Hello friends welcome to engineering Funda family in this video I'll explain you two element antenna array in my last video I have explained n element antenna array if you have seen that video then in that I have derived electric field equation for n element antenna array and based on electric field equation I have explained you aray factor calculation in this video I'll explain you calculation of electric field and array factor for Two element antenna array so here you can observe we have two element antenna array this is element number one that is reference element and this is element number two here reference element that is connected with zero phase and the second element that is provided with phase of alpha here these two are amplifier and here we have power divider circuit so here this two elements that is radiating in space let us assume this antenna elements are radiating in this Direction let us assume it is radiating in this direction and this is antenna axis this is antenna axis with respect to antenna axis let us say this angle is Theta so but obviously this angle is also Theta Here If You observe this element which is reference element so that is radiating in this direction even this element is radiating in this direction but this element that is leading by some phase as it is radiating in this direction but obviously signal from here will take less time compared to signal from this end so here see this antenna that will be leading by some phase this antenna that will lead by some phase and this antenna that will lag by some phase now what is that phase difference if you want to calculate that phase difference then here you will have to have normal see from this line you need to have normal So based on this triangle we can identify this path difference and based on this path difference we can identify phase difference if You observe this angle is Theta this is diagonal that is having spacing D so this path difference that is D cos Theta so here path difference in between these two antenna element that is D cos Theta based on path difference we can identify phase difference over here see for Lambda distance phase difference is 2 pi so for D cos Theta how much phase difference is there so for D cos Theta distance phase difference will be 2 pi by Lambda into D cos Theta right the reason is for Lambda distance phase difference is 2 pi so for D cos Theta distance how much phase difference is there D cos Theta into 2 pi by Lambda right so phase difference over here that is 2 pi by Lambda into D cos Theta and if You observe here with second antenna element we are connected with phase of alpha that is initial phase so here I need to add that initial phase as well so phase difference is s that is 2 pi by Lambda into D cos + Alpha so this sign this value of s that is 2 pi by Lambda is beta D cos Theta + Alpha so now we have phase difference that is beta D cos Theta + Alpha now here see with this antenna structure with this antenna structure if I consider here we have origin if I consider here we have origin o so so what will happen as if origin o is available over here then this antenna element that will be leading by how much phase it will be leading by S by 2 phase and this antenna element that will be lagging by how much space s by 2 right so this antenna element that will leads by S by 2 phase and this antenna element that will lags by S by 2 phase So based on that one can understand calculation of electric field see if I say this antenna element that is having electric field E1 so that has to be e into e to the power plus j s by 2 where here this antenna element is leading phase by S by 2 with respect to origin and this antenna element if I say it is having electric field E2 so that is e into e^ minus j s by 2 the reason is here this antenna element that is lagging phase by S by 2 with respect to origin total phase is s over here right so based on this two electric field one can identify total electric field so total electric field that is algebraic sum of electric field due to element one and electric field due to element 2 so if you take e not common over here then we will be having e the power j s by 2+ e^ minus j s by 2 that is total electric field if you multiply and divide two over here then this is cos sin by 2 right so you can say total electric field that is 2 e into COS of s by 2 right so here now we have total electric field equation that is 2 e COS of s by 2 right and based on this total electric field we can identify a factor what is AR factor a factor is total electric field divide by electric field due to one element right so let us identify a factor first so here totally electric field that is 2 e cos sin by 2 right and electric field due to one element that is e not over here so this e not that is getting cancelled over here so RF Factor will be 2 cos of s by 2 over here where value of s is how much value of s is beta D cos Theta + Alpha right so value of s that is beta D cos Theta + Alpha so here we have calculated two things one is total electric field and second is a factor and in this one should know s is beta D cos Theta + Alpha right now you might be thinking like why I'm deriving it in this way already I have derived electric field and AR factor for n element if you have seen that see I have already derived electric field and r factor for n element So based on this directly we can identify r factor why should we go for derivation so if you take this r factor then also we can derive same equation let me show it to you see for n element a factor is how much for n elements r factor is s of n s by 2 / s of s by 2 that is what I have derived in my last video now see based on this one can identify this equation of AR Factor where if you keep n isal to 2 then we can have AR factor of two elements that will be S of 2 * of s by 2 divid by S of s by 2 see s of 2 Theta that is 2 sin Theta cos Theta right so if you substitute that equation over here then you'll be having 2 * of s of sin by 2 into COS of s by 2 divide by S of s by 2 where see this s of s by 2 that is getting cancelled and will be having error factor for Two element that is 2 * of COS of s by 2 so this is what the equation this is what the equation which I have derived over here by basic standard process right so from n element even one can derive same thing as I have shown it to you over here right and based on this aror Factor one can identify many other parameters like location of Maxima location of Minima half power beam width first null beam width so all those things that I'll be going to explain you in next coming videos still if anything that you like to share then note it down in comment section I'll be happy to help you thank you so much for watching this video