Circuits and systems

Summary

8.1 INTRODUCTION

The term feedback is the basic backbone for all amplifier systems. An electronics engineer named Harold Black working with the Western Electric Company back in 1928 had been searching for various means of gain stabilization in amplifiers used in telephone repeaters. It was then that he intuitively conceived and invented the feedback amplifier. The process or technique by which a fraction of the output voltage or current is combined back/fed back to the input, to produce a desired output of a system is called feedback. But the question is – why does an amplifier circuit need feedback for gain stabilization!

As discussed in Chapters 4 and 5, in a BJT, parameters like DC common-emitter current gain β, base-emitter voltage VBE and collector current IC may vary with temperature. In the manufacturer's data sheet, a range of values for these parameters are specified for a given type of transistor group because of material property tolerance. As a result of this, voltage and current gain, quiescent point and input/output impedances usually tend to differ from one circuit to another and also become temperature dependant. By applying the feedback mechanism, transistor circuit characteristics are made independent of the aforesaid parameters of transistors. Although feedback is being formally introduced to the reader in the present chapter, the concept of feedback was utilized in Chapter 5 in connection with biasing of transistor. For example, in the emitter feedback bias and voltage-divider bias circuits, an emitter resistor (RE) was introduced in common-emitter circuits to stabilize the Q-point. In these circuits, when the collector current increases, the drop across the emitter resistor (RE) increases which decreases the base-emitter voltage and that, in turn, further opposes any change in the collector current. This opposition is actually referred to as negative feedback. Thus, the readers encountered the technique of feedback even before they were introduced to it formally.

The feedback technique is generally known by its two types: positive or regenerative feedback, used in designing oscillators, and negative or degenerative feedback, used in designing amplifiers.

Summary

1.1 INTRODUCTION

Electronics, evolved from the word ‘electron’ (a sub-atomic particle carrying negative charge), is the branch of science and engineering dealing with the study, design and use of devices that depend on the conduction of electricity through vacuum, gas or semiconductor, contributed by the transport phenomenon of the electrons. Earlier, electronics or electronics engineering used to be considered as an integral part of electrical engineering. However, due to the tremendous growth of electronics and its unprecedented applications in various fields over the last few decades, it has evolved as a separate branch of engineering. In addition, due to its widespread application in almost all possible branches of engineering and science, acquiring basic understanding of electronics and fundamentals of electronic devices has become a common requirement for students of all engineering disciplines.

Before we discuss the details of the preliminary concepts required to understand the basic ideas of electronics, let us have a look at the chronological growth of modern electronics:

1850: Geissler, a German scientist, demonstrated the flow of electric current through a vacuum glass tube.

1878: Sir William Crookes, a British scientist, showed how current in vacuum tubes appears to consist of particles.

1890: Perrin, a French physicist, demonstrated that current in vacuum tube is due to the movement of negatively charged particles.

1897: Sir J. J. Thomson, a British physicist, measured some of the properties of the “negatively charged particle” (cathode ray) contributing to current in vacuum tube (named as cathode ray tube). He concluded that these particles are much smaller than atoms possessing high specific charge (charge to mass ratio). Thus, he is credited with the discovery of the first sub-atomic particle (later named as electron).

1904: John Ambrose Fleming, a British physicist, invented vacuum tube that allows current only in one direction. This was named as Fleming valve- the primitive version of a diode- and was also known as vacuum tube or vacuum diode.

1907: Lee de Forest, an American scientist, invented a tube which could amplify weak electrical AC signal. This tube, a primitive version of the transistor, was named as vacuum triode.

1909: Robert Millikan, an American physicist, measured the charge of an electron.

