this is part two of the introduction lecture of the introduction to radar systems course in the first part just to recapitulate the last view graph of the first part we went over how electromagnetic waves are propagated they consist of an electric field and a magnetic field that located right angles one to the other and the direction of propagation of the electromagnetic beam is perpendicular to those two vectors and here you see a little movie of visualization of the propagation of an electromagnetic wave we also introduced the concept of polarization of vertical and horizontal polarization where vertical polarization is when the electric field moves up and down vertically and horizontally polarized when the electric field vector of the electromagnetic wave moves horizontally now let's continue the radar bands over that region from one say up to above excuse me you can see here above the wavelength and frequency for the whole region of the electromagnetic spectrum from wavelengths of 1 kilometer down to one nanometer that's a thousandth of a millionth of a meter a billionth of a meter and from a frequency of one megahertz just up to over a million million Hertz ok way past the visible spectrum in this area from here to here is the portion of the electromagnetic spectrum that radar operates at okay here we have it blown up down here it's roughly we're blowing up the region from 1 to 12 gigahertz and we have some other frequency bands that are notated by these letters that are up in the sixteen thirty five and ninety five gigahertz region now the areas that are colored are the portions of the electromagnetic spectrum that are allocated for use in radar law for use of radar these allocations are made by the International Telecommunication Union and these allocations are made so that one usage doesn't event of the electromagnetic spectrum doesn't interfere with another usage and historically for a long period of time radar has operated in these bands in the early days of radar these bands were given letter nomenclature l-band being at about 1. 25 sent it at one point two five gigahertz you can see here up in the from three to three point seven or eight gigahertz the s-band region and c band is about five and a half gigahertz an X band up in the nine eight and a half to ten and a half gigahertz region and here are the wavelengths that those bands correspond to so the the radars when you hear someone say and if you get used to it we're working with radars and radar people they'll say that radar operates in the X being reagent and pretty quickly you'll learn that the the wavelength is about three centimeters and it's up in this ninety nine to ten gigahertz range and five and a half centimeters and five and a half Giga Hertz's with CBN Dez and roughly Espeon surround three gigahertz with ten centimeters and LB and is about 1. 2 to 1.
3 just in general ballpark terms and 23 centimeters is the number I seem to remember and UHF is it is it's 435 megahertz and VHF is down lower in frequency okay and these correspond to two different wavelengths okay now the I Triple E is the Institute of Electrical electrical and electronic engineers and they have a set of radar standard bands and the in the in that set of standard bands these nomenclature are used for the letter standard for radars that operate in these particular frequency ranges the typical usage of radars that do search as their main and only mission or down at lower frequencies and missile seekers which are would be radars that operate on missiles when missiles have rather small diameters that you're going to need antennas that are very small they in turn and you'll see why need to operate at much higher frequencies and a radars that do both search and tracking functions would tend to operate in this regime and then tracking and fire control radars would operate at these frequencies where you'd be able to get higher resolution and you'll see later on why these they have the higher resolution easy it's easy to obtain at those frequencies now this viewgraph is probably one of the the view graphs that if nothing else in the course you'll end up remembering this view graph because going to see it an awful lot it's a block diagram of how a raid of the different functions performed by a radar and how the radar works it can describe it in pretty simple terms how it works and it breaks down the functions the different functions of the different parts of the radar we call them subsystems instead of the radars of system as a whole it's got a lot of little subsystems and we just like to follow you through what happens when you say turn on a radar and send out a pulse the first thing you do is you have to generate a wave form and then amplify it in the transmitter and then it goes to a switch where that allows the energy the pulse of microwave energy to go out to the antenna but none to leak into the receiver but that it goes out to the antenna and the antenna directs the energy towards the area in space that you'd like to illuminate with microwave energy to look and see if there's a target there the pulse will then go out into the propagating medium the air the atmosphere and and when it hits a target some of the energy will be reflected off that target and the amount of the energy will depend on the effect of electromagnetic size that the electromagnetic wave sees that's called the radar cross-section and that energy will come back a small portion of it to the to the antenna in the meantime the transmitter has been turned off since right after the pulse was transmitted on the and the receiver is listening for echoes okay the farther out the target is the longer it's going to take for the pulse to go out and the echo to come back and so the the delay time before the echo from a target is received is a measure of how father radar is from the target so that antenna collects that very small energy in the millionths of a watt and then it goes into the receiver and then because processing of that data to optimize the ability to detect the target it is much much easier to do digitally and reliably to do digitally that echo is transformed from the analog or continuous domain to the digital of domain with an analog to digital converter and those samples from the analog at the digit digital converter sampled at each little moment of time in range or in time-delay then go into a signal processor where the target echo is processed to get the best resolution you can out of that received pulse a process called pulse compression to optimally process the data and also to look and see if the frequency of the return echo has been shifted and if it does and we'll get in a minute to what that means you'll be able to measure directly the velocity of the target they'll separate it from unwanted backgrounds so we'll also do in the signal processor the process called signal processing then the data will go into this digital data will go into a detection process where we'll look and see what targets are higher than a threshold size which ones we should say are which echoes ah ha that's probably a target and then we'll go into a process called tracking and parameter estimation where we'll keep track from one set of pulses to another of targets detections and correlate them from one scan of the radar to another one set of pulses so that we can say that indeed this set of detections at these different times are all from the same actual