Recombinant 3-Way Wilkinson | Qucs-S S-parameter Viewer Documentation

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# Recombinant 3-Way Wilkinson

## Overview

Alternative 3-way equal-split power divider using a recombinant topology with crossed branches. Features two-stage design with unique impedance distribution providing excellent isolation and balanced power split. Optimized coefficients provide good bandwidth with predictable performance.

## Topology

                                           ┌─[Z2, λ/4]──────[Z2, λ/4]── Output #1
                                           |            |
                         ┌─[Z2, λ/4]───────|           [R2]
                         │            |    |            |
                         │            |    |            |
    Input ─[Z1, λ/4]─────┤           [R1]  └─[Z3, λ/4]──|
                         │            |                 |
                         │            |    ┌─[Z3, λ/4]──────[Z2, λ/4]── Output #2
                         │            |    |            |
                         └─[Z2, λ/4]────────           [R2]
                                           |            |
                                           └─[Z2, λ/4]──|───[Z2, λ/4]── Output #3

Key features:

- Input branch Z₁ splits into two paths

- Upper and lower branches cross in recombinant structure

- Two isolation resistors (R1, R2)

- Three stages per complete path

- Equal power to three outputs

## Design Equations (Equal Split)

### Impedances

    Z₁ = 0.72 × Z₀    (input section)
    Z₂ = 0.80 × Z₀    (first split sections)
    Z₃ = 0.80 × Z₀    (upper recombinant)
    Z₄ = 1.60 × Z₀    (middle path)
    Z₅ = 0.80 × Z₀    (output matching)
    Z₆ = 1.60 × Z₀    (lower recombinant)

    R₁ = Z₀           (first isolation)
    R₂ = 2 × Z₀       (second isolation)

For Z₀ = 50 Ω:

Parameter | Value
--- | ---
Z₁ | 36 Ω
Z₂ = Z₃ = Z₅ | 40 Ω
Z₄ = Z₆ | 80 Ω

All transmission lines: λ/4 at f₀

## References

[1] “A recombinant in-phase power divider”, IEEE Trans. Microwave Theory Tech., vol. MTT-39, Aug. 1991, pp. 1438-1440

[2] “Power combiners, impedance transformers and directional couplers: part II”. Andrei Grebennikov. High Frequency Electronics. 2008

## See Also

- RF Circuit Synthesis Tools