Summary

Almost every undergraduate engineering discipline starting from electronics, electrical, computer science, instrumentation engineering, information technology, mechanical engineering, biotechnology etc. requires a solid foundation in basic electronics which comprises a study of fundamental devices like diodes, transistors and their applications in designing amplifiers, switching/logic circuits etc. While for some disciplines, a basic understanding might be sufficient, for other disciplines like electronics, electrical etc., this course acts as an important building block in the curriculum. Moreover, for various advanced courses like analog electronics, digital circuits and VLSI, in-depth understanding of basic electronics is a prerequisite. This book is written keeping both these aspects in mind and as a result it will serve undergraduate students of various engineering disciplines. In addition, it can also cater to the needs of college and university students belonging to disciplines like physics, electronics, and also in electronics courses in polytechnics. A competent electronics engineer, even in the modern era of integrated-circuit based design, needs a thorough and solid understanding of the basic concepts of semiconductors and a firm grasp of fundamental devices like diodes and various kind of transistors. This book attempts a perfect balance between housing all the basic concepts in accordance with the syllabi of leading institutes and universities and a thorough understanding required for future courses. In solid state electronics and analog electronics, which normally appears at a later stage of the undergraduate electronics curriculum, the approach is significantly different: while solid state electronics provides more emphasis on device physics and detailed understanding, analog electronics concentrates more on the applications, where the device is generally treated as a black box. Even though these two advanced courses are mutually dependent on each other, there exists a significant gap between the two approaches and undergraduate students face real difficulties in making a correlation and correspondence between them. This book attempts to minimize this gap between the different approaches to solid state devices and analog circuits. Special care has been taken to explain all the semiconductor devices in this book from both, physical and circuit approaches. To facilitate this, extra stress is given in chapters 2 and 3 while discussing crystal structures and the p-n junctions. As all modern semiconductor devices are based on clusters of p-n junctions, a detailed explanation about the various aspects of p-n junctions will provide readers a strong foundation for future courses.

Summary

2.1 INTRODUCTION TO SOLIDS AND CRYSTALS

As the atoms or molecules in solids are attached to one another with strong attracting forces, the solid maintains a definite volume and shape. A separate subject named solid-state physics has been evolved for the study of the electrical, thermal and electronic properties as well as behaviour of solids. Solid-state physics can be defined as the branch of physics which deals with physical properties of solids, particularly crystals, and the behaviour of electrons in these solids. A subset of solid-state physics is solid-state electronics, which mainly focuses on the electrical and electronic behaviour of solids, especially semiconductors and the movement/transport of electrons in semiconductor materials and different semiconductor devices, basic and advanced, which have evolved over the last century.

Solids may be broadly classified into two categories depending upon the arrangement of the atoms and molecules:

i) Crystalline Solid: It consists of regular or periodic arrangement of atoms or molecules. Most of the solids are crystalline in nature. This is due to the fact that crystalline state is the low energy state and is, therefore, preferred by most solids.

ii) Amorphous/Non-Crystalline Solid: It consists of completely random arrangement of atoms or molecules. Such type of materials are formed when the atoms do not get sufficient time to undergo a periodic arrangement.

Example: Glass, plastic, rubber, etc.

Crystalline solids may be further subdivided into Single Crystal Solid and Polycrystalline Solid. In single crystal solids, the periodicity of the atoms extends throughout the material, as in the case of diamond, quartz, mica, etc. A polycrystalline material is an aggregate of a number of small crystallites with random orientations separated by well-defined boundaries. Most of the metals and ceramics exhibit polycrystalline structure. Silicon (Si), the most widely used semiconductor material, is also a polycrystalline in its natural form.

2.2 CRYSTALLINE SOLID

Before describing the arrangement of atoms in a crystalline solid, it is always convenient to describe the arrangement of the imaginary points in space which have a definite positional/spatial relationship with the atoms of the crystal. This set of imaginary three-dimensional points forms a framework on which the actual crystal structure is based.

Summary

7.1 INTRODUCTION

The field-effect transistor, customarily known as FET, like bipolar junction transistor (BJT), is a three-terminal semiconductor device extensively used in numerous electronic circuits and systems ranging from digital logic circuits to amplifier design. The term ‘field effect’ arises due to the fact that applied external electric field creates a conduction path called channel and controls the output current of the device. Even though FET has various structural and operational similarities with BJT, they have some fundamental differences, which are as follows:

In BJT, the current is contributed by two types of carriers: electrons and holes (hence the term ‘bi’, meaning two, which justifies its name bipolar). In case of FET, based on its structure, only one type of carrier, i.e. either electron or hole, contributes to the current. Hence, it is known as a unipolar device. Due to this, FETs do not suffer from minority carrier storage effects and consequently have higher switching speeds and higher cut-off frequencies.
BJT is a current-control device, where output current IC is solely controlled by the input current IB with a relation IC ≈ βIB. On the other hand, FET is a voltage-controlled device, where the voltage between two terminals VGS controls the output current ID. This is indicated in the schematic block diagram of Figure 7.1. Thus, FET is termed as a voltage-controlled device.

