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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