

— The input and output impedances of the amplifier are zero or infinite. — If the circuit is to be integrated, the transfer function H(p) contains

only real poles and zeros, as only very small inductors can be integrated. More precise limitations are dealt with in the description of a procedure for the realization of feedback impedance networks.

The configurations containing two loops can be used under a number of restrictions. These restrictions arise from the fact that no non-energic feed­ back is used to fix the transfer. Due to this more than two K-matrix parameters determine the transfer, two of which are dominant. The influence of the remaining stabilized, accurately fixed, K-parameters can be disregarded under the following conditions. In this case, source and load-impedance do not affect the transfer of the input and output quantities. If the source and load impedances are accurately known and if they do not produce distortion the given restrictions may be abandoned.

Three different types of transfer can be distinguished. The require­ ments for each of these types are listed here:

1. The input and output impedance of the amplifier as well as the source and load impedance are all equal. The amplifier is characteristically terminated.

2. The input quantity is a voltage or a flux.

The load impedance is sufficiently large for its influence on the transfer to be ignored.

The input impedance of the amplifier is finite and well defined. 3. The input quantity is a current.

The signal source impedance is sufficiently large for its influence on the transfer to be negligible.

The output impedance of the amplifier differs from zero or infinite. For the single-loop and two-loop configurations that can be realized, a procedure for determining the basic configuration from the input specification is given next.

2.1.2.1 Basic single-loop configuration. The K-parameter P to stabilize is defined by the following table.

input quantity U I

u

u, UjO-z2 ^5U„ V -ou0 i , o 0 —1 1— - + + — r

i

Figure 2. Single-loop configurations

The four basic single-loop configurations are given in Fig.2 and Tab.1. The selection procedure for these single-loop configurations can be well described in the circuit description language FUN. In order to give an example for the use of such a circuit description language in circuit design automation, a description for the basic circuit is given. In this description the specification of the desired transfer type is used to select the proper basic configuration. The selection procedure has been successfully realized in a preliminary implementation of the language FUN.

The procedure involves a number of symbols which are first defined.

1. transfer is a list of t w o symbols. These symbols can be U or I. The first of the two symbols defines the input quantity representing the signal information to be transferred. The second represents the o u t ­ put quantity that is converted into a physical quantity by the

amplifler load. For example, a voltage to voltage transfer is indicated by:

transfer = <U ,U > (2)

2. beta represents the feedback, network.. It is a twoport. At this stage of the design process, beta remains to be defined at component level. In the description of the mapping of the transfer type to the basic configuration this level of detail is not required.

3. Nullor is the symbol for the twoport with nullor transfer properties, meaning that its K-parameters are all zero.

4. ifu is a function that takes the value true if its argument equals the symbol U, otherwise it takes the value false. It is defined as:

ifu =bu eqU (3)

5. connection is the function that combines the nullor and the feedback network beta so that the correct K-matrix parameter is stabilized, thus producing the desired relationship between input and output quantity of the amplifier circuit, connection can be one of the follow­

ing functions:

— sipo, which puts the input ports of the nullor and the feedback network in series, and the output ports in parallel

— siso which puts the input ports in series and does the same for the output ports

— piso which puts the input ports in parallel and the output ports in series

— pipo which puts the input ports as well as the output ports in parallel

connector = (ifu~l)-*((ifu ~2)->%siso ;%sipo ); (4) (ifu ~2)-*%piso ;%pipo

lts argument is the symbol transfer defined above. This consists of two symbols each of which can be either U o r L The first symbol in

transfer indicates the type of the input quantity. If it is a voltage, connector must yield the operator %siso or %sipo, as series coupling of

the input ports of the nullor and the feedback network is required. If the input quantity is a current, connector can take either the value

%piso or the value %pipo, as parallel coupling of both input ports is

then required. The final selection for connector is based on the second symbol in transfer, which represents the amplifier output quantity. If the output quantity is a current, series coupling of the amplifier the feedback network output port is required, otherwise parallel coupling must be applied.

6. blocks is a sequence of the two twoports contained in the basic configuration, defined as:

blocks = <nulior ,beta> (5)

7. configuration yields the basic configuration. It is defined by:

configuration = <connector : transfer > : blocks (6)

The description of the mapping yielding a basic amplifier configuration containing one loop is hereby completed.

