Fig.3 Wilkinson Power Divider [4]
All ports are matched (S11=S22=S33=0). Terminals are isolated so we have S23=S32=0. Since the power is split equally the insertion loss between port 1to2 and also between ports 3 to1 is same. (|S12| = |S13| =1/√2). S-parameters matrix based on the information above can be written for Wilkinson Power divider as equation (6).
\(\left[s\right]=\frac{-j}{\sqrt{2}}\par \begin{bmatrix}0&1&1\\ 1&0&0\\ 1&0&0\\ \end{bmatrix}\) (6)
The parametric values of Wilkinson Power Divider are calculated from bottom formulas.
\(z_{03}=Z_{0}\sqrt{\frac{1+k^{2}}{k^{3}}}\) (7)
\(z_{o_{2}}=z_{03}k^{2}\) (8)
\(R=Z_{0}\left(k+\frac{1}{k}\right)\) (9)
\(\text{R\ }_{2}=Z_{0}K\) (10)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R}_{3}=\frac{Z_{0}}{K}\)(11)
Since Z0 was chosen to be 50 ohm, Z0 √2 is equal to 70.71 ohm and R is equal to 100 ohm. Line width and length of for 50 ohm was chosen 4.87mm and 18.17mm respectively, for 70.71 ohm width was chosen to be 2.7mm and length 18.5mm.