Transmission Lines

Cross-Junction

Q: How does a symmetric waveguide cross-junction divide power among its four ports?

In an ideal, perfectly symmetric H-plane cross-junction with the dominant TE10 mode incident on port 1, power couples into the colinear through arm (port 3) and the two transverse side arms (ports 2 and 4). By geometric symmetry the two side arms receive equal power, but the bare junction is not matched: a significant fraction reflects back to port 1 and the split between the through arm and side arms is uneven, typically favoring the through arm. Reactive matching posts, inductive irises, or a centered tuning post are added to set the desired division and reduce return loss to better than 20 dB over the operating band. A common engineered split is a 3 dB equal division between the through arm and the combined side arms.

Q: Why does a bare cross-junction have poor return loss and how is it tuned?

At the intersection the waveguide cross section abruptly quadruples, creating a large discontinuity that excites local evanescent higher-order modes and presents a strongly reactive, mismatched impedance to the incident TE10 wave. An untuned junction often shows return loss of only 3 to 6 dB. Matching is achieved by placing one or more conducting posts or a dielectric or metallic septum at the center of the junction, and by adding inductive or capacitive irises in the arms. Posts add shunt susceptance that cancels the junction reactance, while their position controls the through-to-side power ratio. Modern designs are optimized in a full-wave field solver to reach return loss better than 25 dB and amplitude balance within 0.3 dB across a 10 to 15 percent bandwidth.

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Where two rectangular waveguides intersect at right angles in the same plane, the resulting four-port structure is called a cross-junction. With the dominant TE₁₀ mode incident on one port, energy divides between the colinear through arm and the two transverse side arms. The bare intersection is highly reactive and mismatched because the cross section abruptly quadruples, so practical junctions add centered matching posts or inductive irises to control the split and push return loss past 25 dB. Unlike a magic tee, a flat cross-junction provides no inherent port isolation; its behavior is governed entirely by geometric symmetry and the tuning elements at the crossing.

Category: Transmission Lines

Ports: 4 (planar)

Tuned Return Loss: > 25 dB

How a Four-Port Waveguide Cross Behaves

A cross-junction is the simplest four-port waveguide intersection: two identical rectangular guides share a common opening where they cross orthogonally. Whether the side arms branch in the broad-wall plane (an H-plane cross) or the narrow-wall plane (an E-plane cross) determines how the dominant TE₁₀ field couples across the discontinuity. Because all four arms meet at one cell, the junction is fully described by a 4×4 scattering matrix whose form is constrained by the structure's two planes of symmetry. That symmetry forces the two side-arm coupling coefficients to be equal and ties the reflection at each port to a single value, but it does not, by itself, make the junction matched or isolated.

The dominant physical effect is the abrupt change in guide cross section at the crossing. An incident wave sees the effective area quadruple, which launches a cloud of evanescent higher-order modes that store reactive energy locally. To an engineer at the reference plane this looks like a large shunt reactance in parallel with the through path, so an untuned junction typically returns 3 to 6 dB of incident power and splits the rest unevenly toward the colinear arm. Engineering a useful device means cancelling that reactance and forcing the desired power ratio.

The standard remedy is a conducting post (or a small set of posts) at the geometric center of the crossing, often supplemented by inductive irises in selected arms. A centered post adds shunt susceptance that tunes out the junction reactance, while its diameter and offset trade the through-arm coupling against the side-arm coupling. With full-wave optimization, a cross-junction can be driven to an equal 3 dB split between the through arm and the combined side arms, or to an asymmetric tap for low-coupling monitoring, while holding amplitude balance within roughly 0.3 dB across a 10 to 15 percent band.

Scattering Matrix and Symmetry Constraints

Numbering the colinear arms 1 and 3 and the transverse arms 2 and 4, the two mirror planes reduce the independent scattering parameters to a reflection term, a through term, and a side-coupling term. The two equations below capture the matched-junction conditions and the lossless power-conservation requirement that any tuned design must satisfy.

Symmetric S-matrix (ports 1,3 colinear; 2,4 transverse):
S₁₁ = S₃₃ = ρ, S₁₃ = τ, S₁₂ = S₁₄ = S₃₂ = S₃₄ = κ

Lossless power conservation (per port):
|ρ|² + |τ|² + 2×|κ|² ≈ 1

Matching-post susceptance condition:
B_post ≈ −B_junction ⇒ ρ → 0

Where ρ = port reflection, τ = colinear through coupling, κ = side-arm coupling, B = normalized shunt susceptance. For an equal 3 dB through/side split with ρ ≈ 0: |τ|² ≈ 0.5 and 2×|κ|² ≈ 0.5, so each side arm receives ≈ −6 dB.

Cross-Junction Versus Related Waveguide Junctions

Junction	Ports	Inherent Isolation	Matched (bare)	Typical Tuned Return Loss	Primary Use
Cross-junction (planar)	4	None	No	> 25 dB	Power tap, equal split, mode sampling
E-plane tee	3	None	No	20 to 25 dB	Series power split / combine
H-plane tee	3	None	No	20 to 25 dB	Shunt power split / combine
Magic tee (hybrid)	4	E and H ports isolated	Yes (matched ports)	> 30 dB	Balanced mixers, comparators
Turnstile junction	6	Mode-orthogonal	No	> 25 dB	OMTs, polarization duplexers

Common Questions

Frequently Asked Questions

How does a symmetric waveguide cross-junction divide power among its four ports?

With TE₁₀ incident on port 1, the two mirror planes force the two transverse side arms (ports 2 and 4) to receive equal power. The bare junction is unmatched, so part reflects to port 1 and the through arm (port 3) takes the larger share. Adding a centered post or irises sets the ratio: a common engineered result is a 3 dB split between the through arm and the combined side arms, with each side arm at roughly −6 dB.

What is the difference between a cross-junction and a turnstile junction?

A planar cross-junction is a four-port device where two rectangular guides cross at right angles in one plane and couple through the TE₁₀ mode. A turnstile junction is a six-port device where four rectangular arms meet a central circular or square stub oriented perpendicular to their plane, using orthogonal modes for mode conversion. Turnstiles are the core of orthomode transducers and polarization duplexers; the flat cross is simpler but has no inherent isolation.

Why does a bare cross-junction have poor return loss and how is it tuned?

At the crossing the cross section abruptly quadruples, exciting evanescent higher-order modes and presenting a strongly reactive, mismatched impedance; an untuned junction often returns only 3 to 6 dB. A conducting post or septum at the center adds shunt susceptance that cancels the junction reactance, and its size and offset set the through-to-side ratio. Full-wave optimization pushes return loss past 25 dB with amplitude balance near 0.3 dB.

Related Terms

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