One of the most important features of FET is its very high input impedance, typically much higher than that of BJT. This makes FETs a very good choice for designing linear amplifiers. Another advantageous feature of FETs is their better temperature stability compared to BJT. At high current level, FET offers negative temperature coefficient of current (meaning that current decreases due to increase in temperature). Due to this phenomenon, FETs can prevent thermal runaway. In addition, FETs are much compact in size. All these features make FET a very good candidate for integrated-circuit (IC) chips.

FETs can be broadly classified into two types: a) Junction Field-Effect Transistor (JFET) and b) Metal Oxide Semiconductor Field-Effect Transistor (MOSFET). The latter can be further divided into depletion and enhancement types. JFET and both types of MOSFETs, based on the structures, can be further divided into n-channel and p-channel types. Figure 7.2 shows various types of MOSFET.

Summary

INTRODUCTION TO SOLIDS AND CRYSTALS

Solids may be broadly classified into two categories depending upon the arrangement of the atoms and molecules:

Summary

6.1 INTRODUCTION

In Chapter 4, we discussed the basic construction, characteristics, various modes and principle of operation of bipolar junction transistor (BJT) in detail. Subsequently, in Chapter 5, we dealt with biasing techniques of the transistor in an elaborate manner. In addition, we understood the fundamental concept of BJT acting as an amplifier in a qualitative manner. While biasing a transistor our main goal is to fix a proper operating point, also known as Q point, based on the specific applications. This is achieved by proper choice of the bias resistor and DC voltages. Once this Q-point is finalized, we apply the AC signal in the input side of the biased transistor circuit. Thus, complete analysis of an amplifier consists of DC analysis followed by an AC analysis. In this chapter, we will focus on the AC analysis of the BJT circuits in an elaborate manner with special emphasis on design of the BJT-based linear amplifiers. One important ingredient in the AC analysis and design of linear amplifiers is to replace the BJT with proper equivalent circuits. Such replacement of BJTs with equivalent circuits, known as ‘modeling’ of the BJT, is applicable under small signal approximations. This assumes the amplitude of the applied AC signal is small enough to consider that BJT is essentially operated in active region and its characteristics can be approximated by linear relations. Such linear relations between input and output signals of the BJT allow superposition theorem applicable in BJT circuits and we can obtain the total response of the BJT circuit by separately determining the response due to i) DC sources alone (called biasing), and ii) AC sources. Figure 6.1 shows a schematic diagram of an electronic circuit driven by both DC and AC input. While the purpose of the DC input is to ensure that the device operates in the desired region of operation, i.e. bias the device properly, AC input provides the required functionality like amplification, switching, etc. By applying the small-signal models of the device, thereby linearizing their performance, we apply the superposition theorem to obtain the overall response of the circuit by separately obtaining the individual responses due to DC input and AC input, as shown in Figure 6.1.

Summary

INTRODUCTION

In Chapter 6, we derived various small-signal models of BJT, followed by detailed analysis of the BJT amplifiers for CE, CB and CC configurations. In designing such small-signal amplifier the main focus is on amplification linearity and magnitude of gain. Since signal voltage and current in the small-signal amplifier is restricted to small amplitude for maintaining linearity, their power handing capability or the power efficiency with which it delivers AC power to the load at the expense of DC power are of secondary concern. A voltage (current) amplifier provides voltage (current) amplification primarily to increase the applied input voltage (current). Thus, in general, these small-signal amplifiers are not capable of delivering large amount of power to a passive load. But most of the practical electronic amplifiers (starting from audio amplifier to switching power supply) require a final output stage capable of delivering large power to the load. Such amplifier/amplifying stage at the output stage of a practical amplifier circuit is known as power amplifier. It can be designed using BJTs, MOSFETs and various special semiconductor devices like thyristors. However, we will consider only BJTs while discussing the design of such amplifiers.

