================================================================================ SCHEMATIC: QUADRATURE (90°) HYBRID COUPLER — BRANCH-LINE TYPE TM-HYB-001 Rev A 90° phase split, equal amplitude; for circular polarization and phased arrays 50Ω system, all ham bands 160M – 23cm ================================================================================ OVERVIEW -------- The branch-line (quadrature) hybrid is a 4-port network providing: Port 1 (input) → Port 2 (through, 0°): −3.01 dB, 0° phase Port 1 (input) → Port 3 (coupled, −90°): −3.01 dB, −90° phase Port 4 (isolated): matched, no output when ports 2 and 3 terminated in Z0 Port numbering convention (clockwise): Port 1 = Input (upper left) Port 2 = Through (lower left, 0°) Port 3 = Coupled (lower right, −90°) Port 4 = Isolated (upper right, terminated 50Ω) Key applications: • Circular polarization feed from linear antenna pair • Antenna beam steering (two crossed Yagis or dipoles) • Balanced mixer / I-Q hybrid • Phased array antenna feed networks • Power amplifier combining (quadrature combining eliminates load-pull) BRANCH-LINE HYBRID — TRANSMISSION LINE SCHEMATIC -------------------------------------------------- PORT 1 ──────── λ/4 @ 35.35Ω ──────── PORT 4 │ │ λ/4 λ/4 @ 50Ω @ 50Ω │ │ PORT 2 ──────── λ/4 @ 35.35Ω ──────── PORT 3 Shunt (vertical) arms: Z = 50 Ω, length = λ/4 Series (horizontal) arms: Z = Z0/√2 = 35.35 Ω, length = λ/4 All four sides are λ/4 at the design frequency. Total ring perimeter = λ. PORT SIGNAL FLOW (PORT 1 DRIVEN): P1 input: splits into two paths. Path A: P1 → top arm (35.35Ω) → P4 → right arm (50Ω) → P3 Path B: P1 → left arm (50Ω) → P2 → bottom arm (35.35Ω) → P3 At P3: paths add (−90° total via Path B, −90° via Path A). At P4: paths cancel (isolation). Port 4 is the "isolated" port. At P2: receives signal at 0° (same phase as input, −3 dB amplitude). At P3: receives signal at −90°. LUMPED ELEMENT QUADRATURE HYBRID (HF) --------------------------------------- Each λ/4 arm replaced by equivalent L-C section. Low-pass T-network for 50Ω arm (vertical): L_sh = 50 / (2πf₀), C_sh = 1/(2πf₀ × 50) Low-pass T-network for 35.35Ω arm (horizontal): L_sr = 35.35 / (2πf₀), C_sr = 1/(2πf₀ × 35.35) Full lumped schematic (one-section approximation): P1 ──[L_sr/2]──┬──[L_sr/2]─── P4 [C_sr] │ GND │ │ [L_sh/2] [L_sh/2] [C_sh] [C_sh] [L_sh/2] [L_sh/2] │ │ P2 ──[L_sr/2]──┬──[L_sr/2]─── P3 [C_sr] │ GND Each arm uses a T-network (L/2 – C – L/2). COMPONENT VALUES — LUMPED ELEMENT QUADRATURE HYBRID ---------------------------------------------------- For 50Ω shunt arms (L_sh, C_sh): L_sh_total = 50 / (2πf₀) C_sh = 1 / (2πf₀ × 50) For 35.35Ω series arms (L_sr, C_sr): L_sr_total = 35.35 / (2πf₀) C_sr = 1 / (2πf₀ × 35.35) Band f₀(MHz) L_sh(µH) C_sh(pF) L_sr(µH) C_sr(pF) ---- ------- -------- -------- -------- -------- 160M 1.85 4.30 1719 3.04 2432 80M 3.75 2.12 849 1.50 1200 40M 7.15 1.113 446 0.787 631 30M 10.125 0.785 315 0.555 446 20M 14.175 0.561 225 0.397 318 17M 18.118 0.439 176 0.310 249 15M 21.225 0.375 150 0.265 213 12M 24.940 0.319 128 0.226 181 10M 28.850 0.276 110 0.195 156 6M 50.500 0.158 63 0.111 89 NOTE: All L values are total arm inductance. For T-network, use L/2 on each side of the shunt capacitor. L_sh/2 and L_sr/2 are used per half. COAXIAL IMPLEMENTATION (2M / 70cm / 33cm / 23cm) -------------------------------------------------- For VHF/UHF, each λ/4 section is cut from coaxial cable. 