 Welcome you to the course on engineering electromagnetic. Let us start the course with a few questions and as we go along we will try to find answers to these questions. The first question we pose is what is electromagnetics? The answer to keep it very simple is as follows. Electromagnetics is the study of electric and magnetic fields. To be more specific we say that electromagnetics deals with the causes and effects of electric and magnetic fields. When we say causes what we have in mind is the sources of electric and magnetic fields how these are produced. And when we say effects what we have in mind is the behavior of the fields themselves of various bodies under the influence of electric and magnetic fields. So that put very simply is the answer to the first question what is electromagnetics. Now fields by their very nature appear somewhat abstract. They appear difficult to visualize. Therefore the next question that will come naturally is why talk about fields. To answer this question we go back and consider the first instance or first instances where we were introduced to the concept of fields. What were these instances? Instances are very simple. We are familiar with the fact of forces between electric charges as observed by many including Coulomb who quantified this force in terms of the charges their magnitude polarity and distance etc. These charges for example, if you take two charges they are non touching and yet they exert forces on each other. How do we explain this? How the force arises? We say that one charge if we consider one of these charges has an electric field around it and this electric field interacts with the charge of the other charge particle and therefore the force arises. This is perhaps the first instance where we invoke the concept of field. Similar example is easy to think of a compass needle deflects when brought in the vicinity of a current carrying wire. The phenomenon was quantified by Orsted and once again the two entities the current carrying wire and the compass needle are non touching and we say that the current carrying wire has a magnetic field around it which interacts with the compass needle poles of the compass needle and hence causes a deflection of the compass needle. So these are two of the first instances where the concept of fields was required to be invoked. These are both phenomena where action at a distance is taking place. Non touching body is experiencing the influence of each other alright and we generalize and say that action at a distance phenomena are explained in terms of fields alright. Typically you will find that this is the case action at a distance phenomena are easiest to explain in terms of fields. These phenomena are important how do we say that let us just consider the applications of these phenomena. Forces between electric charges I am sure you can recall many applications. Two such applications I mention here one is in the electron guns which are utilized in cathode ray tubes which are utilized in display instruments and xeroxing where static charges help us in holding papers etcetera alright. Similarly the second phenomenon we have put down also has important applications for example in measuring instruments like galvanometers or ammeters alright and also motors. So we see that these are phenomena which have very important applications and therefore although they are explained in terms of fields we should learn about these things we should learn about fields. These two examples that we have taken belong to the category of steady fields or static fields because there is no time variation that we have considered so far. So we may call these steady fields. If we permit also time variation so that we are able to go to time varying phenomena then we enlarge the scope of our consideration very considerably and the first phenomenon that perhaps one can think of falling under this category is the phenomenon of electromagnetic induction the law proposed by Faraday which is again an action at a distance phenomenon is explained in terms of a time varying magnetic flux arising out of a time varying magnetic field causing induced voltage in a suitable circuit. This third phenomenon that we have put down where time variation is allowed also has important applications for example in our generation we say magnetic recording something from which we are benefiting now and I hardly need to stress the importance of these various applications individually or in combination and the shape of our present civilization. So we say that these action at a distance phenomena have a large number of important applications. If we go further and continue with time varying phenomena we see that wave propagation and also radiation these two are also explained in terms of fields otherwise they are difficult to explain and together these phenomena are responsible for a large number of applications for example in telecommunication wireless communication which will include radio and TV broadcasting and so on. There is no end to the applications and therefore we say that these are action at a distance phenomena which are explained in terms of fields have important applications and it will be worthwhile to learn about fields but that is only a part of the story. There are other reasons too which call for our study of fields we can look at things from a different point of view and see that there is need for learning about fields from a different point of view also and let me clean up the board. What we will do is we will take up a very simple circuit and then consider its behavior at two different frequencies and it will immediately come to our notice what are the limitations of the familiar conventional approach in terms of voltage and current. We take a very simple circuit just two wires with resistance connected at one end and a voltage source say V dot cosine omega t or 2 pi f t connected at the other end. Let us call these terminals as 1, 2 and 3, 4 and we say that the lower