Microwave Circuit Theory and Foundations of Microwave Metrology
This book provides a thorough understanding of the microwave circuit model and its limitations.
Inspec keywords: noise; parameter estimation; microwave circuits; microwave measurement; network analysers
Other keywords: microwave circuit theory; measurement methods; six-port network analyser; power equation method; parameter identification; noise; microwave metrology foundations; adapter evaluation
Subjects: Microwave circuits and devices; Microwave measurement techniques; Network and spectrum analysers
- Book DOI: 10.1049/PBEL009E
- Chapter DOI: 10.1049/PBEL009E
- ISBN: 9780863412875
- e-ISBN: 9781849193672
- Page count: 256
- Format: PDF
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Front Matter
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1 The world of microwaves
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It is the major objective of this book to develop the subject of microwave metrology in a way which reflects the basic principles in as simple a manner as possible without sacrificing mathematical or analytical rigour.
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2 Foundations of microwave circuit theory
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As noted in Chapter 1, the low-frequency or 'conventional' circuit theory is ordinarily the best model when the wavelength is large in relation to the dimensions of the system components. With increasing frequency and decreasing wavelength, however, the ability of the circuit model to explain the observed behaviour is no longer adequate for many practical problems. In principle at least, and assuming that the phenomena of interest fall within the scope of electromagnetic theory, these limitations can be overcome by recourse to a different model, namely the Maxwell or field equations. Unfortunately, however, this model is also an extremely complicated one. Here the low frequency concepts of 'voltage' and 'current' are, to a large extent, replaced by the electric and magnetic fields associated therewith and these are then described throughout all space! Although there are applications where this detail is useful, if not essential, there are many others where it is not and the problem is how to modify the model so it represents only the details of interest. The conventional low frequency circuit theory is one such simplification. Moreover, it can be shown that this circuit theory is a consequence of Maxwell's equations under the given conditions.
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3 Elementary boundary conditions
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This chapter provides background of elementary boundary condition on microwave circuit theory and foundation of microwave metrology.
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4 Multi-port boundary conditions
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The chapter is about the properties of the media which is included in the multi-port structure, it should be noted that these are well satisfied for a large range of materials. Thus reciprocity ordinarily holds. On the other hand, these criteria are not satisfied by magnetised ferrites, for example, and an important family of nonreciprocal microwave devices exist which exploit these phenomena. These include circulators and isolators.
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5 Elementary two-port applications
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The theory developed in the preceding chapters will now be illustrated in some elementary two-port applications which include, adjust load or generator impedance; isolate generator from changes in load impedance; provide predetermined changes in power level; and provide transition between two different transmission types, e.g. waveguide to coaxial line.
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6 Amplitude stabilisation and multi-channel isolation
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The generator or source model which is implicit in Chapter 3 eqn. 3.10 may in reality be a poor representation of a given source of microwave energy. On the other hand, with appropriate techniques, it is possible, in principle at least, to achieve any desired degree of conformity to the postulated model. In general there are two problems: frequency instability and amplitude instability. In its simplest form, frequency instability may be corrected by sampling the signal of interest, comparing its frequency against some reference and the introduction of appropriate feedback as required to achieve the desired result. This chapter will attempt to develop an understanding of amplitude stabilisation and consider some related topics.
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7 The measurement problem at microwave frequencies
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It has been the author's objective in the preceding chapters to provide an introduction to the basic elements of microwave circuit theory. This model, in turn, has served to identify certain parameters, e.g. power, attenuation, efficiency, reflection coefficient, scattering parameters etc., whose determination is the objective of microwave metrology. Although further details will be added from time to time, it is believed that the foregoing chapters have provided an adequate motivation for the material to follow. This chapter will include a brief summary of some of the more important ideas and attempt to set the stage.
