Passive Components and Devices Couplers and Dividers Informational

What is a Lange coupler and when would I use it at microwave frequencies?

Q: Can I build a Lange coupler on FR-4?

Yes, but with limitations. FR-4 has relatively low dielectric constant (Dk ≈ 4.2) which results in wider traces and longer fingers compared to high-Dk substrates. For frequencies below 5 GHz: the Lange becomes physically large (> 15 mm per arm at 3 GHz). The minimum gap achievable on standard FR-4 PCBs is 75-100 um (3-4 mil), which limits the achievable coupling. For 3 dB at 3 GHz on 0.5 mm FR-4: the design may require 6 or 8 fingers to achieve sufficient coupling with feasible gaps. FR-4 loss: the high loss tangent (0.02) introduces 0.5-1.5 dB excess loss at frequencies above 5 GHz. For frequencies above 6 GHz on FR-4: the Lange coupler performance degrades significantly. Use a lower-loss substrate (Rogers RO4003C or similar).

A Lange coupler is an interdigitated coupled-line structure that achieves tight coupling (3 dB) with broadband performance, overcoming the coupling limitations of standard edge-coupled microstrip lines. Structure: multiple narrow conductor fingers are interleaved (interdigitated) and connected alternately at each end using bond wires or air bridges. A standard Lange coupler uses four fingers (two pairs), each approximately lambda/4 long. The interdigitation increases the effective coupling by connecting multiple coupled lines in parallel, achieving 3 dB coupling that would require impractically narrow gaps in a standard edge-coupled design. Key characteristics: (1) Coupling: 3 dB (quadrature hybrid, equal power split). Achievable coupling range: 1-6 dB (by adjusting the number of fingers and spacing). (2) Phase: 90° between the coupled and through ports (quadrature coupler, same as a branchline hybrid). (3) Bandwidth: 50-100% (much wider than a branchline hybrid, which achieves only 10-15%). The Lange coupler achieves octave bandwidth for coupling flatness within ±0.5 dB. (4) Directivity: 15-25 dB (limited by even/odd mode velocity difference in microstrip). Can be improved to > 30 dB in stripline. (5) Size: approximately lambda/4 × (N_fingers × finger_width + (N-1) × gap_width). Compact for microwave frequencies (< 5 mm at 20 GHz). When to use: (1) Balanced amplifiers (the most common application): the Lange coupler splits the input into two quadrature paths, each feeding an amplifier. The second Lange combines the amplifier outputs. The quadrature combining provides a well-matched amplifier even if the individual amplifiers have poor input/output match. (2) Balanced mixers (image-reject mixers, I/Q demodulators). (3) Any application requiring a broadband 90° hybrid with tight coupling.

Category: Passive Components and Devices

Updated: April 2026

Product Tie-In: Couplers, Dividers, Hybrids

Lange Coupler Design

The Lange coupler, invented by Julius Lange in 1969, solved the practical problem of achieving 3 dB coupling in microstrip. Standard edge-coupled microstrip requires a coupling gap of < 25 um (1 mil) for 3 dB at most frequencies, which is impractical to fabricate. The interdigitated structure achieves the same coupling with gaps of 50-100 um (2-4 mil), which are easily fabricated with standard PCB processes.

Design Procedure

(1) Determine the center frequency f0 and desired coupling C (typically 3 dB for a quadrature hybrid). (2) Choose the number of fingers: 4 fingers (standard Lange): simplest, most common. Achieves 3 dB coupling with moderate gap width. 6 or 8 fingers: achieves tighter coupling or allows wider gaps, but increases complexity and size. 3 fingers (unfolded Lange): simplest interdigitated structure, but narrower bandwidth than 4-finger. (3) Calculate the even-mode and odd-mode impedances: for a 3 dB coupler in 50-ohm system: Z0e and Z0o must satisfy Z0 = sqrt(Z0e × Z0o) = 50 ohms and C = (Z0e - Z0o) / (Z0e + Z0o) = 1/sqrt(2) ≈ 0.707 for 3 dB. Solving: Z0e = Z0 × sqrt((1+C)/(1-C)) = 50 × sqrt(1.707/0.293) = 120.7 ohms. Z0o = Z0 × sqrt((1-C)/(1+C)) = 50 × sqrt(0.293/1.707) = 20.7 ohms. (4) Map the Z0e/Z0o to the finger width, gap, and substrate parameters using a coupled-line calculator (Keysight ADS LineCalc, or open-source tools). The interdigitation modifies the effective Z0e and Z0o from a standard coupled pair. (5) The finger length = lambda/4 at f0 (in the effective dielectric medium). (6) Bond wires or air bridges: connect alternate fingers at each end. The bond wire inductance can detune the coupler at high frequencies. Minimize bond wire length (< 200 um) or use integrated air bridges in MMIC processes.

