WEBVTT 00:20.830 --> 00:33.200 Welcome to this first lecture on the NPTEL course, on Basic Building Blocks of Microwave 00:33.200 --> 00:41.960 Engineering. Now, the theme of this first week lecture will be the mathematical model 00:41.960 --> 00:48.590 of Microwave Transmission, you know that, from the source the electromagnetic energy 00:48.590 --> 00:54.230 propagates. Now it propagates through various channels and then, reaches it is destination, 00:54.230 --> 01:05.040 or receiver or sink. Now will model first, this first part, the transmission and when 01:05.040 --> 01:11.670 the theme, the first lecture today that will address is, concept of mode in Microwave Transmission. 01:11.670 --> 01:20.070 Myself, Amitabha Bhattacharya, here in E & ECE department IIT, Kharagpur; you can reach me 01:20.070 --> 01:22.860 in my email here. 01:22.860 --> 01:35.940 Now, let us see, if we will look at the universe, when we are, if you look beyond our territory 01:35.940 --> 01:45.290 that is earth, you see, we see so many stars, so many galaxies etcetera. Now do know, that, 01:45.290 --> 01:52.070 all of them, they radiate either light, that is why we are seeing them or they are also 01:52.070 --> 02:02.360 radiating electromagnetic radiation, and there is one Nobel laureate Michel Boot, who measured, 02:02.360 --> 02:10.330 and found that in earth everywhere, we have something like 2 degree Kelvin, of microwave 02:10.330 --> 02:15.640 radiation always, that the background microwave radiation. So, always we are getting bombarded 02:15.640 --> 02:25.090 with microwave radiation, we are living with it. Also you know, some emits solar flare, 02:25.090 --> 02:32.050 that is why when the solar flare reaches earth, it is not always, but sometimes when it reaches, 02:32.050 --> 02:34.270 solar flare is different from the normal light. 02:34.270 --> 02:41.890 So, solar flare when it reaches, all the activities in communication etcetera, they get stopped. 02:41.890 --> 02:47.510 So, ISRO has a calendar, they keep track of when they solar flare reaches us, and that 02:47.510 --> 02:53.840 so they notify, and that time all our satellite etcetera, they stop working, because solar 02:53.840 --> 03:01.450 flare creates magnetosphere and that creates huge magnetic, electromagnetic field. 03:01.450 --> 03:07.800 All of you are familiar with this side in rainy season, you will see lightning. Now 03:07.800 --> 03:15.819 you see a lightning striking the earth, it is a huge source of electromagnetic emission 03:15.819 --> 03:23.660 due to the high potential, high static charge potential, there is, air gets break down and 03:23.660 --> 03:29.830 that is why, you see that, due to that break down the light gets produced, the sound gets 03:29.830 --> 03:32.720 produced. Now, sound is not electromagnetic energy, 03:32.720 --> 03:41.680 but this light is and that it reaches earth, it, you know, if you try to received this 03:41.680 --> 03:48.330 energy, you will get killed, but that energy comes here, when it is not striking, either 03:48.330 --> 03:49.590 a tree, or anything. 03:49.590 --> 03:55.450 But, in the whole atmosphere, you are pervaded with these terrestrial lightings. Then you 03:55.450 --> 04:01.950 see satellites, natural satellites in the right side, in the left side the man made 04:01.950 --> 04:06.709 satellites, huge number of them, all of them or communicating with earth by what, by electromagnetic 04:06.709 --> 04:12.959 signal. So, you are always getting signals from them. 04:12.959 --> 04:19.160 Then you see, let us see a typical family, how we are surviving today, there are Wi-Fi, 04:19.160 --> 04:24.660 that is emitting electromagnetic environment. You see satellite, that is doing that you 04:24.660 --> 04:31.130 see TV, that is doing that, you see mobile phone, nothing but electromagnetic radiation, 04:31.130 --> 04:40.770 you see ground station, satellite ground station, you see your tab or pager something, you see 04:40.770 --> 04:47.240 mobile phone, you see the electric towers you see so many devices. So, we are living 04:47.240 --> 04:48.240 with it. 04:48.240 --> 04:54.770 Now, we need to understand this environment, if we want to must have this technology. So, 04:54.770 --> 05:00.779 let us see that electromagnetic spectrum, you see, staring from the soccer field, that 05:00.779 --> 05:08.130 large size of wave length to water molecule etcetera all are electromagnetic environment. 