Electric charge

Before embarking on a study of electrical networks, it is important to understand thoroughly such basic electrical concepts as charge, field, potential, electromotive force, current and resistance. The first few sections of this book are concerned with developing these concepts in a logical sequence.

Phenomena due to static electricity have been observed since very early times. According to Aristotle, Thales of Miletus (624–547 B.C.) was acquainted with the force of attraction between rubbed pieces of amber and light objects. However, it was William Gilbert (1540–1603) who introduced the word electricity from the Greek word ηλεκτρον (electron) signifying amber, when investigating this same phenomenon. Many other materials have been found to exhibit similar properties. For example, if a piece of ebonite is rubbed with fur, then on separation they attract each other. However, an ebonite rod rubbed with fur repels another ebonite rod similarly treated. Also, a glass rod rubbed with silk repels another glass rod rubbed with silk. Yet an ebonite rod that has been rubbed with fur attracts a glass rod that has been rubbed with silk.

All of these observations can be explained by stating that two kinds of electricity exist, that on glass rubbed with silk being called positive electricity and that on ebonite rubbed with fur negative electricity. In addition, like kinds of electricity repel, unlike kinds attract. Actually, all substances taken in pairs become oppositely electrified when rubbed together.

Two-terminal nonlinear networks

The signal responses of two and four-terminal passive linear networks have been considered extensively in the previous six chapters. Attention is now turned to deducing the signal responses of both active and passive nonlinear networks, a topic of great importance in view of the key roles that nonlinear devices play in electronics. The topic has already been briefly broached, of course, in section 5.9, where certain consequences of nonlinearity were established by examining a few illustrative passive circuits. At this juncture the objective is to treat the analysis of nonlinear circuits in a much wider context and in a much more general manner.

Graphical analysis of the response of any nonlinear network can be achieved through its terminal static characteristic or characteristics irrespective of the magnitudes of the signals involved. This approach is, however, clearly most appropriate under large-signal conditions. At the opposite extreme, whenever the signals in a nonlinear network are small enough, the network is effectively linear with respect to the signals so that the methods developed for linear network analysis may be applied with advantage. Although maintenance of such small-signal conditions may appear somewhat restrictive, their occurrence is quite widespread. Electronic systems are very often concerned with processing weak signals and sometimes the nonlinearity involved is sufficiently slight for quite large signals to qualify as small enough for the purpose of linear analysis.

Explanation of the methods of large and small-signal analysis of nonlinear networks is best undertaken initially in terms of two-terminal networks.

Introduction

An ideal filter would perfectly transmit signals at all desired frequencies and completely reject them at all other frequencies. In the particular case of an ideal low-pass filter, for example, the modulus of the transfer function, |J|, would behave as shown in figure 12.1(a). Up to a certain critical pulsatance ωc, |J| would be unity but above this pulsatance, |J| would be zero. Any practical filter can only approximate to such an ideal, of course.

In section 8.2 it was pointed out how |J|2 for a simple single-section L–R or C–R filter comprising just one reactive component only reaches a maximum rate of fall-off outside the pass band of 20 dB per decade of frequency compared with an infinite rate of fall-off for an ideal filter. Remember that the significance of |J|2 is that it indicates the power in the load for a fixed amplitude of input signal. Increasing the number of reactive components in the filter stage to two, as in the simple low-pass L–C filter of figure 8.7(a), causes |J|2 to reach a maximum rate of fall-off outside the pass band of 40 dB per decade of frequency. With n reactive components in the filter stage, the maximum rate of fall-off of |J|2 outside the pass band becomes 20n dB per decade of frequency and the filter is accordingly said to be of nth order.

Where to begin constitutes a difficulty in expounding most subjects. For completeness' sake, the present treatment of the analysis of electrical networks begins by establishing from first principles those basic electrical concepts such as current, potential and electromotive force in terms of which analysis is executed. In covering these basic concepts in the first two chapters it is, of course, recognised that some students will already be thoroughly conversant with them, some will merely need to ‘brush up’ on them and others will prefer to acquire them through studying more-detailed physical texts.

