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# Wilkinson power divider

Microwave Engineering concerns the application of physics to design systems that contain and process microwave energy for useful means. For example communication links, cell phones and microwave ovens.

Power splitters are devices that allow a microwave signal to be split equally between two or more branches. These devices allow signals to be distributed and processed as needed.

The Wilkinson Power Divider, named after Ernest J. Wilkinson, is a lossy N-port network commonly used for power splitting and combining. The Wilkinson power divider is especially useful because the output ports are simultaneously isolated and matched. The S matrix for the common case of a 2-way equal-split Wilkinson power divider at the design frequency is given by

$[S]=\frac{-j}{\sqrt{2}}\begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ \end{bmatrix}$

Inspection of the S matrix reveals that the network is reciprocal (Sij = Sji), that the terminals are matched (S11,S22,S33 = 0), that the output terminals are isolated (S23,S32=0), and that equal power division is achieved (S21 = S31). The non-unitary matrix results from the fact that the network is lossy.

Interestingly, no loss occurs when the signals at ports 2 and 3 are in phase.

## References

1. D. M. Pozar, Microwave Engineering, Third Edition, John Wiley & Sons, Inc., N.J. 2005.

2. E. Wilkinson, "An N-Way Hybrid Power Divider," IRE Trans. on Microwave Theory and Techniques, vol. MTT-8, pp. 116-118, January 1960.

3. K. W. Whites, EE 481 Lecture Notes, September 2004.

4. R. E. Collin, Foundations for Microwave Engineering, Second Edition, IEEE Press, N.Y. 2001