Waveguide hybrids – Magic-Tee properties and what is not true For the four-port magic tee (E-plane port, H-plane port, and two co-linear ports), identify the statement that is incorrect about coupling, matching, and power division behavior.

Difficulty: Medium

E-arm (E-plane port) and H-arm (H-plane port) are mutually decoupled (isolated)
The two co-linear (coplanar) ports are mutually coupled through the hybrid
All four ports can be made perfectly matched simultaneously over a band
Power injected into either co-linear port splits equally between the E and H arms
Excitation at the H-arm produces equal-phase outputs at the co-linear ports

Correct Answer: All four ports can be made perfectly matched simultaneously over a band

Explanation:

Introduction:
The waveguide magic-tee (also called a hybrid tee) is a 4-port passive microwave component formed by combining an E-plane tee and an H-plane tee. It provides sum and difference behavior between the two co-linear ports and is widely used for power division/combining, mixer/antenna feeds, and bridge circuits. This question probes which commonly claimed property is not correct for a practical magic-tee.

Given Data / Assumptions:

Four ports: two co-linear (coplanar) main waveguide ports, one side E-arm, one side H-arm.
Passive, reciprocal, lossless approximation with realistic tuning screws/irises for matching.
Standard phase conventions: H-arm is the “sum” port; E-arm is the “difference” port for the two co-linear ports.

Concept / Approach:

In an ideal hybrid tee, the E-arm and H-arm are isolated (no coupling), while each co-linear port couples to both side arms. Exciting the H-arm yields equal-phase outputs at the co-linear ports; exciting the E-arm yields equal-magnitude outputs that are 180° out of phase. A signal entering a co-linear port divides equally into the E and H arms (with the other co-linear port isolated in the ideal S-matrix). However, due to network constraints and finite element tuning, all four ports cannot be made perfectly matched simultaneously over bandwidth; usually only a subset are critically matched and the others are near-matched with residual reflection.

Step-by-Step Solution:

1) Use the hybrid tee S-matrix properties: isolation between E and H arms; symmetry between co-linear ports.2) Identify correct statements: isolation (E vs H) is true; co-linear ports couple via the hybrid; co-linear excitation splits into E/H arms; H-arm excitation gives equal-phase co-linear outputs.3) Conclude the “all ports perfectly matched” claim is not achievable in practice for broadband operation.

Verification / Alternative check:

Design texts show tuning elements to improve matches at selected ports; perfect 4-port broadband conjugate matching is not simultaneously realized in a passive, lossless hybrid tee.

Why Other Options Are Wrong:

Option A: True—E and H arms are designed to be isolated. Option B: True—co-linear ports are coupled via the junction. Option D: True in the ideal S-matrix sense for co-linear input. Option E: True—H-arm acts as the sum port producing in-phase outputs.

Common Pitfalls:

Assuming “perfect matching everywhere” because individual ports can be tuned near match; ignoring bandwidth and lossless reciprocity constraints.

Final Answer:

All four ports can be made perfectly matched simultaneously over a band.

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Waveguide hybrids – Magic-Tee properties and what is not true For the four-port magic tee (E-plane port, H-plane port, and two co-linear ports), identify the statement that is incorrect about coupling, matching, and power division behavior.

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