A more detailed specification for the feedback network that must be designed is now required. This specification is given as a transfer, described by a Laplace transform. The transfer specified is one of the four K-matrix parameters describing the amplifier transfer. In the case of a single loop amplifier, only one K-parameter is non-zero. This K-parameter P is related to the specification of the required transfer H(p) by

P=±(p) (7)

From Tab.1 it can be seen that the K-parameters A and D are defined by a ratio of two impedance functions, whereas the parameters B and C are defined by a single impedance. Each impedance must be designable as an RC network, as the amplifier must be realizable in IC-technology.

2.1.2.2 Basic two-loop configuration. We will now describe the mapping of the transfer type to a basic configuration containing two feedback loops. The restrictions imposed on source, load and transfer as defined in Sec.2.1.2 must be fulfilled for the mapping. Under these conditions only two K-matrix parameters determine the transfer.

Three basically different transfers can be realized. For each of these transfers, it is now indicated, which K-parameters must be derived from the input specification. This specification contains a description of the transfer and the desired input and output impedance of the amplifier.

input imp Zc Zs=oo Zi output imp Zc Zo Zl=oo in U I U out U U

u

r — i i — Z l + 1 1

b

Figure 3. The basic two-loop configurations

In Tab.2, the allowed specifications are given. Zc equals the characteristic

impedance of signal source, load and amplifier input and output. The feed­ back. network, must be designed on the basis of the data shown in Tab.2. With the specified transfer and the desired input and output impedance of the amplifier, the K-parameters which describe the transfer of the feedback networks can be found. We will not go into a systematic approach of the determination of the impedance values for the feedback networks in the general case. However, in the next section some attention will be paid to a specific case of RC-impedance design, which can easily be automated and used in the design of feedback networks from a desired transfer specification.

2.1.3 Design of the feedback network

The K-parameters derived from the input specification supplied by the designer must each be realized by an impedance network. As the amplifier must preferably be realized in integrated form the impedance network may only contain resistors and capacitors. In the impedance networks to be real­ ized two classes can be distinguished, depending on the K-parameter associ­ ated with them.

If the K-parameters A or D must be stabilized, a network, containing at least two impedances is required to define a current or voltage ratio. The impedance level of these impedance networks is not fixed by the input specification given for the selection of the basic configuration. Therefore, the impedance level must be specified separately by the designer. In speci­ fying an impedance level, the designer may consider the noise contribution of the feedback network with respect to the noise contribution of, for instance, the active circuit. However, we will not deal with this in detail.

In order to define the K-parameters B or C, only one impedance is sufficient. Of course, the impedance level follows from the associated tran-simpedance or transadmittance specified by the designer.

For the RC network synthesis problem, several methods are available and described in the literature. A useful survey is given in '7'. Both for the realization of a network defining a ratio and an impedance methods are described now.

For the realization of a current or a voltage-ratio, one or more ladder, lattice or other types of networks can be used. '8' Although the networks obtained by the design methods described in literature do possess the desired transfer function, their behavior with respect to noise contribution and power dissipation can be rather sub-optimal. It is then left for the designer to find a more suitable network, with or without the use of syn­ thesis techniques.

The synthesis of an RC network from an impedance specification in the form a Laplace transform can be performed automatically in a number of ways, if the following conditions are satisfied '9':

— The poles of the Laplace transform are real and negative. — Poles and zeros interlace on the real axis.

— The lowest critical frequency is a pole, which may be in the origin. We now indicate the data and procedures playing a role in RC-feedback network synthesis.

2.1.3.1 Input data for RC network, synthesis. The first input specification is the type of transfer to be realized. Two types can be chosen from. — A ratio of two currents or two voltages

The required data here are:

1. The Laplace transform describing the required ratio. 2. The impedance level of the dividing network.

— Defining the ratio of a current and a voltage by means of an impedance. Here, a Laplace transform only must be specified.

2.1.3.2 Synthesis procedure for an RC-impedance. A straightforward syn­ thesis procedure is available which does not require the designer to inter­ vene, only if an impedance must be realized. Where a ratio between two voltages or two currents must be realized, the designer must supply infor­ mation in order to arrive at a useful network realization.

In this section, the first case - the synthesis of an impedance - is dealt with. Although several methods exist for the synthesis of the RC-type of impedances of interest here, only one realization method will be described briefly. A more extensive description can be found in '10\

We describe the realization of an RC-impedance network in its first Foster form. This consists of a number of RC-parallel sections connected in series. The impedance can be realized only if the requirements mentioned in Sec.2.1.3 are met. The impedance to be realized is specified by the Laplace transform Z(p):

i=nzr

n(p-n

)

Z{p} = -[= with np=nz or np=nz + l (8)

Using fractional expansion, Zip) can be rewritten as a sum of simple terms, each one containing a simple pole.