PERFORMANCE CHARACTERISTICS OF POWER AMPLIFIERS

The quality of power amplifiers is characterized by the following parameters:

Summary

9.1 INTRODUCTION

In the preceding chapter, we intensively discussed the concept of negative feedback and its effects on amplifiers in detail. In the present chapter, the effect of feedback will be discussed in the context of working and analysis of oscillator circuits to generate sinusoidal and non-sinusoidal pulses and waveforms. The basic concept of oscillator differs from that of an amplifier. An amplifier amplifies a given AC input signal by using the DC power supply VCC and resistive networks to provide proper bias and stability with the aid of negative/degenerative feedback so as to stabilize gain and enhance bandwidth of operation. As completely opposed to this, an oscillator circuit needs no input AC signal. The power supply DC input VCC helps in picking up noise signals from its wide frequency spectrum, which due to regenerative/positive feedback networks and amplifier, gets sustained in the oscillatory circuit. Hence DC input gets converted into AC output. Thus, an oscillator can also be referred to as AC-DC converter. The working of an oscillator is exactly opposite to rectifier; hence it can be called an ‘inverter’. But it should be well understood that an oscillator does not create energy, instead it converts unidirectional current drawn from DC source into alternating current of desired frequency. Hence, the oscillator can be broadly defined as an amplifier with positive feedback. The difference between amplifier and oscillator is explained in the block diagram of Figure 9.1(a).

9.2 CLASSIFICATION OF OSCILLATORS

Oscillators can be broadly classified using following two aspects,

a) Classification based on design principle
b) Classification based on frequency of oscillation

a) Figure 9.2 shows the detailed family tree of various types of oscillators based on the design principle.

From Figure 9.2, based on the design principle, commonly used oscillators can be broadly classified as harmonic and relaxation oscillators. Harmonic oscillators generate sinusoidal waveforms, whereas relaxation oscillators generate pulse/rectangular/sawtooth waveforms. The basic tuning circuit for harmonic oscillators can be made of combination of L-C networks, which are suitable for generating RF (radio frequency) oscillations from 720 KHz up to hundreds of MHz, whereas R-C networks are suitable for generating AF (Audio Frequency) oscillations in the range of 20 Hz–20 KHz. The detailed description of each of the oscillator is performed in subsection 9.5 and 9.6.

Summary

11.1 INTRODUCTION TO THYRISTOR

Thyristors are able to switch large levels of power and are used in a wide variety of different applications. Thyristors find use in low-power electronics, where they are used in many circuits ranging from light dimmers to power supply over voltage protection. The idea of thyristor was first described by William Shockley in 1950. It was referred to as a bipolar transistor with a p-n hook collector. The mechanism for the operation was analysed further in 1952 by Jewell James Ebers and in 1956 John L. Moll investigated the switching mechanism of the thyristor.

The first silicon-controlled rectifiers became available in the early 1960s when it started to gain a significant level of popularity for power switching. It is a multilayered semiconductor device which requires a gate signal to turn it ‘ON’. Once it is turned ‘ON’, it behaves like a rectifying diode. Thus, the name silicon-controlled rectifier is justified by its working principle. In fact, the circuit symbol for the thyristor suggests that this device acts like a controlled rectifying diode.

Four layers are formed by alternating n-type and p-type semiconductor materials. Consequently, there are three p-n junctions formed in the device. It is a bistable device. The three terminals of this device are anode (A), cathode (K) and gate (G). The gate (G) terminal is the control terminal of the device. The circuit symbol is shown in the Figure 11.1.The current flowing through the device is controlled by electrical signal applied to the gate (G) terminal. The anode (A) and cathode (K) are the power terminals of the device which can handle large applied voltage and conduct the major current through thyristor. For example, when the device is connected in series with load circuit, the load current will flow through the device from anode (A) to cathode (K) but this load current will be controlled by the gate (G) signal applied to the device externally.

11.2 CONSTRUCTION: REALIZATION USING TRANSISTORS

Unlike the normal p-n junction diode, which is a two-layer semiconductor device, or the transistor, a three layer (p-n-p or n-p-n) device, the Thyristor is a four-layer (p-n-p-n) semiconductor device that contains three p-n junctions in series, as shown in Figure 11.2.

