What Is the Branch-Line 90-Degree Quadrature Hybrid Coupler Calculator?
The branch-line hybrid coupler is a four-port microwave directional coupler that divides input power equally between a through port and a coupled port with a strict 90-degree relative phase difference.
Consisting of four interconnected quarter-wavelength transmission lines forming a square or rectangle, it provides excellent input matching, high isolation at Port 4, and equal 3dB power division.
This calculator sizes the horizontal series arm impedance (Z_0/√2 ≈ 35.36 Ω for 50 Ω systems), vertical shunt arms (Z_0 = 50 Ω), and electrical quarter-wavelength line lengths across microstrip substrates.
How Does the Branch-Line 90-Degree Quadrature Hybrid Coupler Calculator Work?
The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.
Branch-Line 90-Degree Quadrature Hybrid Coupler Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Even-odd mode analysis criteria for ideal 3dB equal-power 90-degree quadrature branch-line couplers.
How to Use the Branch-Line 90-Degree Quadrature Hybrid Coupler Calculator
- Enter your primary measurements in the input fields above.
- Select your preferred units (e.g. metric or imperial) if applicable.
- Review or adjust operational assumptions such as field efficiency.
- Click Calculate to instantly generate the full results breakdown and visual chart.
- Use the Reset button at any time to clear the form and test a new scenario.
Step-by-Step Example Calculation
2.45 GHz 50Ω Branch-Line Hybrid on FR-4 (ε_eff = 3.65)
Input Values:
Understanding Your Result
Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.
Factors That Affect the Result
Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.
When Should You Use This Calculator?
Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.
Assumptions & Limitations
- Series Horizontal Arms: Z_series = Z₀ / √2 ≈ 0.7071 · Z₀ (35.36 Ω for 50 Ω system).
- Shunt Vertical Arms: Z_shunt = Z₀ (50.0 Ω for 50 Ω system).
- Quarter-Wavelength Line Length: λ_g / 4 = c / (4 · f₀ · √ε_eff).
- Output Phasing: Through port (Port 2) is at 0° phase (-3.01 dB); Coupled port (Port 3) is at -90° phase (-3.01 dB).
- Isolation Port: Port 4 receives negligible power (ideal S41 = -∞ dB).
Frequently Asked Questions
Calculation Accuracy & Reference Note
This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.