Merv's Brain Dump

Chapter 1 — Introduction and Scope

This manual covers four RF hybrid coupler designs for splitting and combining RF power with controlled phase relationships: the branch-line quadrature hybrid (90° phase split, equal amplitude), the Wilkinson 2-way in-phase power divider, the 4-way Wilkinson, and the rat-race (180° hybrid ring). Applications include circular polarization feeds, phased array antenna networks, balanced amplifier stages, and antenna switching networks.

Chapter 2 — Theory of Operation

2-1 Branch-Line Quadrature Hybrid

A 4-port network constructed from four λ/4 transmission line sections. Two shunt arms have characteristic impedance Z₀ = 50Ω; two series (coupling) arms have Z₀/√2 = 35.35Ω. S-parameter matrix at center frequency:

2-2 Wilkinson Power Divider

A 3-port network that splits input power equally between two output ports with 0° phase (in-phase). Ports 2 and 3 are isolated from each other when both are terminated in Z₀. The λ/4 arms have characteristic impedance Z₀√2 = 70.7Ω for a 50Ω system. An isolation resistor R = 2Z₀ = 100Ω connects ports 2 and 3.

2-3 Rat-Race (180° Hybrid Ring)

A ring of transmission line (total circumference 1.5λ) with four ports: sum (Σ) port provides in-phase combination; difference (Δ) port provides 180° phase difference between ports. Ring impedance: Z_ring = Z₀√2 = 70.7Ω. Used for balanced mixers and antenna pattern summation/difference.

Chapter 3 — Equipment and Materials

Chapter 4 — Construction

4-1 Branch-Line Hybrid (144 MHz)

1. Calculate λ/4 at 144 MHz on FR4 (1.6 mm, εr=4.6): λ/4 = c/(4 × f × √εeff) ≈ 350 mm / 4 = 87.5 mm. Account for effective permittivity (εeff ≈ 3.4): 87.5 / √3.4 = 47.5 mm.
2. Draw the four-arm square layout: each arm 47.5 mm long. Shunt arms: 2.9 mm wide (50Ω). Series arms: 5.0 mm wide (35.35Ω).
3. Mount SMA connectors at each of the four corners. The square layout minimizes parasitic coupling between arms.

4-2 Lumped-Element HF Hybrid (7–30 MHz)

1. Replace each λ/4 line section with an equivalent LC π-network: L = Z₀/ω = 50/(2π×14e6) = 568 nH (shunt arms); C = 1/(ω×Z₀) = 1/(2π×14e6×50) = 227 pF.
2. Use 1% tolerance components to maintain amplitude and phase balance.

Chapter 5 — Operating Procedures

5-1 Circular Polarization Feed

1. Connect the transceiver to Port 1 (input) of the branch-line hybrid. Connect a horizontally polarized element to Port 2 (0°) and a vertically polarized element to Port 3 (−90°).
2. Port 4 (isolated) is terminated in a 50Ω load — do not leave it open; it must be terminated for correct operation.
3. Result: the two antenna elements receive equal power with 90° phase offset, producing circular polarization.

Chapter 6 — Calibration

1. Branch-line hybrid: with NanoVNA, measure S11 at Port 1 (must be <−20 dB return loss at f₀) and S21 to ports 2 and 3 (−3 ± 0.5 dB each). Measure S31 vs. S21 phase (must be −90 ± 5°). S41 must be <−30 dB (isolation).
2. Wilkinson: S11 <−20 dB; S21 = S31 = −3 ± 0.5 dB; S23 (isolation) <−20 dB at center frequency.

Chapter 7 — Verification and Acceptance

1. Amplitude balance: |S21| − |S31| <0.5 dB.
2. Phase accuracy: Δφ within ±5° of design value (90° or 0°) at center frequency.
3. Return loss (input match): <−20 dB at center frequency.
4. Isolation: <−20 dB between output ports.
5. Power handling (Wilkinson): verify 100Ω isolation resistor rating. At 100W input, the resistor dissipates up to 50W if ports 2 and 3 are mismatched — use 5W resistor minimum.
6. Log: date, design type, center frequency, S21/S31 balance, phase error, return loss, isolation, operator.

Appendix A — Microstrip Impedance vs. Trace Width (FR4 1.6mm)

Appendix B — Wavelength Scaling Table