Passive Components

Coupler Design

Q: How do I choose the coupling value for a directional coupler?

Coupling is set by how much power you want diverted to the coupled port relative to the input. A 10 dB coupler sends one tenth of the input power (minus a fraction of a dB of insertion loss) to the coupled port and passes the rest through. For signal monitoring and power leveling, 20 dB or 30 dB couplers are common because they sample the line without loading it. For balanced amplifiers and mixers you want tight coupling, so 3 dB hybrids that split power equally are used. Tighter coupling demands smaller conductor gaps in edge-coupled lines, which can be hard to fabricate, so single-section designs below about 6 dB often switch to broadside-coupled or Lange topologies to reach the required line-to-line capacitance.

Q: Why does my coupler have poor directivity at the band edges?

Directivity is the ratio of the coupled-port signal to the isolated-port leakage and is the single hardest specification to hold across a band. In a microstrip coupled-line coupler the even-mode and odd-mode phase velocities differ because part of the field travels in air and part in the substrate. This velocity mismatch leaks forward power into the isolated port and degrades directivity, often to only 10 to 15 dB. Stripline, where the line is fully surrounded by one dielectric, keeps the two modes equal and reaches 25 to 40 dB. Lange couplers interdigitate the fingers to force the modes back into balance, recovering high directivity over an octave. Adding dielectric overlay or compensating capacitors can also equalize the velocities in microstrip.

Q: What is the difference between a 90 degree and a 180 degree hybrid coupler?

Both split input power equally between two output ports, but they differ in the relative phase. A 90 degree (quadrature) hybrid, such as a branch-line or Lange coupler, produces outputs in phase quadrature and is used in balanced amplifiers, image-reject mixers, and reflectometers where the quadrature relationship cancels reflections. A 180 degree hybrid, such as a rat-race ring or a magic tee, produces outputs that are either in phase or 180 degrees out of phase depending on which port is driven, giving sum and difference ports. The 180 degree type is preferred for balanced mixers, push-pull amplifiers, and antenna feed networks that need a clean sum and difference.

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The discipline of synthesizing a four-port (or three-port) network that samples or splits RF power in a controlled way. A directional coupler is specified first by its coupling coefficient, the fraction of input power tapped to the coupled port, and then by its directivity, which measures how well the device distinguishes forward from reverse waves. Good design holds coupling flat (typically ±0.5 dB), keeps directivity above 20 to 30 dB, and maintains return loss across the band, while trading off topology, line geometry, and dielectric to control insertion loss and amplitude or phase balance. Practical realizations span coupled-line, branch-line, Lange, and rat-race structures from below 1 GHz to past 110 GHz.

Category: Passive Components

Typical Coupling: 3 to 30 dB

Directivity Goal: > 20 dB

How RF Couplers Are Synthesized

A coupler design begins with the specification: how much power must reach the coupled port, how clean the isolated port must stay, and over what bandwidth. From these, the engineer selects a topology and then solves for the physical dimensions that realize the required even-mode and odd-mode impedances. In a symmetric coupled-line section the design reduces to two impedances, Z_0e and Z_0o, whose geometric mean equals the system impedance (typically 50 Ω) and whose ratio sets the coupling. The line is made one quarter-wavelength long at the center frequency so the coupled response peaks there and rolls off symmetrically.

The hardest target is directivity. In an ideal coupler the isolated port receives nothing, but in any real structure mode-velocity mismatch, fabrication tolerance, and connector reflections leak energy into it. Microstrip couplers expose the field to both air and substrate, so the even and odd modes propagate at different speeds and directivity often collapses to 10 to 15 dB. Moving to stripline, where a single homogeneous dielectric surrounds the line, equalizes the modes and lifts directivity to 25 to 40 dB. The Lange coupler solves the tight-coupling problem of microstrip by interleaving four fingers, achieving 3 dB coupling over an octave that a single edge-coupled pair cannot reach because the required gap would be only a few microns.

For power-splitting rather than sampling, designers turn to branch-line and rat-race hybrids built from quarter-wave transmission-line sections. These give exact 3 dB splits with defined phase relationships at the design frequency, but their narrowband nature (roughly 10 to 20 percent for a single branch-line section) is widened by cascading multiple sections, reaching an octave or more in a multi-section design.

Governing Coupler Equations

Coupling, Directivity, Isolation (in dB):
C = −20 log₁₀|S₃₁| D = 20 log₁₀(|S₃₁| / |S₄₁|)
I = −20 log₁₀|S₄₁| = C + D

Coupled-Line Mode Impedances:
Z₀ = √(Z_0e × Z_0o) C(voltage) = (Z_0e − Z_0o) / (Z_0e + Z_0o)

Through-Port Coupling (ideal lossless):
|S₂₁|² = 1 − |S₃₁|²

Where S₃₁ = coupled port, S₄₁ = isolated port, Z_0e/Z_0o = even/odd-mode impedance. Example: a 10 dB coupler has |S₃₁| ≈ 0.316, so the through port keeps |S₂₁| ≈ 0.949 (−0.46 dB). For Z₀ = 50 Ω and C = 0.316, Z_0e ≈ 69.4 Ω and Z_0o ≈ 36.0 Ω.

Coupler Topology Comparison

Topology	Typical Coupling	Bandwidth	Directivity	Output Phase	Best Application
Coupled-line (stripline)	6 to 30 dB	Octave+	25 to 40 dB	90° quadrature	Power monitoring, reflectometers
Coupled-line (microstrip)	10 to 30 dB	Octave+	10 to 15 dB	90° quadrature	Low-cost integrated sampling
Branch-line hybrid	3 dB (equal)	10 to 20%	20 to 30 dB	90° quadrature	Balanced amps, IQ networks
Lange coupler	3 dB (tight)	Octave+ (>67%)	20 to 25 dB	90° quadrature	Broadband MMIC amplifiers
Rat-race (ring) hybrid	3 dB (equal)	20 to 30%	20 to 30 dB	0° / 180°	Balanced mixers, sum/difference

Common Questions

Frequently Asked Questions

How do I choose the coupling value for a directional coupler?

Match coupling to how much power you can spare. Signal monitoring and power leveling use loose 20 to 30 dB couplers that sample the line without loading it; a 10 dB coupler diverts one tenth of the input. Balanced amplifiers and mixers need tight 3 dB hybrids for equal splits. Below about 6 dB, edge-coupled microstrip gaps become too small to fabricate, so designs switch to broadside-coupled or Lange topologies to reach the needed line-to-line capacitance.

Why does my coupler have poor directivity at the band edges?

In microstrip the even and odd modes travel at different speeds because part of the field is in air and part in the substrate. That velocity mismatch leaks forward power into the isolated port, dropping directivity to 10 to 15 dB. Stripline surrounds the line with one dielectric, equalizing the modes for 25 to 40 dB. Lange interdigitation, a dielectric overlay, or lumped compensating capacitors can rebalance the velocities in microstrip.

What is the difference between a 90 degree and a 180 degree hybrid coupler?

Both split power equally but differ in phase. A 90° (quadrature) hybrid such as a branch-line or Lange coupler outputs signals in phase quadrature, ideal for balanced amplifiers, image-reject mixers, and reflectometers. A 180° hybrid such as a rat-race ring or magic tee produces sum and difference outputs, preferred for balanced mixers, push-pull amplifiers, and antenna sum/difference feeds.

Related Terms

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