05:08.130 --> 05:15.050 But we would not talk with this whole spectrum our microwave technology means, you see, we 05:15.050 --> 05:21.020 have noted that, radio waves you can see, that up to the soccer field to up to the base 05:21.020 --> 05:27.330 ball size of wave length base ball diameter wave length, that is radio waves, but after 05:27.330 --> 05:35.860 that, from base ball to let us say, this, a point dot, that wave length type of radiation, 05:35.860 --> 05:41.729 the radiation for which wave length is that long, that is denoted as microwave as you 05:41.729 --> 05:51.260 can see, that, this is the zone of microwave. So, here we will mainly talk of that, and 05:51.260 --> 05:57.900 just beyond that, you see if, you go still further in wavelength; that means, still higher 05:57.900 --> 06:03.099 you know, frequency you can appropriately see from here, we are reaching terahertz variation. 06:03.099 --> 06:08.530 Now, microwave radiation, as the technology is progressing day by day, it is going towards 06:08.530 --> 06:17.439 terahertz radiation, and similarly this, terahertz radiation also coming day by day, beyond, 06:17.439 --> 06:24.110 so, almost this 2 technologies are getting merged, or I think, when you people will be 06:24.110 --> 06:27.689 finishing your career, that time it will be completely merged. 06:27.689 --> 06:36.139 So, we need to understand this technology, and for that, this following lectures will 06:36.139 --> 06:42.099 help, you to understand the basics of that. Now you see, from all these field, if I look 06:42.099 --> 06:46.969 at any environment, actually we are doing in a particular place, we are trying to map 06:46.969 --> 06:52.879 the electromagnetic field distribution, and it came sometime like this, there is a color 06:52.879 --> 07:00.839 plot. So, you see the red ones, there the maximum things, maximum radiation that the 07:00.839 --> 07:05.240 electromagnetic radiation, then it is coming down, it is actually the radiation density, 07:05.240 --> 07:08.580 electric field radiation density, at that point. 07:08.580 --> 07:14.800 And you see that gradually it is going down; obviously, this blue etcetera, those are very 07:14.800 --> 07:23.119 low, but you see there are various types of this, field distributions are possible. 07:23.119 --> 07:30.080 Now the question is, if you want to understand, and Microwave Engineering, then we needs a 07:30.080 --> 07:37.289 model, that is the basic task of any engineering, that when we try to analyze or we try to understand 07:37.289 --> 07:42.879 something, we make a model. So, that is why we say that if you want to understand, you 07:42.879 --> 07:48.379 want to design, you want to analyze any practical system, you want a mathematical model. So, 07:48.379 --> 07:54.590 for Microwave Transmission system also we want model of this EM signal. As I shown you, 07:54.590 --> 08:00.300 just before that, if I want to have what is happening, I need a model, mathematical model 08:00.300 --> 08:06.779 of EM signal. Now EM signal again, I have listed for your convenience from that spectrum 08:06.779 --> 08:12.560 graph, that you know x ray light ray, infrared microwave, TV, radio, radar, mobile telephone, 08:12.560 --> 08:21.249 landline telephone, everything comes under EM signal out of that, I can say that, microwave, 08:21.249 --> 08:29.509 TV, then radar, then somewhat mobile telephone these are in our microwave zone. 08:29.509 --> 08:35.719 So, the question is, do we need for each of this type of signals, because each of signal 08:35.719 --> 08:40.760 will be different, that is why, there are co-existing at any place all the signals are 08:40.760 --> 08:41.760 present. 08:41.760 --> 08:46.911 Now that means, if I want to understand, do I need a model for each of these signal? Then 08:46.911 --> 08:55.900 my job is just remembering all those models, it will be a huge task fortunately it is not. 08:55.900 --> 09:04.901 So, now, all these EM signals, they will be Maxwell’s laws. All EM signals, light, you 09:04.901 --> 09:13.330 know proved that, light is indeed a form of electromagnetic radiation. Let us see, light 09:13.330 --> 09:18.270 and mobile phone signal, now both can be see light can be seen, but mobile phone signal 09:18.270 --> 09:24.320 cannot be seen, but still both of them obeys Maxwell’s equation. There are various solutions 09:24.320 --> 09:30.070 of Maxwell’s laws, light signal is one such solution, mobile phone signal is another such 09:30.070 --> 09:33.750 solution, radar signal is another such solution, etcetera, etcetera. 