This book provides an introduction to electrical circuits that will serve as a foundation for courses in electronics, communications and power systems at first degree level. The first three chapters will be found particularly suitable as prerequisite reading for the companion volume in this series; Analogue and digital electronics for engineers by H. Ahmed and P.J. Spreadbury. Engineering and science students not intending to specialise in electrical subjects will find in this book most of the circuit theory required for a first degree.

The level of presentation presupposes that students will have encountered the basic ideas of electromagnetism and electrical circuits, including the laws of Faraday, Ohm and Kirchhoff. These ideas are reviewed in chapter 1. Mathematical skills are assumed to extend to the solution of firstorder differential equations, and to the elements of complex algebra. Courses in mathematics taken concurrently with those in electrical subjects during the earlier part of a degree course would be expected to fill in progressively the additional mathematical background required; the subject matter has been arranged with this in mind. Sections which may give rise to mathematical difficulties on a first reading, or which may be too specialised for the general student's requirements, are indicated by an obelus (†).

A traditional approach to the development of electrical circuit theory is adopted: the concept of linearity, and the circuit theorems and analytical techniques which stem from this concept, are all presented in chapter 2 within the context of d.c. circuits.

Introduction

For the sinusoidal steady state, one can calculate the total power supplied to a circuit consisting of linear elements by adding directly the power absorbed by each individual resistive element in the circuit. However, it is often more convenient to express power in terms of the voltage across and the current supplied to the input terminals of a circuit whose detailed configuration is unknown or is of no interest.

In all electric power distribution networks voltage and frequency are maintained substantially constant. A given load will draw a current whose amplitude and phase (relative to the power line voltage) depend upon the load impedance. On the other hand in electronic and telecommunication networks, signal power rather than voltage is fixed and we are concerned more with arranging source and load conditions to achieve maximum power transfer from one part of a circuit to another.

For the above reasons the treatment of power in electrical circuits depends to a marked extent on the type of circuit under consideration. In this chapter we develop general methods for determining the power and total energy supplied to, or dissipated within, a circuit. We also consider one of the most important components involved in the utilization and transmission of power; namely, the transformer.

Average power

Consider a network or load as shown in fig. 4.1, supplied at voltage V(r.m.s. magnitude V) and drawing current I (r.m.s. magnitude I). If the network contains reactive elements, voltage and current will differ in phase by some angle φ.

Objectives

At the end of the study of this chapter a student should be:

1. familiar with the modelling of different types of active devices

2. able to develop a suitable model of a device for a particular computer analysis

3. familiar with nonlinear d.c. analysis, small-signal a.c. analysis and large-signal transient analysis of simple electronic circuits

4. familiar with the Newton–Raphson algorithms and be able to determine the d.c. operating points of circuits for further analysis, and

5. familiar with the applications of some computer programs.

In recent years computational methods have been very popular for analysing and designing electronic circuits. It is now possible to design integrated circuits having thousands of transistors on a single chip. Such designs cannot be carried out experimentally at the bench. As very large scale integrated circuits make the fabrication of faster and cheaper computers possible, computer aided design is being used more and more to build such circuits. In this chapter, we will discuss various transistor models and parameters needed for computer analysis, different types of analysis and computer programs.

Computer aided design models

Renewed interest in transistor modelling took place in the sixties and seventies with the advent of computer aided design. Various models which had been developed during this period fell into two main categories, the first being single lump models in which transistor terminal currents are described in terms of quantities determined from terminal measurements; the second category of models is completely described by five basic transistor equations (two continuity equations, two current density equations and Poisson's equation) derived from the donor and acceptor concentration pattern.

Objectives

At the end of the study of this chapter a student should be:

1. familiar with the operation of the differential amplifier, its voltage gain, common-mode gain and common-mode rejection ratio

2. familiar with constant current sources and current mirror circuits

3. capable of explaining the principle of Darlington connections

4. able to design level shifting circuits

5. familiar with multistage amplifiers and able to calculate their input and output impedances and overall current and voltage gains

6. able to design class A, class B and tuned amplifiers

7. familiar with different types of heat sinks and able to choose the right heat sink for a particular circuit

Linear integrated circuits

Complete multistage amplifiers and other linear devices can be constructed on a single chip of silicon occupying a very small volume by using modern techniques for the fabrication of integrated circuits. In the case of monolithic integrated circuits, all components may be manufactured on the chip by a diffusion process. A diffusion isolating technique is used to separate the various components from each other electrically. The design techniques used for the construction of these integrated circuits are basically the same as those used to build circuits employing discrete components, although, in many cases some modification in techniques is needed.