physical entity out in space and get a really good estimate of the range and bearing and velocity and motion of that target and then that data is displayed on a console a digital display usually these days and also the data is recorded so that we can understand later what's been going on with the radar now all of these different boxes are very important and the rest of the course what we're going to be doing after this introductory lecture is focusing on each of these different pieces of the radar one at a time and in a sense we've gone over it we'll go over each of these blocks with one or two view graphs in this introductory lecture but then in the lectures that follow each one of those little pieces like for instance the doppler processing portion will be a whole lecture the antennas will be a whole lecture the target cross that the target cross-section properties of different targets will be a whole lecture understanding the propagation medium will be a whole lunch of detection etc etc and that will build up your knowledge from starting with the idea this is a radar now this is a block diagram and lastly one other lecture which is actually going to be the second lecture is how does this all fit together you know the prop how do we build a radar that has the right properties the right power the right sizing antennas so that it will be able to see targets out say aircraft out 200 miles how do you know what power the equation that relates all those properties of the target and the radar and how far away you can detect and that sort of thing it's called the radar equation and it's an essential element of how we build radars and we'll be doing it we'll be studying that in the next lecture ok now let's go over that point the radar equation just for a moment here we this example we have a radar located on a ship and it the two key parameters that tell you how your ability to see target sea of power in your aperture you know the aperture is the size of the antenna it's dying and the transmitted power more power you've got great and the bigger your aperture the more you'll be able to focus that energy to hit a target you know we ought to collect it to receive the the reflected echo so we transmit a pulse out we've got a target here with a radar crush cross section Sigma and then we have a distance from the radar to the target now what in rough terms how much energy do we get back given all these properties okay first we've got you know you're going to get more received energy back if you increase the radar power so we've got a term in there the transmit power and then we've got another term which is the gain of the transmitting antenna which is four PI a over lambda squared is the gain of that antenna that's how much the directivity you get over isentropic and then we have a spreading factor that is because as the energy goes out it drops off the the energy density drops off as one over R squared and that has to be factored in and then all throughout this process of transmitting hitting the target and receiving there are a set of losses things which are inefficiencies in the radar that are just I call it the humanity of the radar that you lose energy when you go from the physical transmitter to the antenna because you send that energy through wave guides and the wave guide is if the energy goes through it heats up a little bit you lose some energy there's going to be energy loss and the attenuation and the atmosphere there's going to be all kinds of different loss ISM we'll get into them later in detail when we study the radar equation but you have to say you know divided by those losses to find out that receiving energy then the greater the cross-section of the target the more power that will be received so that's a multiplied and then for the there's another spread factor of one over R squared because that and reflected echo is going to be sent back to the radar and it's gonna that you'll have that energy density of the echo is going to spread out okay and then the bigger your antenna that they get your antenna will be able to receive that energy so there's another factor a and then the longer you listen you're able to listen for the target the more power you'll get in your receiver so these are all the components that don't come into play to say how much received energy we get we're going to spend a whole lecture on this radar on the radar equation in general now there's a fundamental term which we quantity which we use to describe how powerful the ability of the radar to detect targets and it's it's the received signal energy over the received noise energy okay and here we have a visualization of what could be the the what their receiver hears as a function of time from one you know from it could be from it just it just listens a pulse went out and then what do we hear well you're going to hear the ambient noise noise that's generated in the receiver just because it's at room temperature there'll be the the antenna will collect microwave galactic noise it'll collect noise from power lines man-made effects all kinds of different we'll get into that later but there is noise back there that has nothing to do with a real target and then there'll be a received signal from the target you know after the pulse goes out hits the target and comes back you'll have a received signal and the signal to noise ratio is the ratio of the received signal energy to the nuez energy and that's how we characterize and you and you typically want a signal-to-noise ratio that's about twenty to one you know like you'd like it to be about twenty to one that's a good number but we'll get into that that's just in it just in a general sense okay there's another issue that comes up when discussing radars and radars to a large extent the domain of electrical engineers during World War two a lot of people who develop rate our physicists but today it's it's an engineering field but a lot of people who work in the radar field studied math or physics or the sciences and they're they write their numbers down in what's called scientific notation on the sort of the ordinary way we write numbers we learn I'd say in grammar school or junior high a number like 1 million four hundred and thirty two point six four eight okay now scientific notation would say you'd write that is one point four times ten to the sixth you know and so if we have a number that's like ten the scientific notation will for that would be ten to the one one times ten to the one you know now in dealing with radars there's a lot of times where we want to look at ratios of powers it might be the ratio of the of the gain of one antenna versus another antenna and engineers have found they like to do rather than dealing with scientific notation where you'd multiply all the the the small numbers between one and ten together and then you add all the exponents of ten they'd like to convert the entire number into a power of 10 and that power is an odd number and they they have a relative that a relative value of two things and they measure it on a logarithmic scale and it's it's an entity called a decibel an example of that is the signal-to-noise ratio when it's expressed in decibels and if you have a number like say 20 okay in its natural units 20 is the ratio of the signal power to the noise power okay if you take the logarithm to the base 10 you get 1. 3 that means 10 to the 1 point 3 power is 20 so you need to take that 1.
