 Welcome to the session. Today's topic of the discussion is Smithchart and Microwave Frequency Act. My name is Ajit Subash Suryanshi working as assistant professor in Walsh and Institute of Technology. So learning outcome of the today's session is at the end of the session student will able to solve the problem based on the Smithchart. And second outcome is student will able to differentiate different frequency bands or microwave frequency bands and its spectrum and its application. So before proceed further into the session what the knowledge you require for this you should have a knowledge of basic equation and characteristics of the transmission line that is the reflection impedance equation. And it is for the Smithchart and you should have a knowledge of the entire electromagnetic spectrum, Smithchart. So what is mean by the Smithchart? Smithchart is the plot of the reflection coefficient and the reflection coefficient is the complex number. And so this plot is again overlaid with the normalized impedance or normalized admittance. And all of these are plotted on the same graph or on or just the reflection coefficient and the impedance sometimes and reflection coefficient and admittance sometimes. So again I recall for lossless transmission line you will get the input impedance. This is the equation of the input impedance z in is equal to z0. This is the characteristics impedance. This is the load impedance and this is tan beta and beta is the propagation constant. So this is the input impedance of the lossless transmission line. And from this equation we derive this load impedance can be given by z0 1 plus gamma l 1 divided by 1 minus gamma l. So solving this equation you will get the gamma l that is a reflection coefficient which is again a complex number zl minus z0 divided by zl plus z0. So again this equation this is a load impedance. So normalizing means we are dividing that impedance with the z0 that is we are calculating the quantity for per unit characteristics impedance. So that is the meaning of the normalizing. So after normalizing it when you divide it by the z0 you will get the 1 plus gamma l divided by 1 minus gamma l and it is denoted by the small letter r plus or minus jx plus for the inductive load and n minus is for the capacitive load. So this is gamma l zl minus z0. So when you take the z0 common from the numerator and denominator you will get this equation zl minus this equation. Again this is a complex number. So this is this complex number can be represented in the rectangular form and it is in the polar form. This is the rectangular form real and imaginary part and this is the magnitude and the phase part. Again this is equation of the circle with r as we can see this is a radius. So this is a radius 1 upon r plus 1. So r is the normalized resistance and this is a center of your radius. Again solving for the reactance part that is x you will get this equation. Again this is a equation of the circle and this is the equation of the circle with the center at 1 divided by x and radius at the 1 divided by x. So this is a tau l and this gamma l also can be called as a tau l is equal to real part gamma r and j plus gamma i. So this if you represent it on the polar form as you can see this is a circle and in last session we studied that reflection coefficient cannot be greater than 1 if its magnitude is always less than 1. So this is actually the boundary of the reflection coefficient and this is a real part and this is a imaginary part. So this is again the equation of constant resistance circle. So these are called as constant normalized resistance circles. As you can see this r is a small when you put r is equal to 5 in this equation and when you vary the r value that is normalized resistance you will get the different circles having a different radius and centers. So as you can see in this equation for r is equal to 0 let us take this extreme case r is equal to 0 in that case the circle is a unit circle. So this is outer circle is the unit circle and for r is equal to infinity you will get the point you will not get the circle in this equation and when you put r is equal to infinity in this equation. So this equation for reactance part this are the circles having this center and radius is equal to 1 by x. When you plot it you will get the again this consider this to extreme cases when x is equal to 0 in that case you will get the radius is infinity you will get the straight line here straight line passing through this center as you can see this as a diameter of this circle unit circle and this is again take this case of the x is equal to infinity again it is a point it is not a circle. So for x is equal to 1 you will get the circle. So this is circle have a center point at 1 comma 1 as you can see 1 comma 1 and radius is 1. So this circle will be a radius of 1. So these are the smith chart graph. When you combine this normal resistance normalized resistance and normalized reactance in a unit circle of as a reflection coefficient cannot be a greater cannot be greater than 1 it is always less than or equal to at max it is a 1 for the complete reflection. So when you combine this you will get something like this the smith chart. So in this smith chart you can observe this is a real axis and this is the imaginary axis of the reflection coefficient and these are the black lines are for the constant resistance and red lines are for the constant. Again this is a problem for solving this coefficient coefficient as you can see this is for this load and characteristics impedance 50 ohm. So this blue line is indicating the magnitude and this orange line actually orange is giving the phase. So this is a complex number again. So as you can see when he normalized it we will get the r is equal to 1, x is equal to 1, r is equal to 1 is this circle this black circle and x is equal to 1 this red circle. So point of interaction between these two is this one as you can see here. So can you reverse that process in that if the impedance of the transmission line is given and you can find out the reflection coefficient or a reflection coefficient is given you have to find out the impedance of the transmission line. If yes write down that procedure. So I already discussed that procedure for finding the reflection coefficient if the impedance is given. So you have to just reverse the process and write down your procedure to find out the impedance from the Smith chart. So this is a electromagnetic spectrum as you can see this is a visible spectrum it is entire spectrum from the gamma rays from the lower frequency. So starting with the electromagnetic fifths and these are the microwave band as you can see. So these are the lower frequency band and these are the higher frequency band and in between infrared and ultraviolet there is a visible spectrum as you can see and the temperature is also increases with the increase in the frequency. You can see this in this. So microwave so what is mean by the micro microwave is the pant ranging from the 1300 megahertz to a 300 gigahertz which corresponds to wavelength 1 meter to 1 millimeter. So microwave transmit in the line of sight or it is always travels in the straight line path and it is affected significantly by the moisture in the atmosphere and it is reflected by the metal surface and partial transmission in the dielectrics which are not metals. So that's why the micro communication is limited to the 48 to 64 kilometer that is visual horizon or a line of sight communication. So these are the different microwave band as I have told you the range of the microwave band is from the 300 megahertz to 300 gigahertz. So in this range these are the different bands as you can see L band to the D band F band. So different band have a different application and its uses and these are the L band have a as you can see this is military military purpose it is used for the military telemetry process and GPS and mobile phones. So this L band is used for the mobile phone as you can see and as we also the F band can be used here for the wireless LAN. So F band have a higher frequency and as you can see in this band different band D band have a highest microwave frequency as compared to the L band. So each have a different application and uses. So microwave has apps or so what are the how it is affecting the microwaves. So microwave affecting the two ways it is first way is the normal thermal and thermal. So non-thermal way it is very difficult to find out but thermal can be found out with the cell phone radiation effect. So by observing the thermal image you can see this. This is a normal thermographic image as you can see without a cell phone and this green light is the cooler areas and L1 is the higher bit temperature. But after using a 15 minutes of the cell phone talking on the cell phone as you can see this become a red. So it get heated. So it has a detrimental effect on the health. So these are the one of the aspects of the affecting how the microwaves is affecting our on our health. These are the references. Thank you.