09:33.750 --> 09:41.000 So, do I need to understand all these? So; that means, let us make a set of all EM signals. 09:41.000 --> 09:48.140 So, one can make a set of all such EM signals are all these signals independent? If it was, 09:48.140 --> 09:55.230 then we had to understand all these signals, but no answer is no, fortunate for us there 09:55.230 --> 10:01.770 are a minimal number of independent solutions, such that, all EM signals cab be expressed 10:01.770 --> 10:09.750 as, linear combinations of them. So, we see that, though there are various solutions, 10:09.750 --> 10:17.740 but they are not independent, there is a minimal list of independent solutions and all solutions 10:17.740 --> 10:26.351 are linear combinations of them. So, that we have fortunate and these minimal numbers 10:26.351 --> 10:37.860 of independent solutions are called modes. So, you see, that people generally say, that 10:37.860 --> 10:45.200 modes, what is a mode? Modes are solutions of Maxwell's equation. I say it is partly 10:45.200 --> 10:51.930 to answer because, any electromagnetic signal as I said, that light signal, or a microwave 10:51.930 --> 10:55.300 signal, or a radar signal, that is also solution of electromagnetic signal. 10:55.300 --> 11:01.820 But all signals are not called modes. Modes are the number of independent solutions minimal 11:01.820 --> 11:05.030 number in which we can express. 11:05.030 --> 11:12.240 Now those who are familiar with set theory, they understand, that basically, this we can 11:12.240 --> 11:19.010 call as a basis set you see, if I have a set of signals, then there is a minimal number 11:19.010 --> 11:26.400 of sets, minimal number of elements, of that set, in terms of which, I can express all 11:26.400 --> 11:32.430 the elements of that set, that set it is called the basis set. Like for electric electrical 11:32.430 --> 11:39.190 signals, Fourier proved, the famous Fourier, by this Fourier theorem, he proved, that you 11:39.190 --> 11:46.060 can take a exponential basis set, to express all sorts of electrical signals. That is why, 11:46.060 --> 11:51.880 today we take, either cos or sin sinusoidal signal, and we analyze that and say, we know 11:51.880 --> 11:55.130 all the signals, because all the signals can be linearly expressed like that. 11:55.130 --> 12:01.990 So, Fourier took a basis set. There is other basis set also possible. Now modes, it is 12:01.990 --> 12:08.290 precise definition is, modes are mutually independent solutions of Maxwell's equation, 12:08.290 --> 12:15.420 such that every possible electromagnetic field configuration can be expressed as a linear 12:15.420 --> 12:28.480 combination of the modes. So, for our landing purpose, if I understand the field distribution 12:28.480 --> 12:32.050 in a mode, then I can construct any signal. 12:32.050 --> 12:42.260 So, my model requires that, what will be these modes field distribution. So, let us come; 12:42.260 --> 12:49.950 obviously, when EM signal is produced, there needs to be a source, that source may be near 12:49.950 --> 12:56.070 the signal, because electromagnetic signal propagates as a wave. So, when I am looking 12:56.070 --> 13:03.430 at the signal the source may be near, may be far away, but to start with one kind of 13:03.430 --> 13:10.930 source is a point source. Now, point source is actually an ideal source, 13:10.930 --> 13:17.411 like the concept of point in geometry, which you know, that it is an abstraction. Similarly 13:17.411 --> 13:24.650 ideal point source, it is an ideal source, it is an abstraction, no real source is a 13:24.650 --> 13:31.730 point source, all distant stars as I showing in the first slide, that you see so many stars, 13:31.730 --> 13:40.470 but, they appear to be us as a somewhat, not point something more, but if you are really 13:40.470 --> 13:46.920 far away, then all distance stars appear as point to our eyes, but if we go closer to 13:46.920 --> 13:55.470 the star, what we see, we see the star, it is a huge size, there are variety of contours, 13:55.470 --> 14:01.060 there are mountains here, there are rivers here, there are caves here, craters here, 14:01.060 --> 14:07.700 etcetera, etcetera. So, any far away distributed source of EM field is considered as a point 14:07.700 --> 14:14.010 source. And if the source is nearby, then we know, what is it is contour. So, we can 14:14.010 --> 14:18.240 say that, it is summation of all those point source. 