The analog to digital converter (ADC)

The sub-system which follows the sample and hold circuit, and its sampling pulse generator, in a digitising oscilloscope will be an ADC. In this particular case, the function of the ADC is to convert the output from the sample and hold circuit, which is an analog signal carried by a single channel, into a digital representation of this analog signal, carried in parallel by, typically, eight lines. An eight bit representation would be only just adequate for a digitising oscilloscope because this would give 256 discrete levels, meaning that a vertical display, 8 cm high, would have a vertical resolution of about 0.3 mm. This is about the same as a typical CRO spot diameter. More bits would be needed to handle the display offset, the sign of the signal, and the sensitivity range, but only the circuit problems of the ADC are considered in this chapter.

ADCs are not only found in digitising oscilloscopes. Any instrumentation problem that calls for an interface between a transducer or a sensor, nearly all of which give out an analog signal, and a digital computer, will call for an ADC. There is also another field of application, as Gordon [1] has pointed out in an important review. This is the field of communications where digital techniques are taking over more and more, in telephony and in television.

Introduction

An electronic instrument needs to be connected to whatever circuit or system is under test. Very wide bandwidth instruments, those used for signals above 100 MHz, usually have 50 Ω co-axial inputs. Instruments which accept signals of even higher frequency, in the microwave and optical range, will have waveguide or optical fibre inputs. The more conventional laboratory test equipment is usually supplied with some kind of probe input circuit which may be connected to the circuit under test.

The probes and input circuits used with oscilloscopes provide good examples of the techniques employed. These same probes and input circuits may, of course, be used in a variety of instruments: vector voltmeters, network analysers, spectrum analysers, and so on. Very high impedance probes are used for voltage measurement, while very low impedance sensor probes must be inserted for current measurement. These voltage and current probes may be passive or active, and both kinds will be considered in this chapter.

Voltage and current measurements are not the only ones that are called for in electronics. Measurements of incident, transmitted and reflected power may also be required. This is the approach often used for high frequency, wide-band circuits which work as part of a transmission line system; for example, a repeater amplifier in a cable television system. The input circuits needed for these power measurements are particularly interesting in that they may exhibit directional properties.

This book has been written for people who like to build electronic circuits and then experiment and make measurements on them. Such an experimental approach to understanding electronics does not mean that the work need be restricted to well-known or simple circuits. Some very recent circuit ideas are put forward as experimental exercises here, and the book should prove interesting both to students and to people, of all ages, who are already working in industry and research, and who would like to have experience of some recent developments in the field of electronic instrumentation.

In writing the book I have been greatly helped by conversation and correspondence with many people. In particular, Dr Asad Abidi, now at UCLA, Dr David Haigh, at UCL, London, and Dr Bhikhu Unvala, at ICSTM, London. Dr Unvala has also been most helpful in providing some of the experimental facilities. Finally, sincere thanks to Mr Ali Mehmed, whose careful reading of the typescript resulted in a number of changes for the better, along with many corrections.

Introduction

As Wilmshurst [1] has written, noise in electronics has, today, come to mean ‘almost any kind of unwanted signal in an electronic system’. This is in contrast to the classical picture of noise as being a problem area which is only concerned with the fact that electronic circuits operate at a finite temperature and also have to operate with electric currents that are really made up of a flow of discrete charged particles. Further evidence for the wider view which is now taken of noise problems in electronics can be taken from the use of the term ‘electromagnetic compatibility (EMC) [2]’.

For the above reason, this chapter is really in two parts. To begin with, circuit shapes and circuit ideas that attempt to minimise the effects of the intrinsic thermal and shot noise of electronic devices will be considered. This calls for a brief summary of some well-known theory which will be given first. The topic then divides fairly naturally into low and high frequency amplifiers, and some interesting experimental circuits can be proposed for both fields. After this look at these classical kinds of noise problems, the chapter concludes by considering some of the circuit ideas which have been proposed to eliminate very special noise problems in various signal processing systems.

Intrinsic thermal noise sources

An excellent reference for the fundamentals of noise in electronic circuit design is chapter 11 of the book by Gray and Meyer [3].

Introduction

Waveform generators make up a group of instruments which are essential to the electronic circuit designer. At the simplest level, the sine wave, square wave and triangle waveform generator, covering the frequency range from a few hertz to several megahertz, is used to measure the gain and frequency response of amplifier circuits, and as a basic timing or input signal to the kind of experimental circuits that have been discussed so far in this book. Pulse generators are also of great value for circuit testing, providing both positive and negative going pulses with very fast rise and fall times, together with the facility of a separate trigger pulse from the instrument which precedes the main output pulse by some time which may be varied. A recent book by Chiang [1] covers many of these classical topics in detail and also deals with quite advanced instrumentation and signal processing techniques that rely heavily upon waveform generation.

In recent years, laboratory instruments using digital techniques for very complex waveform generation have been introduced. In these instruments, a microprocessor is used to generate the required waveform as a continuously changing digital output of eight, or more, bits, and this digital output is then converted into the required analog output by a digital to analog converter (DAC).

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.