Branch-Line Coupler (Quadrature Hybrid)

Overview

The branch-line coupler is a four-port network that provides 90° phase difference (quadrature) between output ports. Also called a quadrature hybrid or 3 dB coupler, it’s essential for applications requiring phase quadrature.

Topology

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

Design Equations

Power Split Ratio

K = P₂/P₃

Transmission Line Impedances

\[ZA = Z₀ / √2 ≈ 0.707 × Z₀ ZB = Z₀ R = Z₀\]

For Z₀ = 50 Ω:

Parameter

Value

ZA

35.4 Ω

ZB

50 Ω

R

50 Ω

Advantages

  1. Quadrature outputs

  2. Broader BW: with respect to the single box Branch-Line coupler

Limitations

  1. Narrowband: 10-20% fractional BW (single octave max)

  2. Large size: Four λ/4 lines (larger than Wilkinson)

  3. Low ZA for large K: ZA → 0 as K → ∞ (hard to fabricate)

Comparison with Wilkinson

Feature

Branch-Line

Wilkinson

Phase

90° (quadrature)

0° (in-phase)

Outputs

2

2

Bandwidth

10-20%

20-40%

Size

Larger (4 lines)

Smaller (2 lines)

Isolation

15-25 dB

20-30 dB

Application

IQ, mixers

General power split

References

[1] Pozar, D. M. (2012). Microwave Engineering (4th ed.), Section 7.5, pp. 347-352. Wiley.

See Also