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

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.