50Ω shunt arms: RG-58 (VF=0.66) or RG-316 (PTFE, VF=0.70) 35.35Ω series arms: Use 2 × RG-58 in parallel (25Ω × 2 = 50Ω parallel ≠ 35.35Ω) PRACTICAL: Construct 35.35Ω from: Option A: Wind 2-turn coax stub on form (effective Z combination) Option B: Use RG-59 (75Ω) with connector matching Option C: Use microstrip (see below) Physical λ/4 lengths (50Ω, RG-58, VF=0.66): Band f₀ (MHz) Length (mm) ---- -------- ----------- 6M 50.5 976 2M 146 337 1.25M 223.5 220 70cm 435 113 33cm 915 54 23cm 1296 38 For 35.35Ω sections, cut at same length but use different cable type or construct 2-conductor transmission line. MICROSTRIP BRANCH-LINE (70cm / 33cm / 23cm) --------------------------------------------- On FR-4, h=1.6mm, εr=4.4, copper 1 oz: 50Ω trace: w = 2.9 mm 35.35Ω trace: w = 5.2 mm (wider) Effective εr ≈ 3.3 for both (slight variation with width). VF ≈ 0.55; physical λ/4 = c × VF / (4 × f) Band f₀ (MHz) 50Ω section 35Ω section (mm) ---- -------- ----------- ----------- 70cm 435 41.0 mm 41.0 mm 33cm 915 19.5 mm 19.5 mm 23cm 1296 13.8 mm 13.8 mm Layout: Square geometry. Ports at four corners. Port 4 (isolated) terminated externally with 50Ω SMA load. For circular polarization feed: connect Port 2 to vertical element, Port 3 to horizontal element. PERFORMANCE SPECIFICATIONS --------------------------- Parameter Ideal Typical --------- ----- ------- Insertion loss (P1→P2) 3.01 dB 3.0–3.5 dB Insertion loss (P1→P3) 3.01 dB 3.0–3.5 dB Phase difference P2–P3 90° 88–92° Amplitude balance 0 dB < 0.3 dB Return loss (all ports) ∞ dB > 18 dB Isolation (P1–P4) ∞ dB > 20 dB Bandwidth (90° ± 5°) 0.7–1.4f — Maximum CW power limited by R (transmission line version: only PCB trace/coax ratings) CIRCULAR POLARIZATION WIRING ------------------------------ For circular polarization from two crossed dipoles: Port 1 ──→ Hybrid ──→ Port 2 ──→ Dipole (0°, e.g., horizontal) └──→ Port 3 ──→ Dipole (−90°, e.g., vertical) Result: RHCP (right-hand circular polarization) For LHCP: swap Port 2 and Port 3 connections, or feed Port 4 instead of Port 1 (with Port 1 terminated). Phase error effect on axial ratio: Phase error ε (degrees) → Axial ratio ≈ 20 × log10(tan(45° + ε/2)) dB At ε = 5°: AR ≈ 1.6 dB At ε = 2°: AR ≈ 0.6 dB PARTS LIST — QUADRATURE HYBRID (HF LUMPED, ONE UNIT) ------------------------------------------------------ Ref Qty Value Description --- --- ----- ----------- L_sh1–4 4 per table 50Ω arm inductors (T/2 each = L_sh/2) L_sr1–4 4 per table 35.35Ω arm inductors (T/2 each = L_sr/2) C_sh1–4 4 per table 50Ω arm shunt capacitors C_sr1–4 4 per table 35.35Ω arm shunt capacitors J1–J4 4 SMA or BNC Port connectors R_term 1 50Ω (1W) Port 4 termination (if not connected to load) Total: 8 inductors, 8 capacitors, 4 connectors. (Compact HF: 8 components vs 6 for Wilkinson — more complex) ================================================================================