Double-Box Branch-Line Coupler

Overview

Enhanced quadrature hybrid using two cascaded branch-line sections providing wider bandwidth and better impedance transformation than single-box design. Maintains 90° phase difference while achieving 50-75% wider bandwidth through dual-box structure.

Topology

Port 1 ─────────[ZB]────────[ZB]───────  Port 2
(Input)    │           |            |  (Through, 0°)
           │           │            │
          [ZA]        [ZB]         [ZA]
           │           │            │
           │           │            │
Port 4 ─────────[ZB]────────[ZB]───────  Port 3
(Isolated)                           (Coupled, -90°)

Design Equations

For equal split (K = 1):

\[ \begin{align}\begin{aligned}t = √(2 × 1) = √2\\ZA = Z₀ × √(r × (t² - r)) / (t - r) = Z₀ × √(1 × (2 - 1)) / (√2 - 1) = Z₀ / (√2 - 1) = Z₀ × (√2 + 1) ≈ 2.414 × Z₀\\ZD = Z₀ × √(r × (t² - r)) / (t - 1) = Z₀ × √(1 × 1) / (√2 - 1) = Z₀ / (√2 - 1) ≈ 2.414 × Z₀\\ZB = Z₀ × √(r - r²/t²) = Z₀ × √(1 - 1/2) = Z₀ / √2 ≈ 0.707 × Z₀\\R = Z₀ (isolation resistor)\end{aligned}\end{align} \]

For Z₀ = 50 Ω:

Parameter

Value

ZA = ZD

120.7 Ω

ZB

35.4 Ω

R

50 Ω

Advantages Over Single-Box

  1. Wider bandwidth: 25-35% vs. 15-20%

    • 50-75% improvement

    • Better match across band

Limitations

  1. Larger size: 7 lines vs. 4

    • More PCB area

    • Approximately 2× size of single-box

  2. More complex layout

  3. Higher impedance (ZA, ZD): 120.7 Ω

    • Narrow lines

    • Challenging on thin substrates

    • Fabrication tolerance critical

  4. Still narrowband

See Also