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 f and ignoring excess losses, what are the possible power levels Pi at the outputs? For each Pi how many outputs Ni have power level Pi-k
c) Derive the expression for Pi and Ni for a n x n coupler, where n = 2 for some integer k.