terminal on the second lead is grounded. Now depending on the length of this connection which we say is L and we take a rather specific value of L for the sake of convenience so many centimeters. The reason for this will be obvious when we do the calculations usually the signal will travel at the velocity of light or close to it and this time taken by the applied signal in reaching from the input end to the output end where the resistor is connected will be L upon the velocity of light C and for this case taking the values of 30 by 4 and 3 into 10 to the power 10 centimeters per second we have a value which is 10 to the power minus 9 by 4 seconds or alternatively 0.25 nanoseconds quite a small value. Now we consider specific values of the frequency f, we consider a typical low frequency say f 1 equal to 10 to the power 4 hertz. The corresponding time period being inverse of this so that it is 10 to the power minus 4 seconds and if you plot this voltage waveform as a function of time at t equal to 0 it starts with v naught and at one fourth of the time period t 1 it will go to 0 and that way this sinusoidal variations will continue. So we plot it somewhat like this and it crosses here at t 1 by 4. Now what is this time delay tau in comparison with this time period t 1 very small almost insignificant as a consequence the moment the signal is applied here we can say that there is an instantaneous response of the circuit to the stimulus and since this time delay is so small we can say that all parts of this connecting lead connecting wire are at the same potential or at the same voltage difference and same kind of current same amount of current flows from terminal 1 2 3 2 4 and completes the circuit and very neatly one can apply Kirchhoff's current law Kirchhoff's voltage law and analyze this kind of circuits without any difficulty this is what we are familiar with. Now let us go to a higher frequency say f 2 equal to 10 to the power 9 hertz 1 giga hertz. So it falls in the microwave frequency range the corresponding time period going to 10 to the power minus 9 seconds and now the time delay tau begins to become significant substantial in terms of the time period and if you plot this waveform although it is not possible to draw it to the same scale. So one applies visual expansion and contraction and one plots the signal like this and where it first crosses 0 that point is t 2 by 4 somewhere here starting with v naught at t equal to 0 this t 2 by 4 is equal to the time delay for the case that we have set up and now what happens is that while this initial voltage v naught reaches the other end of the circuit the source voltage drops to 0 and we cannot at all say that all parts of the circuit are at the same potential. We cannot even say for surety that the current is the same everywhere because the potential is different at different points and as you think about it you see that KCL and KVL begin to land in trump. Why this has happened? Does this happen for this specific circuit? No it is a consequence of the time delay being significant in terms of the time period. Any circuit any entity where this happens we will have this kind of problems we will have trouble in working only with voltage and current in most cases. And therefore we say that time delay in terms of time period is insignificant at low frequencies but may be quite significant at high frequencies and we generalize saying that circuit theory laws are inadequate at high frequencies. Why they are inadequate? It is because of the time delay becoming significant as a function of the time period that relative aspect we must not forget alright. In fact if we consider the high frequency work we find that the circuit forms at high frequencies are quite different from those at low frequencies. I will give you examples to illustrate this. Consider what is called a dipole antenna the construction of which is very simple it is just a straight wire and it is connected to a generator high frequency generator somewhere in the middle. Using our low frequency voltage current concepts we do not expect this open circuited wire to accomplish anything much but it is a very useful antenna type and perhaps it is the most commonly used antenna in practice. In fact the antennas that we use for television reception are a derivative of this dipole antenna. Similarly one can consider other antenna types for example what is called a loop antenna which again has a simple construction circular conducting wire connected to a generator which is short circuited and therefore using our low frequency concepts will perhaps only damage the generator but it is a very useful antenna and is used very commonly for direction finding applications. On one hand we say that the circuit forms at high frequencies are different from those used at low frequencies. We have just seen two examples there are other examples that one can consider for example a wave kite. As a corollary we can also say that the forms which perform a certain function at low frequencies do not work as expected or do not maintain that function at high frequencies. As an example we can consider the usual circuit components like the resistance inductance and capacitance and at high frequencies what we find is that a resistance may have considerable amount of reactance and inductance may have considerable amount of capacitance and so on. All this is a consequence of the time delay between the signal reaching from one part of the circuit to the other being significant in terms of time. So what is the conclusion? First we saw that there are phenomena which are action at a distance phenomena which are explained in terms of fields and then we see that at high frequencies we cannot utilize simple Kirchhoff's laws for analysis and the solution is that we have to work in terms of fields. Since some of these problems as I have mentioned may occur at high frequencies now that we have started the course by asking questions. Another question