Electronic Waves & Transmission Line Circuit Design
Your Illustrated Guide to Wave EngineeringBy Matthew M. RadmaneshAuthorHouse
Copyright © 2011 Matthew M. Radmanesh, Ph.D.
All right reserved.ISBN: 978-1-4389-6862-9Contents
Preface...................................................................xixAcknowledgements..........................................................xxiiiWhat sets this book apart.................................................xxivPART I THE FUNDAMENTALS...................................................1Chapter 1 THE POSTULATES OF RF & MICROWAVES...............................3Chapter 2 THE DISCOVERY OF FORCE FIELDS...................................35Chapter 3 THE MATHEMATICS OF ELECTRICITY..................................63Chapter 4 THE LAWS OF ELECTROMAGNETICS....................................87PART II PROPAGATION OF WAVES..............................................141Chapter 5 RF & MICROWAVES BASICS..........................................143Chapter 6 PLANE WAVES IN MATERIAL MEDIA...................................169Chapter 7 TRANSMISSION LINE FUNDAMENTALS..................................203Chapter 8 LOSSLESS TRANSMISSION LINES.....................................213Chapter 9 STANDING WAVES & THE SMITH CHART................................247Chapter 10 LOSSY TRANSMISSION LINES.......................................265Chapter 11 LUMPED ELEMENTS ON THE SMITH CHART.............................289Chapter 12 DISTRIBUTED ELEMENTS ON THE SMITH CHART........................303Chapter 13 FREQUENCY RESPONSE OF PASSIVE NETWORKS.........................339PART III CIRCUIT DESIGN ESSENTIALS........................................359Chapter 14 LUMPED MATCHING NETWORK DESIGN.................................361Chapter 15 DISTRIBUTED MATCHING NETWORK DESIGN............................385Chapter 16 QUASI-TEM TRANSMISSION LINE DESIGN.............................411Chapter 17 TRANSIENTS IN LOSSLESS LINES...................................425PART IV APPENDICES........................................................443Appendix A PHYSICAL CONSTANTS.............................................445Appendix B INTERNATIONAL SYSTEM OF UNITS..................................446Appendix C UNIT PREFIXES & CONVERSIONS....................................447Appendix D GREEK ALPHABETS................................................448Appendix E FRAGMENTED ENERGY FORMS........................................449Appendix F MATERIALS CONSTANTS............................................453Appendix G MATHEMATICAL IDENTITIES........................................457Appendix H CD ROM DOWNLOAD................................................465Appendix I CD ROM DOWNLOAD-ANALYSIS & DESIGN EXAMPLES.....................471Appendix J POWER CALCULATIONS.............................................545Glossary of Technical Terms...............................................553Index.....................................................................587Technical References......................................................593About the Author..........................................................595
Chapter One
The Postulates of RF and Microwaves
1.1 INTRODUCTION
There are very basic concepts that underlie all education in electrical or electronics engineering. Knowing these basic concepts enables one to have a much deeper grasp of the more sophisticated concepts and prevents great amount of confusion and discouragement in studying this subject.
The science of electrical engineering sits squarely on the premises of the science of physics and its fundamental postulates. The science of physics deals with the fundamental building blocks of the whole physical universe, which has been discovered to be composed of matter and energy in constant interaction with each other through a medium called linear space. This constant interaction leads to another factor, i.e., time.
These components will be specifically defined so that the reader may gain familiarity and understand their nature and properties. For example, take a transistor operating in a circuit. This transistor has a mass (semiconductor materials, metal, etc. used in its fabrication) and handles electrical energy (current, voltage, etc.). Furthermore, it is presupposed that it occupies a certain space in which the device exists and also has time built into it due to the interaction of various energy forms with its matter from its inception until now.
To proceed further in our study of electronics we have to have specific definitions of the building blocks of the science of physics, i.e., energy and matter.
1.2 UNDERSTANDING POSTULATES
We need to define the term "postulate" at this stage of our work, because it will be used over and over throughout this book. By "Postulate" we mean, "An assumption or assertion set forth and assumed to be true unconditionally and for all times without requiring proof, especially as a basis for reasoning or future scientific development."
Of course, if postulates are chosen as close as possible to the truth of the situation at hand, then they can be used as a basis for reasoning and, more importantly, as a solid foundation for a workable science.
On the other hand, totally arbitrary postulates can be formed, without any basis in truth or reality of the situation. Adoption of such arbitrary postulates would bring about a field of study, which is totally void of any valid truth or natural laws and would be a constantly shifting subject. The subject would be randomly workable and have a lot of false data.
As an example, one may consider the field of art where the critic, the artist, the reviewer, and the public each have introduced their own arbitrary postulates to create a totally unworkable subject without the discovery of any natural laws. Based on this observation, the following conclusion can be drawn:
In any given subject, the number of arbitrary postulates made in that subject, which have no basis in fact or truth, inversely determine the workability of that subject. Moreover, the lesser the number of arbitrary postulates and the closer they are to truth, the more workable that subject becomes.