14:18.240 --> 14:26.910 So, any distributed source nearby, we call it is summation of point source. Now point 14:26.910 --> 14:34.779 source, it radiates equally in all direction. This point, it does not have any preference 14:34.779 --> 14:41.190 of radiation to any particular direction, again I am remind you, that no real source 14:41.190 --> 14:47.710 is a point source. Every real source has a preferred wave of radiating, a preferred direction 14:47.710 --> 14:57.860 in which it radius more than others, but when we idealize or when we point source we defined 14:57.860 --> 15:00.420 as which radiates equally in all directions. 15:00.420 --> 15:06.870 So, these; that means, that has origin there is a point source. So, in all possible directions 15:06.870 --> 15:13.240 you are giving a wave can be seen equally bright in all directions. You have not seen 15:13.240 --> 15:19.910 anything till now, which does like that, but ideally we can say, because if you observed 15:19.910 --> 15:26.860 a distant star, now in the earth if you move reasonable distance, suppose in a region etcetera, 15:26.860 --> 15:32.770 you do not think that there is any change in that; that means, that is, to you to it 15:32.770 --> 15:37.370 is appearing is a point source. But if you really travel far, then you are 15:37.370 --> 15:41.560 travelling much. So, something, suppose from northern hemisphere to southern hemisphere, 15:41.560 --> 15:47.300 if you come then you see that, that is changing. So, we can say that energy is coming equally 15:47.300 --> 15:53.380 in all direction from point source, and people have found out the solutions for that, if 15:53.380 --> 15:59.430 it has been seen that emits spherical waves in all directions. So, if you are center of 15:59.430 --> 16:05.089 a sphere, then the energy is equally going along larger and larger spheres, and coming 16:05.089 --> 16:13.190 to you. At a particular distance from the source, if we connect all the equal amplitude 16:13.190 --> 16:19.090 and equal phase point that mean whose, any field electric field or magnetic field is 16:19.090 --> 16:24.450 equal amplitude and equal phase points if you connect, then the locus become a spherical 16:24.450 --> 16:28.830 surface. So, it is phase front is call spherical so; 16:28.830 --> 16:34.660 that means, when elect any, any point source is emits electromagnetic signal, then, at 16:34.660 --> 16:41.410 a particular distance, if we connect all the equal amplitude and equal phase; that means, 16:41.410 --> 16:47.150 equal signals, where they are then if you connect that that becomes a spherical surface. 16:47.150 --> 16:56.940 That is why we say, that point source emits, spherical waves, in all directions. Now at 16:56.940 --> 17:04.709 a large distance from the source, you know that, sphere, if you go and constructing larger 17:04.709 --> 17:11.890 and larger spheres, now, very large sphere, at a particular place you will see, that the 17:11.890 --> 17:18.329 spherical surface is almost becoming a planer surface. So, that is why we are saying that 17:18.329 --> 17:23.360 at a large distance from the source, this spherical surface becomes appropriately a 17:23.360 --> 17:27.809 plane, then, these waves are called plane waves. 17:27.809 --> 17:33.940 Now, will see plane waves, and or we have already seen plane waves in EM theory. Plane 17:33.940 --> 17:40.080 waves means, in that plane, there are electric field vector, magnetic field vector, they 17:40.080 --> 17:45.639 do not have any variation, there constant over the plane, that is called uniform plane 17:45.639 --> 17:52.539 wave. First plane wave, that all equal amplitude and equal phase points, they are plane, and 17:52.539 --> 17:58.000 then if you have uniform plane wave, which is the variety of plane wave, where they will 17:58.000 --> 18:04.840 have there is no variation in that plane, of the amplitude, or phase of that thing. 