RF Power Combining/Dividing Design Tool | Qucs-S S-parameter Viewer Documentation

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# RF Power Combining/Dividing Design Tool

## Overview

The Power Combining/Dividing Design Tool provides synthesis of various RF power splitter and combiner topologies. All designs support both power division (1→N) and power combining (N→1) by reciprocity.

## Supported Topologies

The tool supports 10 different power divider/combiner topologies:

Topology | Outputs | Power Split | Isolation | Bandwidth | Notes
--- | --- | --- | --- | --- | ---
Wilkinson | 2 | Equal/Unequal | Excellent | Medium | Most common, simple
Multistage Wilkinson | 2ⁿ | Equal | Excellent | Wide | Cascaded 2-way stages
T-Junction | 2 | Equal/Unequal | None | Narrowband | Simplest, reactive
Branch-Line | 2 | Equal/Unequal | Good | Medium | 90° phase, quadrature hybrid
Double-box Branch-Line | 2 | Equal/Unequal | Better | Medium | Improved branch-line
Bagley | N | Equal | Good | Narrowband | Multi-way, planar
Gysel | 2 | Equal | Excellent | Medium | High power, grounded resistors
Lim-Eom | 2 | Equal | Excellent | Wide | Wideband improvement
3-way Improved Isolation | 3 | Equal | Excellent | Medium | Enhanced 3-port isolation
Recombinant 3-way Wilkinson | 3 | Equal | Excellent | Medium | Alternative 3-port design

## Common Parameters

### Electrical Specifications

Parameter | Range | Default | Description
--- | --- | --- | ---
Z₀ | 1 – 1000 Ω | 50 Ω | System impedance
Frequency | 1 Hz – 1 MHz | 1 GHz | Design frequency
Output Power Ratio | -20 to +20 dB | 0 dB | Power split ratio (where applicable)
Number of Outputs | 2, 3, 4, 8, 16 | 2 | For multi-way topologies

### Implementation Options

1. Ideal TL: Lossless transmission lines (schematic simulation)

2. Microstrip: Physical microstrip layout (requires substrate parameters)

3. Lumped: LC equivalent circuits (low frequency, Wilkinson only)

## Key Concepts

### Reciprocity

All power dividers are reciprocal:

- Divider mode: 1 input → N outputs (signal split)

- Combiner mode: N inputs → 1 output (signal combining)

Performance (insertion loss, isolation, match) is identical in both directions.

### Power Split Ratio

For 2-way dividers, the power split ratio K determines how power divides between outputs:

    K = P₂/P₃ = 10^(K_dB/10)

    where K_dB is the ratio in dB

Equal split: K = 1 (K_dB = 0 dB) → P₂ = P₃ = Pin/2 Unequal split: K ≠ 1 → P₂ = K×P₃

### Isolation

Isolation is the signal attenuation between output ports (Port 2 ↔ Port 3):

    Isolation (dB) = -20 × log₁₀(|S₂₃|)

High isolation (>20 dB) is critical for:

- Combining independent amplifiers (prevents interaction)

- Antenna systems (reduces coupling)

- Measurement systems (prevents crosstalk)

### Insertion Loss

Insertion Loss is the power loss from input to each output:

    IL (dB) = -10 × log₁₀(Pout/Pin)

Ideal 2-way equal split: IL = 3.01 dB (50% power loss is fundamental) Real dividers: IL = 3.01 dB + losses (resistor, conductor, dielectric)

## Topology Selection Guide

Requirement | Recommended Topology
--- | ---
General-purpose 2-way | Wilkinson
High power handling | Gysel (grounded resistors)
Wideband (multi-octave) | Multistage Wilkinson or Lim-Eom
Narrowband, simple | T-Junction
90° phase quadrature | Branch-line
Multi-way (N > 2) | Bagley or cascade Wilkinsons
3-way optimized | 3-Way Wilkinson (Improved)
No isolation needed | T-Junction (simplest)

## Design Flow

1. Select topology based on requirements (power, bandwidth, isolation, outputs)

2. Set system impedance Z₀ (typically 50Ω)

3. Specify frequency (center frequency for narrowband designs)

4. Choose power split ratio (for 2-way unequal dividers)

5. Select implementation (Ideal TL / Microstrip / Lumped)

6. For microstrip: define substrate parameters

7. Generate schematic → Tool outputs component values and layout

## Implementation Comparison

### Ideal TL (Schematic)

- Use for: Circuit simulation, proof-of-concept

- Pros: Lossless, frequency-independent impedance

- Cons: Not physically realizable

### Microstrip (Layout)

- Use for: PCB fabrication, physical prototype

- Pros: Manufacturable, accurate EM behavior

- Cons: Requires substrate parameters, frequency-dependent

- Substrate needed: εᵣ, height, tan δ, conductor σ, thickness

### Lumped LC (Low Frequency)

- Use for: Low frequency (<100 MHz), compact size

- Pros: Smallest footprint, no TEM mode required

- Cons: Limited to Wilkinson, component Q limits performance

## Key Performance Metrics

### Return Loss

Impedance match at each port:

    RL (dB) = -20 × log₁₀(|Γ|) = -20 × log₁₀(|Sᵢᵢ|)

Good match: RL > 20 dB (VSWR < 1.22:1)

### Amplitude Balance

Difference in output power levels (equal split):

    Balance (dB) = |IL₁ - IL₂|

Good balance: < 0.5 dB

### Phase Balance

Phase difference between outputs:

    Phase Balance (°) = |∠S₂₁ - ∠S₃₁|

Wilkinson: 0° (in-phase) Branch-line: 90° (quadrature)

## Bandwidth Considerations

### Narrowband Topologies (10-20% FBW)

- T-Junction

- Bagley

- Single-stage Wilkinson

### Medium Bandwidth (20-50% FBW)

- Branch-line

- Gysel

- 3-Way Wilkinson variants

### Wideband (>50% FBW, multi-octave)

- Multistage Wilkinson

- Lim-Eom

## Power Handling

### Resistive Topologies

Wilkinson, Gysel, Lim-Eom: Power limited by isolation resistors

Average power rating:

    P_max ≈ (Isolation_dB - 10) × P_resistor

Example: 20 dB isolation, 2W resistors → ~20W max

### Grounded Resistors (Gysel)

- Better thermal management

- Easier heat sinking

- Higher power capability

### Reactive Topologies

T-Junction, Branch-line: No resistors → very high power (limited by TL breakdown)

## Multi-Way Combining

For N-way power combining:

1. Tree topology: Cascade 2-way dividers

   - N = 2, 4, 8, 16, … (powers of 2)

   - Simple, modular design

2. Bagley: Direct N-way planar design

   - Any N

   - More compact than tree

   - Narrower bandwidth

3. Corporate feed: Multistage Wilkinson

   - Wideband

   - Good isolation

   - Larger size

## References

[1] Pozar, D. M. (2012). Microwave Engineering (4th ed.), Chapter 7. Wiley.

[2] Wilkinson, E. J. (1960). An N-Way Hybrid Power Divider. IRE Trans. Microwave Theory Tech., MTT-8, 116-118.

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

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