may come up amounting to why go to high frequencies and the answer to this question is that the mankind is desiring faster operations of circuits of various things. We need more information and these things can be done conveniently at high frequencies. One particular frequency range in the high frequency category is the microwave frequency range which nominally we say extends from 300 megahertz to 30 gigahertz. Somewhat higher frequencies are called millimeter wave frequencies. The corresponding wavelengths range from 100 centimeters to 1 centimeter and this frequency range has many useful applications. For example in radar in communications there are applications of microwave frequencies in basic and applied sciences. For example microwave frequencies are used in radio astronomy and nuclear physics. There are consumer applications for example in microwave oven and cellular phones. There could even be medical applications. Microwaves have been utilized for detection and treatment of tumors and cancers. Similarly there are other ranges different from microwave frequency range falling under the category of high frequencies and they will have their own particular applications apart from satisfying this requirement of faster operation more information. And therefore it may be necessary for us to go to high frequencies where we may need to work in terms of fields. This course will form background for a number of follow up courses which relate to many important engineering applications. Microwave engineering, antennas, wave propagation. Some of these applications we have mentioned here but a whole lot of concepts and aspects relate to these phenomena which are necessary to be considered for their practical application. And therefore we say that for these various reasons we need to work with fields because there are phenomena which cannot be dealt with in terms of simple voltage and current. How are we going to work in terms of fields? What will be the basic mathematical tool? That will be Maxwell's equations which we hope you have done in an earlier course. We will review this topic of Maxwell's equations to the extent required by us here and I am sure there will be no difficulty in using these. We can mention what is the, what are the course objectives and the course objective is going to be to understand the behavior of fields in various structures that are utilized for the transmission of electromagnetic signals. What could be these transmission structures? I think you have some idea by now. These would be transmission lines, wave guides and even free space or an unbounded medium can be used for transmission of electromagnetic waves and we will see what is the behavior of the fields in these different types of situations. We will consider the behavior of fields when these are infinite in the direction of propagation. So when these structures, transmission structures are infinite we will see what kind of fields are supported on these structures and also when discontinuity appears in these media, in these transmission structures then what happens and finally when we have covered some basic types of these transmission structures we will go on to what we can call the radiating conditions. In all these considerations you will find that wave propagation will be a recurring theme and therefore we will make an attempt to understand this phenomenon of wave propagation in fair amount of detail. The skills or the capabilities that we hope to develop by the end of the course are mentioned here. We should be able to analyze that is predict the behavior of fields given this kind of transmission structures, transmission lines or wave guides or unbounded media and what happens when there is a discontinuity which appears in any one of these and we should be able to design these structures for efficient transmission of signal at the desired frequency. This is what we attempt in this course. Next we go on to the course content. Starting with the introduction we go on to consider transmission lines and there is a very important reason for starting with transmission lines. And we have said that it is the field theory and the Maxwell's equations which are more general and Kirchhoff's laws are specific special cases of Maxwell's equations and in general for predicting the behavior accurately at high frequencies and in certain other situations we need to work in terms of fields. Transmission lines are one special area where with some care it is possible to work in terms of voltage in current and in terms of Kirchhoff's laws which surely will be easier for us and yet it will be possible for us to introduce, understand and explain the various aspects of wave propagation. And therefore we have particularly chosen to start with transmission lines. It is not that the transmission lines cannot be analyzed in terms of fields and Maxwell's equations. It can be done but the effect or the result will be the same in most cases as by carefully applying the circuit theory laws. The care that we will have to take will be the time delay in the signal reaching from one part of the circuit to the other appropriately. We will model the transmission line as a distributed parameter circuit and then see that the mathematical solution of the various equations leads to what is called a wave equation the solutions to which indicate propagating waves. Then we go on to defining an important quantity that is the characteristic impedance and then consider some simple travelling wave situations and consider what happens when a pulse propagates on transmission lines. And a new phenomenon which we are not familiar with so far that of standing waves and then we take up how transmission line sections could be used as circuit elements. I have mentioned some time ago that familiar circuit forms the low frequency circuit forms do not work as expected at high frequencies which means we have to go to some other circuit form so that we get a predictable accurate behavior and