Summary

This book provides a rigorous yet intuitive explanation of jitter and phase noise as they appear in electrical circuits and systems. The book is intended for graduate students and practicing engineers who wish to deepen their understanding of jitter and phase noise, and their properties, and wish to learn methods of simulating, monitoring, and mitigating jitter. It assumes basic knowledge of probability, random variables, and random processes, as taught typically at the third- or fourth-year undergraduate level, or at the graduate level, in electrical and computer engineering.

The book is organized as follows: Chapter 1 provides a qualitative overview of the book and its contents. Chapter 2 covers the basics of jitter, including formal definitions of various types of jitter and the key statistical concepts, starting from jitter mean and the standard deviation up to random and deterministic jitter. Phase noise will be first introduced in Chapter 3, and its relation to jitter and to the voltage spectrum of the clock signal will be extensively investigated. In particular, how to derive from phase noise the values of the several jitter types introduced previously will be explained. Chapter 4 is dedicated to the effects of jitter and phase noise in basic circuits and in basic building blocks such as oscillators, frequency dividers, and multipliers. Chapters 5 to 8 discuss the effects of jitter and phase noise in various circuit applications. Chapter 5 is dedicated to the effects of jitter on digital circuits, Chapter 6 to data converters, Chapter 7 to wireline, and Chapter 8 to wireless systems. More advanced topics on jitter are covered in Chapter 9, followed by numerical methods for jitter in Chapter 10. This chapter also explains how to generate jitter and phase noise, with various characteristics, for simulation purposes. The corresponding Matlab code for producing jitter is included in Appendix B.

As mentioned earlier, this book assumes the reader has a basic knowledge of random variables and random processes. However, to refresh the reader's memory of the definitions of some key terms, Appendix A simply lists these key terms along with their basic definitions.

Guidance for the Reader

The book does not require the reader to adhere strictly to the order in which the chapters appear, nor to read all of them.

Summary

The most common approach to the investigation of the behavior of electronic systems in the presence of jitter is to use linear modeling in the frequency domain and phase noise profiles. However, especially in the presence of complex or non-linear systems, it is often beneficial to perform transient simulations and evaluate the results in the time domain. To use this approach, it is necessary to provide numerical methods to, first, generate clock signals in the time domain that have given phase noise profiles and, second, analyze the results of transient simulations and possibly convert them into phase noise plots. The goal of this chapter is to provide some of these techniques.

Most of the chapter is dedicated to algorithms and numerical recipes to generate jitter samples with several different phase noise profiles, and to compute jitter and phase noise given a vector of time instants, typically obtained from transient simulations. Following that, basic algorithms to perform tail fitting are presented. All algorithms are implemented and demonstrated using Matlab and are coded such that they can be easily ported to any other common programming language. The code is included in Appendix B.

Numeric Generation of Jitter with Given Phase Noise Profiles

The problem addressed in this section is how to generate a sequence of numbers tk representing the instants of the edge transitions of a clock having nominal frequency f0 and a desired phase noise profile L(f).

As a starting point, the sequence tk can be decomposed into the sum tk = tid,k + ak of a vector describing an ideal clock, tid,k = k/f0 with k ≥ 0, and a vector ak describing the jitter process. Note that the ak corresponds to the absolute jitter, according to the definition given in Section 2.1.1. The problem translates then into the generation of the sequence ak showing a given phase noise profile L(f).

Before proceeding it is important to recall that the PSD of the sequence ak is independent from its probability density function (PDF). To make it clearer, imagine one realization of the process ak being plotted on a graph, where the x-axis is the index k and the y-axis is the value (amplitude) of ak.

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Contents

Dedication

Chapter 8 - Feedback Amplifiers

Summary

Chapter 1 - Introduction to Electronics: Basic Ideas

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Preface

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Chapter 2 - Introduction to Semiconductor

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5 - Transistor Biasing and Stabilization

Chapter 7 - Field-Effect Transistors

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Index

13 - Operational Amplifier

2 - Introduction to Semiconductor

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Chapter 6 - Modelling of BJT and Design of Amplifiers

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10 - Power Amplifiers

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Frontmatter

Chapter 9 - Oscillators and Multivibrators

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Preface

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Chapter 11 - Silicon Controlled Rectifiers

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14 - Analog Communication

Preface

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10 - Numerical Methods

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