================================================================================ SCHEMATIC: 180° HYBRID — RAT-RACE (RING) COUPLER TM-HYB-001 Rev A Sum (Σ) and Difference (Δ) ports; 180° phase split 50Ω system, VHF/UHF primary (coaxial/microstrip); lumped HF option ================================================================================ OVERVIEW -------- The rat-race (ring) coupler is a 4-port network providing: Port 1 (Σ, sum): In-phase sum of ports 3 and 4 (-3 dB each) Port 2 (Δ, diff): 180° difference between ports 3 and 4 (-3 dB each) Port 3 (input A) Port 4 (input B) When driven at Port 1 (Σ): → Port 3: −3 dB, 0° → Port 4: −3 dB, 0° → Port 2: isolated When driven at Port 2 (Δ): → Port 3: −3 dB, 0° → Port 4: −3 dB, 180° → Port 1: isolated Key applications: • Phased array beamforming (sum/difference monopulse) • Balanced mixer/modulator • Antenna diversity switching • DF (direction-finding) antenna networks • Push-pull amplifier combining • 2-element broadside array with switchable endfire/broadside RING COUPLER DIMENSIONS ------------------------ Ring characteristic impedance: Z_ring = Z0 × √2 = 70.71 Ω Total ring circumference: 3λ/2 (1.5 wavelengths in ring medium) Port spacing around ring: Port 1 → Port 3: λ/4 Port 3 → Port 2: λ/4 Port 2 → Port 4: λ/4 Port 4 → Port 1: 3λ/4 (← this is the "long way around") Total: 3λ/2 ✓ SCHEMATIC — TRANSMISSION LINE VERSION ---------------------------------------- PORT 1 (Σ) │ 3λ/4 │ λ/4 ←────────┼────────→ ╱ Z=70.71Ω ╲ ╱ ╲ PORT 4 PORT 3 ╲ Z=70.71Ω ╱ ╲ ╱ ←────────┼────────→ λ/4 │ λ/4 │ PORT 2 (Δ) Ring: single loop of 70.71Ω transmission line, 3λ/2 total length. Ports tap into ring at λ/4 spacing (except Port 4 → Port 1 = 3λ/4). Port 1 is the Σ (in-phase/sum) port. Port 2 is the Δ (antiphase/difference) port. Ports 3 and 4 are the two signal inputs/outputs. SIGNAL FLOW ANALYSIS --------------------- From Port 1 (Σ port driven): → Port 3: λ/4 clockwise → −90° phase → Port 4: 3λ/4 clockwise (or λ/4 counter-clockwise through ring) → −90° phase Both equal amplitude, equal phase: in-phase split. From Port 2 (Δ port driven): → Port 3: λ/4 clockwise → −90° → Port 4: λ/4 counter-clockwise → +90° (then through 3λ/4 to P4 alternatively) Net: 180° difference. Isolation: Port 1 → Port 2: λ/2 and 3λ/2 paths cancel exactly at design f. PHYSICAL RING DIMENSIONS (COAXIAL) ------------------------------------- Total ring = 3λ/2 in the line medium. Physical length = (3 × c × VF) / (2 × f) Band f₀ (MHz) VF=0.66 (RG-58) VF=0.70 (PTFE) VF=1.0 (air) ---- -------- ---------------- --------------- ------------ 6M 50.5 5855 mm total 6208 mm 8911 mm 2M 146 2025 mm 2148 mm 3083 mm 1.25M 223.5 1322 mm 1402 mm 2014 mm 70cm 435 679 mm 720 mm 1034 mm 33cm 915 323 mm 342 mm 491 mm 23cm 1296 228 mm 242 mm 347 mm Physical λ/4 spacing between ports = (total ring) / 6. Physical 3λ/4 spacing (Port 4 → Port 1) = 3 × (total ring) / 6 = total/2. Construction: Form ring coaxial line into circle. Junction tees: SMA-T adapters or custom PCB/jig. Ring Z = 70.71Ω: use RG-59 (75Ω ≈ 70.71Ω, acceptable substitute) or construct 2-wire balanced line. MICROSTRIP RAT-RACE (70cm / 33cm / 23cm) ------------------------------------------ On FR-4, h=1.6mm, εr=4.4: 70.71Ω trace: w ≈ 0.9 mm Effective εr ≈ 3.2 → VF ≈ 0.56 Band Total ring λ/4 segment 3λ/4 long seg ---- ---------- ----------- ------------- 70cm 570 mm 95 mm 285 mm 33cm 271 mm 45 mm 136 mm 23cm 191 mm 32 mm 96 mm Layout: Circle or square ring geometry. Ports attach at ring via stub transitions. Port 2 (Δ) is the "long arm" port (3λ/4 from Port 1 around the short path). CAUTION: At 23cm the ring is small (191 mm); SMA connector bodies may interfere. Use end-launch SMA connectors and careful PCB layout. LUMPED ELEMENT RAT-RACE (HF) ------------------------------ Replace each λ/4 section with lumped T-network. The ring has six λ/4 sections: four short ones and combined 3λ/4. For Z_ring = 70.71Ω, per λ/4 section: L_section = Z_ring / (2πf₀) = 70.71 / (2πf₀) C_section = 1 / (2πf₀ × Z_ring) Band f₀(MHz) L_sec(µH) C_sec(pF) 6 inductors 6 caps ---- ------- --------- --------- ----------- ------ 160M 1.85 6.08 1216 6×6.08µH 6×1216pF 80M 3.75 3.00 601 6×3.00µH 6×601pF 40M 7.15 1.574 315 6×1.574µH 6×315pF 30M 10.125 1.111 222 6×1.111µH 6×222pF 20M 14.175 0.793 159 6×793nH 6×159pF 10M 28.850 0.390 78 6×390nH 6×78pF 6M 50.500 0.223 44.7 6×223nH 6×44.7pF This requires 12 inductors + 12 capacitors per divider — large component count. For HF phase arrays, consider using the lumped Wilkinson + phase-shifting network instead. ALTERNATIVE: Use only 4 sections (non-ring topology): For HF beamforming, a simpler approach is the transformer-based 180° hybrid (see sch_tl_transformer.txt for 1:1 balun-based hybrid). 180° HYBRID FROM TRANSMISSION LINE TRANSFORMER ------------------------------------------------ Simpler HF implementation using bifilar wound toroid: IN ───────────────────────────────── Σ OUT (+in-phase, −3dB) │ │ [T1: 1:1 BALUN] [50Ω load] │ │ IN ───────────────────────────────── Δ OUT (−antiphase, −3dB) T1: BN-43-202 binocular core, 6 turns bifilar 26 AWG. Bandwidth: 1.5 MHz – 30 MHz (limited by core permeability and SRF). Insertion loss: < 0.3 dB. This is a narrowband approximation; true rat-race is more broadband. PERFORMANCE SPECIFICATIONS — RAT-RACE COUPLER ----------------------------------------------- Parameter Ideal Typical --------- ----- ------- Insertion loss (Σ port) 3.01 dB 3.0–3.5 dB Insertion loss (Δ port) 3.01 dB 3.0–3.5 dB Phase difference (P3, P4 from Σ) 0° < 2° Phase difference (P3, P4 from Δ) 180° 178–182° Amplitude balance 0 dB < 0.5 dB Isolation (Σ–Δ) ∞ dB > 20 dB Return loss ∞ dB > 18 dB 1 dB bandwidth 0.75–1.33f (about 1.8:1) PHASED ARRAY FEED APPLICATIONS -------------------------------- 2-ELEMENT ENDFIRE ARRAY (using Δ port for 180° phasing): • Feed two λ/2 dipoles spaced λ/2 apart. • Drive Δ port of rat-race. • Port 3: element 1, 0°. • Port 4: element 2, 180°. • Result: broadside null, two endfire lobes. • Rotate array 90° for endfire in one direction. 2-ELEMENT SWITCHABLE ARRAY: • Drive Σ port: both elements 0° → broadside pattern. • Drive Δ port: elements 0°/180° → endfire pattern. • Switch between Σ and Δ for pattern diversity. • Use PIN diode switch or relay to select port. MONOPULSE DIRECTION FINDING: • Two antennas connected to P3 and P4. • Σ port: sum signal (maximum signal strength). • Δ port: difference signal (null at boresight, proportional to angle error). • Use Σ for tracking, Δ for angle measurement. PARTS LIST — RAT-RACE COUPLER (COAXIAL VERSION) ------------------------------------------------- Ref Qty Value/Part Description --- --- ---------- ----------- TL1 1 RG-59 or RG-316 70.71Ω coax ring (3λ/2 length per band) J1 1 SMA/BNC (Σ) Sum port J2 1 SMA/BNC (Δ) Difference port J3, J4 2 SMA/BNC Antenna ports A and B T1 4 SMA-T or jig Coax junction tees R_term 1 50Ω (1W) Spare port termination NOTE: SMA-T adapters introduce insertion loss; minimize by using PCB-based implementation for UHF and above. ================================================================================