Consider a Wilkinson power divider with the common node labeled as Port 1 and the two other nodes labeled as Ports 2 and 3.

a)Show that if a₂=a₃, then b₂=b₃=0, and, and no power is dissipated in the resistor. This is Wilkinson power divider which is used as a power combiner.

b)Calculate b₁, b₂ and b₃ if a₂=1 and, where beta is given in radians (all ports are matched).

c) Use Matlab to plot the contours of 3 dB minus 0.0, 0.3, 0.6 dB loss of |b₁|² for different values of and (a₂=1). The x-axis is and the y-axis is in radians. The 3 dB-0.0 dB contour must pass by the point of with =1 and =0.