Thus we can see that in any given subject, the number of arbitrary postulates made in a subject, which have no basis in fact or truth, inversely determine the workability of that subject. Moreover, the lesser the number of arbitrary postulates and the closer they are to truth, the more workable that subject becomes.
Physics and engineering have become two dominant fields in our highly technical society. There are a series of exact postulates, which have led to the current high degree of workability and successful application techniques and sophisticated technology.
The main postulates that have been discovered by observations of the physical universe can be summarized as:
1) Existence of energy in many forms such as thermal, optical, electrical, magnetic, audio, electromagnetic, etc.
2) Existence of matter in gas, fluid, plasma, and solid forms.
3) Conservation of all forms of energy to hold valid at all times.
4) Conservation of any form of matter under all conditions and at all times (primarily used in classical physics).
5) Existence of a viewpoint to act as a reference point for all subsequent measurements. This postulate is implicit in physics.
6) Existence of a linear space in which to place matter and energy. This is another postulate implicit in physics.
8) Existence of a constant rate of motion or constant rate of change of particle's position in space. This postulate instantly leads to a linear time base, which is also implicit in physics and can be considered to be the seventh postulate. Such a constant and linear time base is currently supplied by the earth's spin around itself and rotation around the sun. It should be noted that this choice of time measurement is completely arbitrary but very convenient since the concept of time has existed from the beginning of man's civilization on earth.
Time, in general, is an abstract consideration, which can be measured by any constant motion or oscillation and does not necessarily have to be in terms of seconds, minutes, hours, days, years, or even closely associated with the earth's movement in space. The fact that we take the notion of time for granted and measure it exclusively in terms of the above units is an insidious act of disregard for its more general concept and deeper connotations, of which more later.
In the above discussion, postulate #5 (viewpoint) is the most senior of the seven postulates, followed by postulate #6 (space), #1 (energy), #2 (matter), #3 (conservation of energy), #4 (conservation of matter) and #8 (time) in importance. However, the order of presentation of these postulates is, of course, to conform to the current state of physics texts, which make no mention of #5 and #6 as the senior postulates.
However, the presented sequence of postulates is universally accepted as valid in the scientific community and most scientists take it for granted. This can be considered to be a major oversight and shortcoming in the extant physical sciences.
1.3 THE MAIN POSTULATES
We can see that the physical universe, at first glance, appears to be built upon four primary postulates of:
a) Space,
b) Energy,
c) Matter, and
d) Time.
However, upon further examination of these four postulates we can see that the third and the fourth postulates have a common denominator, which allows us to further reduce the four primary postulates to only three. The new and reduced set of three postulates essential to the creation of the physical universe, are called the original postulates, which are but irreducible!
The three original postulates can be summarized as:
I. Space
II. Energy (or Force)
III. Change
Combining postulates (II) and (III), we can actually obtain the third and the fourth primary postulates discussed earlier (i.e., matter and time). For example, if we "change" the created space, in which certain energy particles exist, in such a way that the volume is reduced, then the energy particles become more condensed and thus we get "matter" (the third primary postulate).
On the other hand, if we "change" the position of a matter particle or an energy form in space, we get "time" as the fourth primary postulate. Upon these four primary postulates, which furnish the necessary building blocks of postulates for the creation of any universe or physical science, the microscopic and macroscopic universes are founded as shown in Figure 1.1.
Therefore, we can see that we only need three original postulates to create the entire physical universe—from an atom to a galaxy and beyond. The three original postulates bring a considerable simplification of the primary postulates and display a higher level of truth than one can ever obtain from a detailed examination of the components of the physical universe as done in the science of physics.
Of course, one should be reminded that once these three postulates, on a microscopic and macroscopic level, were implemented and put into effect on an automatic level of operation, the ensuing complexities of great magnitude, which was brought forth as a result may have well been outside the scope and grasp of the original postulates and may actually have been totally unforeseen to this day.
It is interesting to note that from pure observation, one can see that the third original postulate (change) has actually been put on automatic in the physical universe. We can take earth as an example. We can see that our planet revolves around the sun at a predetermined rate of 66,000 miles per hour while spinning around itself at a fantastic speed of about 1000 miles per hour—all done on an automatic, unthinking, and involuntary manner, causing an automatic time stream called mechanical time.
1.4 THE FOUNDATION OF ELECTRICITY
From the viewpoint of considerations, any extant science (including electricity) has a foundation upon which it is built. This is very similar to a building structure where its footing and foundation is of essential importance, since it supports the weight of all the upper floors and its contents. The foundation of electricity consists of two parts:
a) The fundamental postulates
b) Natural laws
Upon this solid foundation rests all theoretical research, extrapolations and design methodologies, application mass and all future explorations, inventions and discoveries. The natural laws are discovered by observation and study but nevertheless have a lot in common with the fundamental postulates of electricity.
It can be observed that the fundamental postulates of electricity forms the bedrock upon which all natural laws rest. This means that the postulates and the discovered natural laws together, form the foundation of electricity. It is an important concept, which is omitted in the majority of scientific texts. All the remaining considerations such as scientific conclusions, technical data, design methods, rules, etc. and the entire application mass of the subject rests on top of the foundation. Figure 1.2 shows the pyramid of knowledge in a workable science such as electricity.