The operational amplifier is the most common type of integrated circuit (small scale integration) which is widely used with different forms of external circuitry to build summers, subtractors, integrators, filters, etc.

Objectives

At the end of the study of this chapter the student should be:

1. familiar with the main imperfections in operational amplifiers, able to describe their effects on the output and stability of various circuits, and compensate for the errors due to them.

2. able to design several important linear and nonlinear circuits using operational amplifiers: phase shifting circuits, instrumentation amplifiers, comparators, precision rectifiers and logarithmic amplifiers.

3. familiar with different methods of design of active filters and able to choose the right design for a particular need.

4. able to describe the operating principles of multivibrators and triangular wave generators, and design these circuits given the specifications.

5. able to solve differential equations using summers, integrators and potentiometers, and apply amplitude and time scaling if necessary.

6. familiar with the principles of inverse function generators and able to design dividing, square rooting and RMS circuits using multipliers and operational amplifiers.

The name operational amplifier is derived from the fact that the amplifier was originally used to perform electronically various mathematical operations such as differentiation, integration, addition and subtraction. However, due to its versatility its use has been extended to other types of electronic circuits mainly in the fields of instrumentation and control engineering. The availability of inexpensive high performance operational amplifiers in the form of integrated circuits has obviously extended their use especially in analogue electronic circuits and systems.

Objectives

At the end of the study of this chapter a student should be:

1. familiar with three basic functional blocks of a phase-locked loop

2. familiar with the principle of operation of a phase-locked loop as a whole

3. able to determine important PLL parameters such as lock range and acquisition range

4. familiar with typical applications, both in electro-mechanical and telecommunication systems.

The phase-locked loop (PLL) is a very useful and versatile building block in the frequency domain. It is available from manufacturers as a single integrated circuit. It helps to synchronise the output signal of an oscillator with a reference signal in both frequency and phase. While synchronised in frequency, the phase difference between the output signal and the input signal is zero, or very small. It works in much the same way as a general feedback loop which acts in most control systems, e.g., electronic, mechanical, as shown in Fig. 5.1. Here the input is a function of the desired output. If the output is different from the desired value, the mixer produces an error signal which is then amplified and corrects the output. Although its concept has been known since 1932, its application was restricted until the 1960s, when it first became available in an integrated circuit form.

Components of phase-locked loops

The PLL contains a phase detector, a low-pass filter and a voltage-controlled oscillator in an arrangement as shown in Fig. 5.2.

Objectives

At the end of the study of this chapter a student should:

1. be able to design different types of digital-to-analogue (D-to-A) converters

2. be familiar with various kinds of analogue-to-digital (A-to-D) converters; their advantages and disadvantages and be able to construct them

3. be familiar with the errors in the converters

4. be conversant with the design of discrete multiplexers and demultiplexers and be familiar with their limitations and errors

5. be familiar with the principles of sample-and-hold circuit and be able to design them

6. be able to develop a suitable data acquisition or distribution system for a particular need and find the accuracy of such a system.

In order to process analogue signals which are continuous and of varying magnitude over a period of time, with the aid of computers, conversion of analogue currents or voltages into digital codes is essential. Again, conversely, in order to control machines with the help of computers, digital signals have to be converted into analogue currents and voltages. A typical system is shown in Fig. 7.1. Here the analogue sensors measure physical quantities such as temperatures, pressures, etc., and the analogue controls switch on (or off) heaters, pumps and so on.

Sometimes it is necessary to acquire or distribute more than one signal simultaneously. This can be achieved by using the time-sharing techniques. The time required for acquiring data from many sources, or distributing data to many controls can be reduced dramatically if a single channel is time-shared for transferring data.