1=0 Kp—p,)

Each sum term can be realized by an RC parallel network, containing a resistor Rt and a capacitor Ct. For Rt and C,, the following component

values are required.

C,=p,/K,

Rt = UK, 0 0 )

Z(p) can be realized by connecting all sets R,, C, in series.

2.1.3.3 Vague knowledge in realizing feedback networks. The design of feedback networks very often requires the intervention of the designer who has to supply knowledge in order to arrive at a useful feedback net­ work configuration. Practical limitations, such as the technology used for the realization of the amplifier, impose restrictions on the use of the syn­ thesis procedure. Usually the realization must be integratable. Then feed­ back networks must be designed as RC-impedance networks. Such net­ works can only be synthesized for a limited set of amplifier transfers. If a transfer is specified that requires a feedback network unrealizable by a known synthesis procedure, the designer has to take charge of the feedback network design. Then, a design system can only help, by offering a design environment where the designer can easily manipulate networks and tools applicable in his design activities. No complete automation is then possible.

What is more standard network synthesis techniques often result in sub-optimal solutions where noise and distortion properties are concerned. The designer has to judge this overall performance of the amplifier if he is to make a reasonable choice for the feedback network realization. Again, a design system can help him by offering an environment where the tools for the judgements to be made by the designer are easily accessible. Up to now no general criterion for the performance of an amplifier has been formu­ lated that would allow automatic evaluation of the quality of the amplifier transfer.

As stated before, an extra complication arises if the transfer to be real­ ized is a ratio of two currents or voltages. Here, an impedance level must be determined for the impedances in the feedback, network. This impedance level influences nearly all quality aspects of the amplifier. It has an effect on the noise performance, the bandwidth, and also the distortion contribu­ tion. As no simple criterion exists for the quality of the amplifier, the designer has to judge the influence of the impedance level selected. General design rules often lead to a limited influence of the feedback network on the transfer quality. At the moment, the designer himself has to apply these general design rules.

2.1.3.4 Resulting feedback, network. The result of the design step just given, is a description of a feedback network that determines the amplifier transfer specified by the designer. It can be described as a twoport in a suitable network description language such as FUN.

2.1.4 Vague knowledge i n d e t e r m i n i n g t h e basic amplifier configuration

Restrictions on the implementation technology of the designed amplifier usually lead to exclusion of transformers and gyrators as circuit elements. Due to this only a subset of the basic amplifier configurations are realiz­ able. If a designer supplies a transfer specification that can only be met by an unrealizable basic amplifier configuration, automatic generation of an amplifier circuit is impossible. Alternative solutions may use two or more amplifier circuits instead of one. The use of active feedback circuits may also be considered. As general rules for these cases are difficult to formu­ late, we will exclude these cases in the following and restrict ourselves to the regular, realizable basic circuit configurations. However, in developing tools for the design procedure an attempt has been made for these tools to be as general as possible.

2.1.5 Resulting basic configuration

The result of the design step for the basic configuration is an amplifier cir­ cuit description, consisting of the following items.

1. The signal source and amplifier load described in the input specification supplied by the designer.

2. A nullor circuit.

3. A completely dimensioned feedback network. The impedance level of a network defining the ratio of two voltages or currents may be sub­ ject to change later on in the design procedure.

22 THE FIRST STAGE OF THE ACTIVE CIRCUIT

In the previous design step an amplifier was found which consists of the following circuit blocks.

1. A nullor

2. A completely specified feedback network

In this and subsequent steps an active circuit is generated that serves as an approximation for the nullor. This approximating circuit has a non-ideal behavior that reduces the quality of the amplifier transfer. One of these properties is that the active circuit introduces noise into the circuit. In the design step described here the influence of the most important noise sources is reduced to a minimum. We indicate now w h y the configuration derived in the previous section is taken as a point of departure for the design of the active circuit. Further, we describe how the first stage of the active circuit can be designed so that the amplifier noise-behavior becomes optimal.