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8 The fundamental equationof microwave metrology
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In recognition of its all pervading nature and widespread application, equation 7.3 in Chapter 7, which may be wriiten as b1 = A1a2 + B1b2, is given the title 'The fundamental equation of microwave metrology'. It is the primary objective of this chapter to provide its derivation under a fairly general set of initial conditions. This task, in turn, will become a vehicle for developing certain analytical techniques which find repeated application in microwave metrology. In the process, the equation will actually be obtained via several different methods, each of which provides a different perspective.
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9 The linear fractional transform
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The chapter discusses properties of the linear fractional transform.
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10 The slotted line technique of impedance measurement
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Even though it has been largely replaced by other methods, no text on microwave metrology would be complete without at least a brief treatment of the 'slotted line'. The basic form of the measuring instrument includes a section of the appropriate transmission line. In any case, the perturbation due to the slot can be minimised by keeping it narrow and parallel to the current paths. The other source of perturbation is due to the probe itself. In general this is minimised by the use of a sensitive detection system and by keeping the depth of penetration, or coupling, to a minimum. From the viewpoint of careful metrology, its sources of error include impedance discontinuity introduced by the slot, inability to maintain uniform probe coupling to the fields due to imperfections in the (nonideal) transport mechanism, and violation of the 'uniformity requirement', and distortion of field patterns due to probe 'loading'. Unfortunately, however, the success of this scheme is contingent on a known value for the 'shunt admittance', or probe coupling, and this is not easily determined.
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11 Attenuation measurement
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From the historical perspective, no other aspect of microwave metrology has been characterised by a greater proliferation of techniques than attenuation. As was the case with the slotted line, this text would certainly be incomplete without a chapter on this subject. On the other hand, a comprehensive treatment calls for a book rather than a chapter. To a substantial degree, moreover, this task has been taken over by the automated network analyser as described in the chapters to follow. For these reasons, this chapter will only provide a brief review of the prior art and identify certain basic features of the measurement task.
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12 The microwave reflectometer
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The technology described in this chapter at one time represented a highly developed art and provided much of the basis for precision microwave metrology. Although failing to yield phase information, the need for this was in some cases circumvented by 'generalised reflectometer techniques' which specifically addressed certain problems of major interest, particularly in the area of power measurement. At best, however, these methods were both frequency sensitive and time consuming. With the increasing interest in broadband systems, and the advent of digital technology, these methods have to a large degree been replaced by others which are more amenable to automation. In the process, a major shift in measurement strategy has also occurred. In particular, the foregoing tuning methods were largely developed in an era where the key to better accuracy was an improved item of hardware. As such, they represent a set of highly developed techniques for making in-situ adjustments of the hardware parameters such that the 'ideal' response is more nearly realised. By contrast, the more recent strategy, as reflected by the 'vector' network analyser, for example, is that of specifically identifying and characterising the hardware imperfections such that they may be eliminated by software corrections. Although much of this earlier technology is still embodied in the 'scalar' network analyser, in other cases the shift in emphasis has been from trying to build a better piece of hardware, to 'smarter' use of that already in existence.
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13 Precision power measurement
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The importance of power measurements in assessing the performance of a microwave system may be easily recognised since it is power which 'does the work' or in the communications environment, 'carries the information'. The amount of power needed for a communications application is dictated, in turn, by the required rate of information transfer, carrier frequency, noise thresholds etc. By tradition the field of microwave metrology is divided into the areas of power, attenuation and impedance measurement. The primary role of attenuation measurement, however, and to a substantial degree that of impedance as well, is ultimately in support of power measurement.
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14 Power meter applications
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Microwave power meters fall into the categories of 'terminating' and 'feed-through' types. The bolometric technique, as described in the preceding chapter, (ideally) terminates the line in its characteristic impedance. It thus absorbs the energy which it measures and falls into the first category. By contrast, the feed through type may absorb only a fraction of the available energy and pass the remainder to a termination. The first type tends to be the basis for calibrating or assessing the operation of the second type and its applications will be described first.