18:04.840 --> 18:14.970 So, that plane waves, you have seen already, it solution we have seen in thing, it is that, 18:14.970 --> 18:22.110 cos omega t minus k z type of thing e to the power minus z k z, that thing. So, for plane 18:22.110 --> 18:29.429 waves, you have all also seen that, electric field vector, magnetic field vector, and direction 18:29.429 --> 18:36.200 of EM energy, propagation of EM energy, direction, that form a right handed orthogonal triplet, 18:36.200 --> 18:37.730 these you have already seen. 18:37.730 --> 18:46.659 So, for plane waves this is true. Now, we see the second type of, or another type of 18:46.659 --> 18:52.789 source, instead of point source, suppose we have all these are abstractions, but it will 18:52.789 --> 18:59.299 help you to understand, what is the source? And how it radiates? Suppose we have, an infinite 18:59.299 --> 19:07.169 sheet of, surface current source; that means, a whole plane, where we have, a one directed 19:07.169 --> 19:13.369 surface current, it is call sheet of surface source. So, here we have taken that, in the 19:13.369 --> 19:21.500 z is equal to 0 plane, the sheet of surface current source is So, what we have written 19:21.500 --> 19:26.399 that not only point sources, some other sources also can produce waves whose electric and 19:26.399 --> 19:31.149 magnetic field, field vectors, both are orthogonal to the wave propagation direction. 19:31.149 --> 19:36.970 So, consider an infinite sheet of conducting surface, current density, let us call that, 19:36.970 --> 19:42.539 surface current density, J s and consider; obviously, since we have talking of electromagnetic 19:42.539 --> 19:49.210 field; that means, this is not a DC current, it is an AC current, that is why I am writing 19:49.210 --> 19:54.799 considered time varying j s, the surface current density is time varying, it has a time function 19:54.799 --> 20:03.280 it is depend function of t and also for simplicity I have assumed that it is in the x y plane, 20:03.280 --> 20:10.149 it is x directed. It can lie in any direction, but we can orient our x y thing. So, that 20:10.149 --> 20:19.100 for a simplicity, it comes x directed thing. Now, since you see the source, these source, 20:19.100 --> 20:25.010 it is an infinite source, though my drawing does not represent that, but in x y plane, 20:25.010 --> 20:32.870 it has an infinite variation. Actually there is an x, here you see, this is x, though I 20:32.870 --> 20:40.450 do not think it has mixed with the contour. So, in x y plane, it is infinite. So, since 20:40.450 --> 20:45.929 it is infinite and you know that if there is an electric, there is a conduction current; 20:45.929 --> 20:56.070 that means, in that direction there are the electric field also. So, it j s is in a x 20:56.070 --> 21:00.470 direction; obviously, the electric field will also be in the x direction, but since there 21:00.470 --> 21:07.649 is no variation in the whole infinite plane, in either x or y, please remember that it 21:07.649 --> 21:12.970 may be x directed the current is x directed electric field is also x directed, but they 21:12.970 --> 21:17.850 do not have any variation, because the whole source does not have any variation, in the 21:17.850 --> 21:22.779 neither x or y direction. But if definitely has a variation in the z 21:22.779 --> 21:30.749 direction, because suddenly it is here, just as z is equal to 0 minus, it is not there 21:30.749 --> 21:36.620 at z is equal to 0 plus it is not there. So, it has a variation only in the z direction, 21:36.620 --> 21:40.259 but in x or y direction, it does not have any variation. 21:40.259 --> 21:47.980 So, this type of source, due to the discontinuity as was saying in the z is equal to 0 plane, 21:47.980 --> 21:53.519 there will be EM waves propagating away, from the source in plus minus z direction. This, 21:53.519 --> 21:58.870 we will always remember, that if there is any source has a discontinuity, that it is 21:58.870 --> 22:04.230 suddenly there, and then not there, then it will radiates. So, it will radiate; obviously, 22:04.230 --> 22:11.340 in plus minus z direction and already we have discussed that the electric field is x directed 22:11.340 --> 22:19.730 the movement electric, the propagation of wave or propagation of energy is in z direction. 