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Waveguide junctions and magic tee operation

Short answer

Waveguide junctions are passive multiport connections for dividing, combining, or routing microwave power. The magic tee’s S-parameters show H-arm input gives equal in-phase outputs at ports 1 and 2; E-arm input gives equal anti-phase outputs; collinear arms are isolated. All ports are matched, lossless, and reciprocal.

What are waveguide junctions? Describe the operational principles of magic tee based on s-parameters.

Waveguide junctions

Waveguide junctions are passive devices where three or more waveguide sections meet, used to divide, combine or route microwave power. The common types are:

  • E-plane tee: side arm on the broad wall; splits power into two equal parts 180° out of phase.
  • H-plane tee: side arm on the narrow wall; splits power equally in phase.
  • Magic tee (E-H tee): combination of E- and H-plane tees; a four-port hybrid.
  • Hybrid ring (rat-race) and directional couplers.

Operation of magic tee using S-parameters

Ports 1 and 2 are collinear, port 3 the H-arm, port 4 the E-arm:

              | 0   0   1   1 |
 [S] = (1/√2) | 0   0   1  -1 |
              | 1   1   0   0 |
              | 1  -1   0   0 |
  • Input at H-arm: b1 = b2 = a3/√2, b4 = 0 – equal in-phase split, nothing to E-arm.
  • Input at E-arm: b1 = a4/√2, b2 = −a4/√2, b3 = 0 – equal anti-phase split.
  • Input at port 1: b3 = b4 = a1/√2, b2 = 0 – collinear arms isolated.
  • Equal in-phase inputs at 1 and 2: all power at H-arm (sum); anti-phase: all at E-arm (difference).
  • All ports matched, lossless and reciprocal; used in mixers, duplexers and bridges.

✓ Answer checked by Claude Opus 5.5 (high effort)

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