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Power Division & Combining•4-Port Sum/Diff

Rat-Race Coupler (180° Hybrid Ring)

Ring hybrid coupler producing sum (Σ) and difference (Δ) phase distributions.

Rat-Race Coupler (180° Hybrid Ring) — Photorealistic 3D PCB Hardware Render
NIKOLARF
Insertion Loss
-3.15 dB (Sum & Difference ports)
Isolation / Return Loss
> 30 dB Isolation between Σ and Δ ports
Bandwidth
20% - 25% around design center
Power Rating
High power CW handling (Pure copper distributed ring)

Device Topology & Electromagnetic Behavior

A circular microstrip ring with a circumference of 1.5 guided wavelengths (6 quarter-wave sections). Features characteristic impedance of √2·Z₀ = 70.7 Ω. When driven at Port 1, outputs at Ports 2 and 4 are in-phase; when driven at Port 3, outputs are 180° out of phase. Essential for balanced mixers and monopulse radar.

ANALYTICAL FORMULATIONS & S-MATRIX MAPPING
C_ring = 1.5λ_g = 6 × (λ_g) / (4), Z_ring = √(2) Z₀ ≈ 70.71 Ω
• Circumference split into three λ/4 sections and one 3λ/4 phase-inverting branch.
Port 1 (Sum): ∠ S₂1 = ∠ S₄1; Port 3 (Diff): ∠ S₂3 - ∠ S₄3 = 180°
• Constructive and destructive interference creating sum and difference signals.
Recommended Substrate Stackup

Rogers RT/duroid® 5870 or 6002 for phase-critical radar applications.

Nikola RF Fabrication Directives
  • Center island grounding hole or anti-pad clearance to suppress parallel plate resonance.
  • Radius curvature chamfering to prevent discontinuity reflections at port junctions.
Full-Lifecycle Engineering Services

Design, 3D EM Simulation & Handoff for Rat-Race Coupler (180° Hybrid Ring)

We provide turnkey synthesis, multi-frequency full-wave simulation, and fabrication-ready packaging for the Rat-Race Coupler (180° Hybrid Ring).

1. 3D Full-Wave FEM Modeling

Complete Ansys HFSS 3D CAD modeling with true edge-launch SMA or SMP connectors, via fence stitching, and adaptive mesh refinement down to ΔS < 0.007.

2. Sensitivity & Tolerance Sweeps

Monte Carlo statistical analysis over copper etching tolerances (±15 µm) and substrate permittivity variations to guarantee first-pass high-yield manufacturing.

3. Manufacturing Handoff

Delivery of verified simulation models, parameterized layout geometries, and photolithography-compliant Gerber RS-274X fabrication packages.

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