then one can use sections of transmission lines as capacitors inductors or even resonators. Then we go on to using various techniques for working with transmission line circuits namely the Smith chart and then the parameters which are going to be utilized for modeling the transmission line how those can be evaluated from the electromagnetic theory that is what we will consider. We go on to a review of Maxwell's equations and then we see that the simplest situation when we consider fields in an unbounded medium time varying fields in an unbounded medium will lead to a similar situation that is the combination of these Maxwell's equations will lead to wave equation which again has solutions as propagating waves. Lane waves will be the simplest solution as I mentioned and then we go on to consider various aspects of propagating waves that is polarization. The pointing vector which helps us in determining the power flow and then wave propagation in conducting media we could have to deal with different types of media may be perfect electrics may be conducting media. So, what is the difference between these two that is what we will consider here and then we come to what happens when discontinuities arise in these unbounded media. So, we will apply boundary conditions and see how reflection and refraction etcetera take place at different boundaries. And then we will also see that plane wave propagation has very close analogy with waves propagating on transmission lines and therefore, various methods that we have developed we would have developed for transmission lines would become applicable to plane waves. After this we will be ready to consider what are called wave guides which are particularly useful for high frequencies such as microwave frequencies. And we will be using microwave frequencies and wave guides for an associated laboratory course. We will start with the simplest wave guide that is the parallel plane guide consider the phenomena of dispersion and attenuation and then go on to consider the rectangular wave guides see what are the various modes supported on these wave guides. So, far the types of waves we would have considered on transmission lines or as plane waves would be TEM waves transverse electric and magnetic waves. The waves supported on wave guides would be different they will be categorized as TEM and TE waves or TEM and TE modes. What is their exact meaning what is the difference between these and the TEM waves we shall consider this in some detail. If time permits we will consider some types of cylindrical wave guides. And then resonators form a very important circuit element at low frequencies for helping us in processing the signals in various ways. So, we will see how we can make resonators using transmission lines and wave guides. And then as I mentioned already we will consider radiation. What is the phenomenon of radiation? What are the mathematical tools which we utilize when dealing with the radiating situations? So, starting with these basic concepts retarded potentials we will go on to the simplest radiator that is the Hertzian dipole which was utilized by Hertz in his experiments with the help of which experiments he was able to validate the Maxwell's predictions. And then go on to consider a more practical radiator that is the half wave dipole as I just mentioned. The books that we are going to utilize or we may consider for reference are listed here. The book that is listed first that will be the most important book for this course Jordan and Balmain. It is available in a very low cost Indian reprint edition. The next one is N Nara and Rao. The second book we may not take any material directly from this book, but it has excellent problems on various aspects that we will be touching upon in this course. And this third book Ramovineri Van Duser which also is available in a low cost edition I believe the cost is about 6 dollars is not restricted to just the topics we will be considering in this course. So, as a communication engineer it should be a good reference book. So, for those who develop a more permanent interest in this area this would be a very good book. There are many other good books on this topic it is a classical subject. So, there is no shortage of books. Some of these I have listed here. Many of these are available in low cost editions or as Indian reprints, but some are not. For example, cross and pose are not available in low cost editions, but their copies will be available in the library. With this we are ready to have quick summary of what we have done today. We have posed a few questions and we have answered these also hopefully. What is electromagnetics? We say that it is the study of electric and magnetic fields. Then we have seen why it is important to talk about fields. We said that there are many phenomena important phenomena which are explained in terms of fields. These phenomena are important because they have important applications. And next we went on to see how fields would be required from another point of view. And we saw that time delay in terms of time period can be significant at high frequencies. And in such a case circuit theory laws are inadequate. And therefore, even the circuit forms may be different at high frequencies. Then we considered why we may go to high frequencies at all. And then we saw that there are many important applications which are served by high frequency signals. And we said that what we learn in this course will be a very important background for a number of follow up courses. And then we said that for working with fields we will mainly draw upon Maxwell's equations. And then we considered what we proposed to cover in this course. What are the course objectives? And what capabilities we aim at developing through this course? And what will be the course content? If you have any questions we can have those now. Then we stop this lecture here. And we will meet for the next lecture on Thursday. One day is a holiday. Thank you.