Problem 3: a) Draw a block diagram of an 8X8 coupler built using 2X2 couplers b) Suppose the above device is to be used as an 8-way power splitter (let's say only the top-most input is used). Let the input power be P. Assuming a cross-coupling coefficient of a and ignoring excess losses, what are the possible power levels Pi at the outputs? For each P, how many outputs N have power level P,? c) Derive the expression for P, and Ni for a n x n coupler, where n = 2k for some integer k. Problem 3: a) Draw a block diagram of an 8X8 coupler built using 2X2 couplers b) Suppose the above device is to be used as an 8-way power splitter (let's say only the top-most input is used). Let the input power be P. Assuming a cross-coupling coefficient of a and ignoring excess losses, what are the possible power levels Pi at the outputs? For each P, how many outputs N have power level P,? c) Derive the expression for P, and Ni for a n x n coupler, where n = 2k for some integer k