22:19.730 --> 22:27.249 Now, let us put the, you all know boundary conditions of electromagnetic fields. So, 22:27.249 --> 22:35.750 boundary condition at z is equal to 0, if we apply, we know that, what this is saying, 22:35.750 --> 22:43.429 you know n is a normal vector. So, n cross e 2 minus e 1; that means, what tangential 22:43.429 --> 22:48.739 component should be continuous tangential component of the electric field should be 22:48.739 --> 22:56.259 continuous, that is the boundary condition one of electromagnetic field. Similarly, the 22:56.259 --> 23:04.649 tangential component of magnetic field n cross h 2 minus h 1 that is discontinuous and the 23:04.649 --> 23:09.790 amount of discontinuity is the surface current density. It is the second boundary condition 23:09.790 --> 23:17.389 of electromagnetic field in our particular case, n is the outward normal. So, n is positive 23:17.389 --> 23:24.869 a z directed and e 1, h 1, we are calling it is the electric and magnetic field in region 23:24.869 --> 23:33.190 one, region one we are defining as, z less than 0; that means, below the current sheet, 23:33.190 --> 23:38.960 and z greater than 0 is above the current sheet, where the fields are e 2, h 2, that 23:38.960 --> 23:44.950 is why we have written this boundary condition. Now, to satisfy this boundary condition n 23:44.950 --> 23:57.059 is a z. So, a z cross e 2 minus e 2, we know that, e 2 minus e 1 will come, then the h 23:57.059 --> 24:06.279 2 minus h 2. So, a z cross these, is equal to some a x component so; obviously, it says 24:06.279 --> 24:12.179 that, h 2 and h y, they must have y component, simple mathematics. 24:12.179 --> 24:23.980 So, we can write the fields as E 1 that will be equal to, in a x directed, and then we 24:23.980 --> 24:33.730 assume some amplitude a, first we assume, since h 1 is y directed. So, H 1, let us assume, 24:33.730 --> 24:39.020 in the lower one, you see, to satisfy that equation, lower one it will be minus. So, 24:39.020 --> 24:44.999 minus a y, a is some amplitude, then we know that the field is propagating in z direction, 24:44.999 --> 24:53.909 means, it is variation will be e to the power j k naught z, and E 1 and H 1, we know, that 24:53.909 --> 24:59.549 always they are related by the wave impedance, in free space it is propagating eta naught, 24:59.549 --> 25:04.760 by intrinsic impedance of free space. So, they, e 1 will be like this. 25:04.760 --> 25:11.299 Similarly, at z greater than 0, we can write H 2 and E 2m some other constant, b amplitude, 25:11.299 --> 25:20.151 and some other constant, b here. So, a b needs to be found out. So, to satisfy boundary condition 25:20.151 --> 25:29.470 one, we get a is equal b to satisfy boundary condition two, you get this. So, solving we 25:29.470 --> 25:35.110 get that a and b, their values we get. So, by that, we can find out, that there is an 25:35.110 --> 25:41.690 electromagnetic field. So, we see that it also produces the surface current, infinite 25:41.690 --> 25:47.519 surface current, that produces and electric field, so that you can have, the propagation 25:47.519 --> 25:50.759 in the plus minus z direction. 25:50.759 --> 25:58.230 Now, so, in this case also, you see that we have, electric and magnetic field vectors, 25:58.230 --> 26:05.851 both are orthogonal to the wave propagation direction z. So, you see that, e and h, they 26:05.851 --> 26:11.960 are all lying in x y plane, the wave is going in z direction, the e and h will does not 26:11.960 --> 26:20.359 have any component in the propagation direction. This is the first mode that we introduced, 26:20.359 --> 26:30.539 that if and both the electric and magnetic field, they are lying on the transverse plane; 26:30.539 --> 26:36.859 that means, transverse to the direction of propagation, then we call that has TEM mode, 26:36.859 --> 26:43.119 or transverse electromagnetic modes, to any propagation direction, one can draw infinite 26:43.119 --> 26:51.870 number of perpendiculars; that means, if you have any direction to that, you can draw a 26:51.870 --> 26:55.340 perpendicular, draw perpendicular. 