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15 Power equation methods
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As noted in the previous chapter, an important part of the assessment of microwave system performance is derived from the measurement of power, and in which attenuation and impedance measurements often have a supporting role. As described therein, the role of impedance measurement is frequently that of providing a determination of the (mismatch) correction which must be applied to compensate for a failure of the different components to satisfy the 'matched' condition. These techniques, in turn, are based on microwave circuit theory, which was developed in an earlier chapter and which is based on a solution of Maxwell's equations in a uniform waveguide.
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16 The automatic network analyser
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The application of automation to the field of microwave measurements is perhaps best illustrated by the (vector) automated or automatic network analyser (ANA). The large reduction in measurement time and operator effort which it provides are well known, but this feature may tend to obscure a more fundamental aspect of its impact. Although techniques for measuring complex microwave impedance, scattering coefficients etc. have been known since the inception of the art, until the advent of the ANA much of microwave metrology was focused on the more easily determined scalar parameters such as power, attenuation and reflection coefficient magnitude. In the absence of phase information, it was common practise to determine 'worst case' limits for certain phase interactions which were labelled 'mismatch errors'.
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17 The 'Six-port' network analyser
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The (vector) automatic network analyser (ANA) was introduced. Moreover, it was noted that a key element in its (usual) implementation is a detection system which provides both amplitude and phase response. This generally calls for a heterodyne detection system, possibly involving multiple frequency conversion and the associated local oscillators etc. In practise these components make a substantial contribution to the overall complexity and their realisation becomes increasingly difficulty as one moves into the millimeter wave region. Much of the earlier technology which it replaces was, by contrast, built on a much simpler detection system whose response was to amplitude (or power) only. Here the need for phase response can be avoided in certain problems by the use of techniques based on tuning transformers. However, these are both frequency sensitive and time consuming. The so-called 'six-port' technique represents an attempt to combine the better features of the two technologies. In particular, the simplicity of the detection system is retained, while the phase response is achieved (and the tuning requirement eliminated) by the use of additional (usually a total of four) detectors.
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18 Adapter evaluation techniques
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Because the microwave art is characterised by the use of a variety of waveguides or transmission lines, the subject of adapters and their evaluation is an important one to the microwave metrologist. A typical problem is that of using a power or noise standard in a waveguide (for example) to calibrate an 'unknown' in coaxial line. Today, as will be described below, an explicit and complete adapter evaluation is possible using the automated vector network analysers. In addition, however, the prior art also includes techniques which provide an approximate elimination of the adapter parameters from the problem of interest. It is the purpose of this chapter to provide, with the help of specific examples, a brief survey of the existing methods.
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19 Noise in communication systems
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The purpose of this chapter is that of giving an elementary and tutorial introduction to the description of noise in communication systems and where the basic features of the problem have often been obscured by the sophisticated mathematical tools employed. The objective is to introduce and define the quantities: mean, variance, power spectral density, stationarity and distribution function, in an intuitive and elementary manner and with a minimum use of mathematics.
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20 Noise standards and radiometry
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The existing techniques for evaluating the noise contributions from microwave amplifiers, mixers etc. call for the use of noise generators or sources of known parameters or characteristics. This chapter will focus on noise sources, standards and their intercomparison.
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21 A scattering description ofAmplifier noise
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The use of noise figure or noise temperature to describe amplifier performance is a well established practise. As usually defined, these are functions of both the amplifier parameters and the source impedance. It is quite possible, however, for amplifiers to have the same noise temperature, but markedly different sensitivities to changes in source impedance. If optimum use is to be made of a given amplifier, its performance characteristics must be known in sufficient detail to predict its operation in an arbitrary environment, including the options which may be available in attempting to optimize the system performance and the extent or nature of the penalties which may be incurred if this is not done. This calls for a 'complete' amplifier description and the problem is one of putting this description in the most convenient form. At microwave frequencies, and in keeping with remainder of the book, this is probably in terms of the scattering parameters. It would be possible to obtain the scattering description by a reinterpretation of a number of earlier results, which are based on low-frequency circuit concepts. It will prove more instructive, however, to give its derivation from an elementary model.
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Back Matter
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