Gysel Power Divider | Qucs-S S-parameter Viewer Documentation

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# Gysel Power Divider

## Overview

High-power divider topology with grounded isolation resistors for superior thermal management. Maintains Wilkinson-like performance (matched ports, high isolation) while enabling significantly higher power handling through direct heat-sinking of resistors to ground plane.

## Topology

    Output1 ──────┬──────[Z0, λ/4]──────┬─── R0
                  │                     │
               [Z1, λ/4]                │
                  │                     │
    Input ────────|                 [Z4, λ/2]
                  |                     │
               [Z1, λ/4]                │
                  │                     │
    Output2 ──────┴──────[Z0, λ/4]──────┴─── R0

Key features:

- Two λ/4 input branches at Z₁

- One λ/2 center line at Z₄

- Two λ/4 output lines at Z₀

- Two grounded isolation resistors R

## Design Equations

    Z₁ = √2 × Z₀ ≈ 1.414 × Z₀    (input quarter-wave arms)
    Z₄ = Z₀ / √2 ≈ 0.707 × Z₀    (center half-wave line)
    R = Z₀                         (grounded resistors)

For Z₀ = 50 Ω:

Parameter | Value
--- | ---
Z₁ | 70.7 Ω
Z₄ | 35.4 Ω
R | 50 Ω

## Advantages Over Wilkinson

1. Grounded resistors:

   - Direct thermal path to ground plane

   - Easy heat-sinking (metal slug, thermal vias)

## Limitations

1. Larger size: λ/2 center section makes it bigger

   - Gysel: ~1.5× area of Wilkinson

2. More complex: Five transmission lines vs. two

3. Unequal split difficult

4. Cost: Slightly more expensive (more PCB area, complexity)

## Comparison with Wilkinson

Feature | Gysel | Wilkinson
--- | --- | ---
Power handling | Very high | Moderate
Resistors | Grounded (2) | Floating (1)
Thermal management | Excellent | Poor
Size | Larger (λ/2 section) | Smaller
Complexity | More complex (5 TL) | Simple (2 TL)
Isolation | 20-30 dB | 20-30 dB
Bandwidth | 20-30% | 20-40%
Match | Excellent | Excellent
Cost | Higher | Lower
Unequal split | Difficult | Easy
Best for | High power | General use

## References

[1] Gysel, U. H. (1975). “A New N-Way Power Divider/Combiner Suitable for High-Power Applications.” IEEE MTT-S Int. Microwave Symp. Digest, pp. 116-118.

## See Also

- RF Circuit Synthesis Tools