26:55.340 --> 27:01.080 So, all these are perpendiculars, to it, you can have many, because with these I can have 27:01.080 --> 27:09.090 these as a perpendicular, with that I can have other perpendiculars also. 27:09.090 --> 27:17.460 So, but all these perpendiculars, they will lie a plane, that is in this transverse plane, 27:17.460 --> 27:28.280 this plane. So, there any line is perpendicular, and now electric field vector can lie along 27:28.280 --> 27:33.609 any of these infinite number of perpendiculars. Now in the transverse plane, we can always 27:33.609 --> 27:39.179 find in a plane we can find always a couple, another perpendicular, two perpendicular couple 27:39.179 --> 27:44.989 we can always locate. So, along the perpendicular to the electric plane, we can always locate 27:44.989 --> 27:53.019 another perpendicular, which is a magnetic field vector. So, these TEM wave is a mode. 27:53.019 --> 28:00.749 In a guided structure, like in normal transmission line, this mode propagates, in unguided fields; 28:00.749 --> 28:09.619 that means, when we radiate by antennas, then at a far off distance from the antenna this 28:09.619 --> 28:15.379 is becomes a TEM wave, that we have discussed that, from that stars, when we are far away, 28:15.379 --> 28:22.039 they becomes plane waves plane waves are an example of TEM mode but, reverse is not true 28:22.039 --> 28:26.760 apart from plane waves also, there are many examples of TEM wave field distribution. 28:26.760 --> 28:31.100 So, any antenna is a distribution of point sources, where at a far off distance from 28:31.100 --> 28:37.210 the antenna the radiated fields show TEM mode field distribution. This is the TEM mode field 28:37.210 --> 28:42.629 distribution you see, that it is in a coaxial line we get this type of distribution, here 28:42.629 --> 28:49.129 you see that we have so many all the elec this only one electric field I am showing, 28:49.129 --> 28:53.799 it is entirely in the x y plane the propagation is taking place in the z direction. 28:53.799 --> 28:58.440 So, it is the magnitude is changing as you see from the color plot, but it is changing. 28:58.440 --> 29:05.159 So, you see if we look in the z direction, this is z direction the in a transverse plane, 29:05.159 --> 29:10.739 there is no z component. So, this is an example of a TEM field distribution. 29:10.739 --> 29:18.470 Now, let us see an infinite line source. So, this z directed line source, a, instead of 29:18.470 --> 29:25.610 infinite sheet of current which produces TEM waves, we are now seeing an infinite line 29:25.610 --> 29:33.220 source. So, the source is a line infinite line I L, let us call. 29:33.220 --> 29:39.729 Now in the z plane will be the transverse plane to this. Consider an infinitely long 29:39.729 --> 29:44.909 conducting line current source no magnetic field can exist along this infinite line source 29:44.909 --> 29:51.379 that is Biot Savart law or Maxwell’s law. That you, if you have a current source, magnetic 29:51.379 --> 29:56.081 field is always perpendicular to the; that means, in the along this line source, there 29:56.081 --> 30:00.280 is no magnetic field component. So, where is the magnetic field vector then, it should 30:00.280 --> 30:06.570 lie along the transverse plane; that means, that z is equal to 0 plane. So, magnetic field 30:06.570 --> 30:14.570 should lie there, now electric field vector can be anything, but, you have already seen 30:14.570 --> 30:20.220 TEM case. So, we say that, they are both the electric 30:20.220 --> 30:25.350 field vector, and magnetic field, field vector was in the perpendicular plane. Here we say 30:25.350 --> 30:31.009 that since we are trying to see, whether another mode is possible and another solution of Maxwells 30:31.009 --> 30:36.850 equation, in another independent solution is possible. So, that is why we are checking 30:36.850 --> 30:41.119 that electric field vector should not be lying entirely in this plane, because if it lies 30:41.119 --> 30:46.989 entirely in this plane, that is the TEM case. So, if it is in this plane, we are going back 30:46.989 --> 30:51.409 to the TEM case. So, we have trying to say another fundamental variety of mode. 30:51.409 --> 30:58.649 So, electric field vector should have a component in this transverse plane as well as some component 30:58.649 --> 31:06.179 along the line source direction. So, this mode is called transverse magnetic; that means 31:06.179 --> 31:13.200 magnetic field is entirely in a plane and if you do the mathematics this line source 31:13.200 --> 31:19.039 gives that TEM mode. It does not give any TEM mode. The energy is propagating, how energy 31:19.039 --> 31:26.009 is propagating? If you consider that, considering that line current has an axis, if you consider 31:26.009 --> 31:31.559 a cylinder throughout that cylinder surface, the energy is propagating. These waves are 31:31.559 --> 31:33.869 called cylindrical waves. 