There were a series of monumental discoveries over approximately a period of three hundred years, spanning form from 1600 to 1894. This period of time in Man's history, an unparalleled period of intense scientific developments, started with the discovery of electric charge (by William Gilbert) and culminated in the discovery of electronic waves directly related to and as a result of "electric charge" and its motion, by James Maxwell and Heinrich Hertz.
These were a series of breathtaking discoveries, which put man, as a species, a head and shoulder above the rest of the creatures of this forlorn planet and shaped our current highly sophisticated and fast-paced society!
A very brief introduction of these discoveries is quite appropo if we plan to grasp the foundation of this subject and achieve a mastery of this mazing subject.
1.5 THE FUNDAMENTAL POSTULATES OF PHYSICS
It is of interest to briefly introduce the postulates behind the science of physics so that we have a better understanding of electricity since its laws are uniformly derivable from physics.
1. Postulate #1: Existence of energy, on a classical and/or quantum level.
2. Postulate #2: Existence of matter particles.
3. Postulate #3: Principle of conservation of energy to be held valid under all circumstances and for all times.
The above three postulates presuppose the existence of a continuous and linear space, in which all the energy and matter particles can be placed. Thus, a primary postulate should be added to the list, that is:
Postulate #4: Existence of a continuous and linear space.
The above four postulates in action (i.e. particles in motion relative to one another in a linear space) instantly gives birth to a new phenomenon: time. Thus, a secondary and fifth postulate can also be added to the list:
Postulate #5: Existence of a continuous and linear index of motion commonly known as time.
To compare and measure all other motions relative to one another, a linear time reference is needed. Such a linear time reference is best furnished by having a number of particles, which are moving relative to one another at a definite and fixed rate of motion.
For example, rotation of the planets and their associated moons in the solar system (e.g. earth and its moon) around the sun at a regular and constant rate of motion establishes the necessary time standard against which all other motions can be measured.
1.6 THE SCIENCE OF ELECTRICITY
The science of electricity subdivides itself into two main areas: a) Static electricity, and b) Kinetic electricity. These two main subdivision of electricity further subdivide into many subtopics and ramifications, which bring about a panoramic view of the whole field of study known as "electricity" as shown in Figure 1.3.
Furthermore, electricity as actually shown in this book, is derived from six monumental discoveries and no more. All of the known laws, working principles and equations of electricity, magnetism, electromagnetism, wave propagation, etc., can all be derived from these six powerful discoveries. Moreover, most of the supplemental discoveries can be derived from these monumental discoveries
This means that to understand the essence of any subject, one needs to discover and understand the relevant principles and postulates and then work out all of the derivations and ramifications of the basic principles to achieve a full knowledge of that subject.
Once the basic principles of a subject have been discovered and the subject has been thoroughly codified and understood, the most complex situations can be dissected and solved with relative ease.
Figure 1.4 shows how the discovered principles in the field of electricity form the apex of the pyramid of knowledge in electricity.
Moreover, Figure 1.4 also shows the emergence of six distinct fields of study, i.e.,
* Electrostatics,
* Electrokinetics,
* Magnetostatics,
* Electrodynamics,
* Electromagnetics and
* Electronic Waves
Using any of these fields of study, one can develop a plethora of application mass, which will benefit man in many ways for all future generations to come. The entire application mass thus generated in all of these fields of study will accompany this precisely formulated and codified mental triumph called "electricty!"
Electricity as briefly discussed above is merely a subset of a much larger arena, namely, the physical universe. The physical universe, itself, could be categorized as a "total-effect" or "action-reaction" type universe. However, it is the life force imbuing the physical universe, with the consequence of using electricity in so many applications in daily routine (from mental recordings and digital computations to tele-communications and image/data transmission) that has made the subject of electricity such an exciting field of study with unlimited capability.
1.7 THE POSTULATES OF LOW FREQUENCY (LF) ELECTRICITY
Having discovered electricity in terms of the six monumental and the eight supplemental discoveries, we are now ready to state the two classes of postulates of Low Frequency electricity: a) Main LF postulates, and b) Auxiliary LF postulates.
1.7.1 The Main LF Postulates
There are five main LF postulates that form the most fundamental aspects of electricity. These are:
MAIN LF POSTULATE #1: Let there be electric charges existing in opposite characteristics, or more precisely in a dual pair form (i.e., positive and negative charges).
MAIN LF POSTULATE #2: Let there exist electric field emanating from the positive charges and terminating on the negative charges. The electric field is capable of exerting a force on a nearby charge.
MAIN LF POSTULATE #3: Let there be an electromotive force (emf) required to cause a charge to move in a closed path of travel, i.e., creating a current. In other words, let the source or cause of a 16 Electronic Waves & Transmission Line Circuit Design circulating current be the emf, which is the electric pressure. This causes a current to flow from a higher potential to a lower one.
MAIN LF POSTULATE #4: Let there be a magnetic field circulating an E-field, which lies in the path of a moving charge (i.e., a current), whose direction is given by the right-hand rule.
(Continues...)
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