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.