31:33.869 --> 31:40.159 Their field distribution is TEM field distribution, this is a TEM field distribution, this comes 31:40.159 --> 31:46.200 in, we will see later, in circular type of guides not coaxial cable; that means; only 31:46.200 --> 31:55.210 one conductor is here. So, in a hollow metallic pipe, cylindrical pipe, you see electric field 31:55.210 --> 32:01.869 vector, it is like this, also electric field vector, we are showing in the any between 32:01.869 --> 32:08.269 thing at x is equal 0, it has a longitudinal component. This is an example of a transverse 32:08.269 --> 32:10.409 magnetic mode. 32:10.409 --> 32:17.979 Now consider another example, that instead of that line source, let us make a loop, infinite 32:17.979 --> 32:25.919 loop of current, current carrying I. So, consider an infinite loop. 32:25.919 --> 32:31.210 Obviously, the electric field will be azimuthal, you see at every point electric field is, 32:31.210 --> 32:35.309 because it should be in the direction of this conduction current, there is a conduction 32:35.309 --> 32:41.629 current here. So, it is in the e 5 direction, that is called azimuthal and entirely lying 32:41.629 --> 32:47.190 in the z 0 plane, you see here, e 5, all are lying in the z is equal to 0 plane. 32:47.190 --> 32:51.720 So, the magnetic field vector should not be lying entirely in this plane, why, because 32:51.720 --> 32:57.309 then we are going back to the TEM case, again that same logic. So, magnetic will should 32:57.309 --> 33:04.159 have a component in the transverse plane and also some component along the z direction. 33:04.159 --> 33:09.200 These waves are called TE Modes their field distribution is like this. This come, we will 33:09.200 --> 33:11.330 see, in wave guides. 33:11.330 --> 33:18.080 You are familiar with that, that it is a example of a TE 1 0 mode this type of various modes, 33:18.080 --> 33:22.119 but all of them, they have that you see in the transverse plane the electric field is 33:22.119 --> 33:30.499 lying, we are seeing in a longitudinal plane, you see it is basically the wave guide. Between 33:30.499 --> 33:36.059 that, if we can see, will see that field distribution will like this there is no component which 33:36.059 --> 33:38.429 is in the z direction. 33:38.429 --> 33:46.320 So, electric field is entirely in the transverse direction, and as I was saying that, with 33:46.320 --> 33:52.730 mixing these type of various modes, you see three TEM t type of electric field distribution, 33:52.730 --> 33:56.980 if they are mixed, then you get a field distribution like this. 33:56.980 --> 34:05.190 So, all these various things, but all are linear combinations of these modes. So, a 34:05.190 --> 34:11.869 particular field may be, suppose when in a coaxial line, transmission line, you can have 34:11.869 --> 34:17.480 all the modes possible, TEM, TE, TM, all the them can be possible. In wave guides, you 34:17.480 --> 34:22.360 cannot have TEM and if you see the actual field distribution, you will see something 34:22.360 --> 34:27.700 haphazard, but if you break it into this components you will then understand, that how much of 34:27.700 --> 34:35.770 T, how much of TEM, and which type of T also have various with numbers, this two numbers, 34:35.770 --> 34:40.850 they are giving two dimensional modes. So, various numbers are possible. So, with that 34:40.850 --> 34:46.330 you get all the real life signals. So, if you understand modes, you can easily 34:46.330 --> 34:52.100 a break the fields in to these modes, and then your analysis will precede. So, that 34:52.100 --> 34:57.960 was our first lecture, that what is the concept of mode. I think I have tried to make you 34:57.960 --> 35:03.060 understand, that there are 3 fundamental modes, TEM, TE and T0, and where from they come, 35:03.060 --> 35:08.100 have given you examples, that which type of sources can produce a pure of that variety. 35:08.100 --> 35:14.400 In real life, you have a source which is mixture, of all these various sources I have shown. 35:14.400 --> 35:20.550 So, with that they produce various types of TEM, TE, and T0. Now we need a supporting 35:20.550 --> 35:27.090 structure which can carry that. So, that energy will be coming from transmitted to receiver 35:27.090 --> 35:30.690 that will see, one by one in the next lecture. Thank you.