Quadrature Coupler
Understanding Quadrature Couplers
The quadrature coupler has four ports: input, direct (through), coupled, and isolated. When a signal enters the input port, it splits equally between the direct and coupled ports (−3 dB each), with the coupled port output lagging the direct port by exactly 90 degrees at the center frequency. The isolated port receives no power (in the ideal case). If the direct and coupled ports are both terminated in matched loads, the input port sees a perfect 50-ohm match regardless of the individual port impedances.
This 90-degree property is what makes the coupler invaluable for balanced circuits. In a balanced amplifier, two identical gain stages are connected between a pair of quadrature couplers. Reflections from the amplifier inputs arrive back at the input coupler with a 180-degree phase difference (90 degrees out plus 90 degrees back) and cancel at the input port, redirecting the reflected energy to the isolated port's termination. The result is excellent input return loss even when the individual amplifiers have poor match.
Ideal S-Parameter Matrix
S11 = 0 (perfect input match)
S21 = −j/√2 (direct port, −3 dB, −90°)
S31 = −1/√2 (coupled port, −3 dB, −180°)
S41 = 0 (isolated port, infinite isolation)
Phase Difference Between Outputs:
∠S21 − ∠S31 = −90° − (−180°) = 90°
Branch-Line Impedances:
Series branches: Z0/√2 = 35.35 Ω (for 50 Ω system)
Shunt branches: Z0 = 50 Ω
All branches: λ/4 long at center frequency
Coupler Type Comparison
| Type | Bandwidth | Coupling Accuracy | Phase Balance | Power Handling | Complexity |
|---|---|---|---|---|---|
| Branch-Line | 10-15% | ±0.5 dB | ±2° | High (waveguide: kW+) | Simple |
| Lange | 20-40% | ±0.3 dB | ±3° | Medium (planar) | Wire bonds required |
| Short-Slot Hybrid (WG) | 10-15% | ±0.2 dB | ±1° | Very high (kW CW) | Precision machining |
| Broadside Coupler | 30-50% | ±0.5 dB | ±5° | Low (stripline) | Multilayer PCB |
Frequently Asked Questions
What is the difference between a branch-line coupler and a Lange coupler?
A branch-line coupler uses two quarter-wavelength transmission lines connected by shunt branches, forming a rectangular loop. It provides exact 3 dB coupling at center frequency but only 10 to 15% usable bandwidth. A Lange coupler uses 4 to 8 interdigitated parallel fingers with edge coupling, achieving 20 to 40% bandwidth through the multi-section coupled-line effect. The Lange is preferred for wideband applications but requires wire bond connections between alternating fingers during fabrication, increasing manufacturing complexity and cost.
How does a balanced amplifier use quadrature couplers?
Two identical amplifiers sit between an input and output quadrature coupler. The input coupler splits the signal with 90-degree offset. Each amplifier amplifies its path. The output coupler recombines them coherently. Reflections from the amplifier inputs cancel at the input port because they arrive with 180-degree phase difference (90° out + 90° back), redirecting reflected energy to the isolated port termination. This produces excellent input return loss (typically > 20 dB) regardless of individual amplifier match, which is why balanced topology is the standard for wideband MMIC amplifier modules.
Can quadrature couplers be implemented in waveguide?
Yes. The short-slot hybrid coupler places two rectangular waveguides side-by-side with a coupling slot in the shared broad wall. The slot length is designed for 3 dB coupling with 90-degree phase. Waveguide hybrids handle kilowatts of CW power with insertion loss below 0.1 dB and isolation exceeding 25 dB. They are used in high-power radar duplexers, balanced mixer assemblies, and monopulse antenna comparator networks.