A high-performance feedback amplifier realizes a specified transfer of a sig­ nal obtained from a signal source with known impedance to a load with known impedance, preserving the quality of the signal as much as possible. Only a non-energic feedback amplifier configuration possesses accurately stabilized K-matrix parameters, which define an accurate transfer that does not depend on source or load impedances. This independence is required since the source impedances or load impedances usually are not accurately known and since they may introduce nonlinear distortion if they enter into the transfer function.

This configuration contains a non-energic feedback network and a nullor circuit. Both circuits must be approximated in a practical realization.

The feedback circuit usually is realized as an energie impedance net­ work. Such network introduces extra noise sources. The feedback network is not modified during the optimization of the amplifier noise behavior. Hence, the noise sources introduced by the feedback network do not vary during the optimization. The feedback network does, however, affect the

noise contribution of the noise sources present in the active circuit, usually increasing their contribution. This effect is accounted for by the introduc­ tion of transfer functions as shown below.

As stated above, the nullor is approximated by an active circuit con­ taining one or more transistor stages, the configuration of which is deter­ mined during the design process. The noise introduced by the transistor stages can be represented by a current and a voltage source placed at the input of the active circuit. Further, for the purpose of calculations per­ formed on the noise properties of the amplifier circuit, the transfer proper­ ties of the active circuit may be approximated by a nullor. The non-energicness of the feedback, network increases the influence of the noise added by the active circuit. This effect can be modeled by appropriate transfer functions expressing the influence of the feedback network, on the amount of noise that is contributed by the active circuit noise sources to the amplifier output noise.

If the active circuit is properly designed, its equivalent input noise sources are determined mainly by its first stage. Although a Common Emitter (CE) or Common Source (CS) stage or their balanced versions should preferably be used in the input stage, no strict limitation on the type of input stage is imposed by the procedure described here, as, if the second and further stages are designed properly, only little extra noise is produced.

The amplifier noise contribution consists of two fractions. The first, that of the feedback, network., is assumed constant. The minimization is performed on the second contribution, that of the active circuit. Its noise contribution can be measured at the amplifier output.

Source f n < —o—

i

Figure 4. Simplified circuit for output noise calculation

In order to calculate the amount of output noise, the basic amplifier configuration is used, extended with the equivalent noise sources for the active circuit.(Fig.4) In the following, we will assume that the first stage contains an unbalanced CE or CS stage. The expressions involved in noise optimization for a balanced input stage can be derived in a way similar to the description given below.

The expression for the noise voltage and current in Fig.4 depends on the kind of transistor selected. In low-noise design, JFET's or BJT's are used in the first amplifier stage. MOSFET's are considered less suitable due to their large excess-noise contribution. For each transistor, the noise voltage and current are determined by the parameters and the bias current of the transistor. The optimal first stage of the active circuit can be found by determining the optimal bias current for a set of candidate devices charac­ terized by their device parameters, after which the best performing device is selected.

As an optimization criterion in this selection procedure, the value of the integral of the possibly weighted noise spectrum of the amplifier output noise voltage can be used. The noise at the amplifier output is mainly determined by the input stage of the active circuit, which contributes a dominant noise voltage source and a dominant noise current source. In order to find the noise contribution of these dominant noise sources, the

transfer of the sources to the amplifier output must be calculated. These transfers can be calculated from the basic amplifier circuit obtained in the previous design step. In these calculations it is assumed that the transfer properties of the active circuit, which still has to be designed in detail, will remain sufficiently close to the ideal transfer properties of a nullor circuit. Practical experience has shown that this simplification does not introduce serious error.

The transfers can be expressed point-wise, as a set of values at certain frequencies, or as Laplace transforms. As the Laplace transform is the most complete means of expressing a transfer, it is preferred as a means of description. The following transfers must be found from the basic amplifier circuit.

— The transfer Hl(p) from in to the output quantity x0. In the following expression, /„(/>) and X0(p) are the Laplace transforms of in and x0.

— The transfer from un to x0. Analogously, Un(p) and X0(p) are the

Laplace transforms of un and x0.

" W - B & T

These transfers can be calculated with a network analysis program such as ANP3, which is capable of finding transfers specified as Laplace transforms. '2' In order to be able to use this program the description of the basic circuit, which is given in a symbolic network, description language, must be converted first to a netlist. We will not go into this conversion here, but will describe in some detail the further procedure steps that play a role in the design of the first stage of an active circuit.

The noise sources introduced by this first stage produce a noise contri­ bution to the output signal. This contribution depends on the frequency, on the device parameters of the transistors used in the first stage, and on the bias current of these transistors. The analytical expressions for the output