Hybrid ring (rat-race) coupler — basic properties Consider a hybrid ring. Evaluate the following statements: 1) Ports 1 and 2 are decoupled (isolated). 2) Ports 3 and 4 are coupled. 3) A signal entering either port 1 or 2 splits equally between ports 3 and 4. 4) A signal entering either port 3 or 4 splits equally between ports 1 and 2. Which statements are correct?

Introduction / Context:
The hybrid ring (rat-race) is a 3 dB four-port coupler built from a ring one-and-a-half wavelengths in circumference with ports spaced 90 degrees. It produces sum and difference combinations with port-to-port isolation depending on which port is used as input.

Given Data / Assumptions:

• Ideal, lossless hybrid ring with ports equally spaced.
• Standard port labeling where opposite ports act as isolated pairs for specific excitations.

Concept / Approach:
When excited at one port, the signal splits into two paths around the ring that recombine with appropriate phase at the output ports, giving equal magnitudes at two ports and isolation at the fourth. For the common labeling, ports 1 and 2 are isolated from each other when driven at 3 or 4, and a drive at 1 (or 2) divides equally between 3 and 4. Symmetry implies reciprocal statements when driving the opposite pair.

Step-by-Step Solution:

Verification / Alternative check:
Ideal S-matrix of a rat-race confirms 3 dB splits with port pairs isolated depending on excitation. Practical units show finite directivity but follow the same pattern.

Why Other Options Are Wrong:

• Any subset (B, C, D) omits at least one true statement about equal splitting or isolation inherent to the hybrid ring.

Common Pitfalls:
Confusing port numbering schemes; mixing hybrid ring behavior with that of a magic-tee or directional coupler.

Final Answer:
1, 2, 3 and 4