Network analysis begins in earnest in chapter 3 where network laws and theorems, such as Kirchhoff's laws and Thévenin's theorem, are introduced in the easy context of direct-current networks. Following descriptions of the physical nature of capacitance and inductance, traditional methods of deducing transient and sinusoidal steady-state responses are developed. These encompass the solution of linear differential equations and the application of phasor and complex algebraic methods. Consideration of the powerful Fourier and Laplace transform techniques is delayed until towards the end of the book, by which stage it is hoped that any reader will have acquired considerable mathematical and physical insight regarding the signal responses of circuits. Overall, the intention is that the book will take a student from ‘scratch’ to a level of competence in network analysis that is broadly commensurate with a graduate in Electrical or Electronic Engineering, or one in Physics if specialising somewhat in electrical aspects.

Alternating-current meters

Any system that measures direct current or potential difference can be adapted to measure the corresponding alternating quantity by inserting a rectifying circuit in front of it. The term rectification refers to rendering the alternating current or potential difference unidirectional through removing or reversing it whenever it is one of its two possible polarities. It should be clear that, with sufficient damping, a direct measuring system will respond to the mean level of a rectified alternating input. Removal of alternating half-cycles is termed half-wave rectification. Reversal of alternate halfcycles is described as full-wave rectification and is illustrated in figure 7.1(a) for a sinewave. The neatest and most popular way of implementing fullwave rectification is by means of four diodes arranged in a Wheatstone bridge formation as shown in figure 7.1(b). Understandably, this form of circuit is called a bridge rectifier. As explained in section 2.3, a diode is a device that presents a very low resistance to current flow when appreciable potential difference of one sign, known as forward, is applied while it presents a very high resistance to current flow when appreciable potential difference of the opposite sign, known as reverse, is applied. In the case of modern silicon P–N junction diodes, appreciable here means >0.6 V. The direction of the arrow head in the circuit symbol for the diode indicates the direction of easy current flow.

Introduction

Feedback occurs where some part of the output of a system also appears back at its input and so modifies the input signal. It occurs in every system. If the feedback is undesired, then the input and output circuits of a system must be well separated and screened. Remember that if the circuit is meant to handle signal frequencies of a few megahertz, which are in the broadcast band, these will be readily radiated from the output circuit wiring and could easily be picked up by the input wiring. Also, if the input and output stages share a common power supply, then care must be taken to ‘decouple’ this as far as signal frequencies are concerned. Otherwise feedback could occur.

This chapter describes intentional feedback, which, when it is properly applied, can improve almost every performance feature of an amplifier. It can widen its frequency response, reduce the effects of component ageing, microphony and hum pickup, and stabilise the overall gain closely to some figure required by a designer. These are a few of its benefits which are more fully explained in the following sections. The subject is important because virtually every good quality or precision amplifier made today is likely to use feedback.

There is one troublesome effect of feedback on amplifier performance; it can create a tendency towards instability if the system is poorly designed. However, feedback which is specifically designed to make oscillators or switches is useful in its own right and it is described in chapter 6.

Introduction

Although a semiconductor amplifier using a field-effect phenomenon was postulated by Shockley in 1952, it was not successfully made until 1963. A bipolar transistor was devised and made by Brattain and Bardeen in 1948: it has developed from almost individually made devices which were sealed in glass envelopes like little valves to the mass produced, robust, cheap devices that we know today. Many of the present integrated circuits, described in chapter 4, use bipolar transistors as their active elements whether they be switches or amplifiers. Some integrated circuit designs using the field-effect transistor are also available but their higher cost must be offset by definite requirements for low noise or very high input resistance. A more detailed comparison of bipolar with field effect transistors is made in §3.16.

The bipolar transistor is used in the power amplifiers of our domestic sound equipment, in the largest computers, and in the most complex integrated circuits. This chapter describes first the principle of operation of the bipolar transistor and its typical characteristics. Then §§3.6 on will describe its use in simple amplifier circuits and discuss problems such as its biasing, stability of operating point, likely gain and frequency response. Lastly some more advanced circuits are considered and a numerical example is worked through.

Principle of operation

Consider the n–p–n sandwich of semiconductor shown in fig. 3.1 (a). This contains two back-to-back p–n junctions; see §§2.1 to 2.4 if you are not familiar with p- and n-type materials, junctions, leakage currents, etc.