Comparison with Branchline Hybrid

Both the Lange coupler and the branchline hybrid are 90° hybrid couplers with 3 dB coupling. Differences: (1) Bandwidth: Lange: 50-100% (octave). Branchline: 10-15% (single section). The Lange is preferred when wideband operation is needed. (2) Size: Lange: lambda/4 long × a few mm wide. Branchline: lambda/4 × lambda/4 (square). The Lange is more compact. (3) Coupling accuracy: Lange: sensitive to finger width and gap tolerances. A 10% gap variation changes coupling by approximately 1 dB. Branchline: less sensitive to line width tolerance (the coupling depends on impedance ratios, which are more robust). (4) Directivity: Lange: 15-25 dB in microstrip (limited by mode velocity mismatch). Branchline: 20-30 dB (better than Lange in microstrip). (5) Power handling: Lange: limited by the narrow gap between fingers (voltage breakdown at high power). For 50 um gap in air: breakdown at approximately 100 V peak (< 100 mW). Use wider gaps (with more fingers) for higher power. Branchline: wide traces, high power handling (limited only by substrate and connector ratings). (6) Fabrication: Lange: requires bond wires or air bridges (additional fabrication step). Branchline: simple microstrip routing (no bond wires).

MMIC Implementation

In MMIC (monolithic microwave integrated circuit) design: the Lange coupler is the standard quadrature hybrid because: (1) The fine lithography of MMIC processes (0.1-1.0 um feature size) easily achieves the required finger gaps. (2) Air bridges are a standard MMIC process step (no additional fabrication). (3) The compact size fits MMIC die areas (< 1 mm^2 at 20 GHz). (4) GaAs and InP substrates have high dielectric constant (epsilon_r = 12.9 for GaAs), which shortens the lambda/4 dimension. A 20 GHz Lange coupler on GaAs: fingers ≈ 1 mm long. Total size: 1 mm × 0.3 mm. A 60 GHz Lange: 0.3 mm × 0.1 mm. At 77 GHz (automotive radar): the Lange coupler is common in the LO distribution and balanced amplifier stages of radar front-end MMICs.

Lange Coupler Equations

C = (Z₀ₑ - Z₀ₒ)/(Z₀ₑ + Z₀ₒ)
Z₀ = √(Z₀ₑ × Z₀ₒ) = 50Ω
3 dB: Z₀ₑ = 120.7Ω, Z₀ₒ = 20.7Ω
Length = λ/4 at center frequency
BW: 50-100% (octave bandwidth)

Common Questions

Frequently Asked Questions

Can I build a Lange coupler on FR-4?

Yes, but with limitations. FR-4 has relatively low dielectric constant (Dk ≈ 4.2) which results in wider traces and longer fingers compared to high-Dk substrates. For frequencies below 5 GHz: the Lange becomes physically large (> 15 mm per arm at 3 GHz). The minimum gap achievable on standard FR-4 PCBs is 75-100 um (3-4 mil), which limits the achievable coupling. For 3 dB at 3 GHz on 0.5 mm FR-4: the design may require 6 or 8 fingers to achieve sufficient coupling with feasible gaps. FR-4 loss: the high loss tangent (0.02) introduces 0.5-1.5 dB excess loss at frequencies above 5 GHz. For frequencies above 6 GHz on FR-4: the Lange coupler performance degrades significantly. Use a lower-loss substrate (Rogers RO4003C or similar).

What is the power handling of a Lange coupler?

The power handling is limited by: (1) Voltage breakdown: the narrow gap between interdigitated fingers has a lower breakdown voltage than wider-spaced structures. For a 50 um gap in air at sea level: breakdown ≈ 150 V peak ≈ 225 W in 50 ohms. On a substrate: the breakdown voltage is higher (dielectric strength of the substrate fills the gap). For alumina substrate: approximately 300 V/mil = 12 kV per mm. A 50 um gap: 600 V breakdown. Corresponding power: > 1 kW. (2) Thermal dissipation: the narrow finger conductors have higher resistance and can overheat at high CW power. Finger width of 50 um, 5 mm long, gold on GaAs: resistance ≈ 1 ohm. At 1 W: dissipation is manageable. At 10+ W: thermal design is needed (thicker metallization, heat spreading). For most MMIC applications: Lange couplers handle 0.1-1 W. For higher power: use branchline hybrids with wider traces.

How does the Lange coupler compare to a rat race hybrid?

Lange coupler: 90° phase difference between outputs. Bandwidth: 50-100%. Compact (lambda/4 long). Requires bond wires. Used for: balanced amplifiers, I/Q systems, image-reject mixers. Rat race (ring hybrid): 180° and 0° outputs available (sum and difference ports). Bandwidth: 20-30% for a single ring. Larger (ring circumference = 1.5 × lambda). No bond wires. Used for: balanced mixers, monopulse comparators, push-pull amplifiers. They are used for different applications: the Lange is a quadrature (90°) device, and the rat race is a 180° device. They are not interchangeable.

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