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):

Let $t = \sqrt{2}$, $r = 1$. The shunt and series arm impedances are:

\[Z_A = Z_D = \frac{Z_0}{\sqrt{2} - 1} = Z_0\,(\sqrt{2} + 1) \approx 2.414 \times Z_0\]
\[Z_B = \frac{Z_0}{\sqrt{2}} \approx 0.707 \times Z_0\]
\[R = Z_0 \quad \text{(isolation resistor)}\]

For Z₀ = 50 Ω:

Parameter

Value

Z_A = Z_D

120.7 Ω

Z_B

35.4 Ω

R

50 Ω

Advantages Over Single-Box

  1. Wider bandwidth: 25–35% vs. 15–20% (50–75% improvement)

Limitations

  1. Larger size: 7 lines vs. 4 — approximately 2× the area of a single-box design

  2. More complex layout

  3. Higher impedance (Z_A, Z_D): 120.7 Ω results in narrow lines, challenging on thin substrates where fabrication tolerance is critical

  4. Still narrowband relative to other broadband coupler topologies

See Also