Identify device from S-matrix with ±S14 entries

Identification

       | S11   S12   S13   S14 |
 [S] = | S12   S22   S13  -S14 |
       | S13   S13   0     0   |
       | S14  -S14   0     0   |

• Port 3 receives equal signals in phase from ports 1 and 2 (S31 = S32 = S13): port 3 behaves as the H-arm.
• Port 4 receives equal signals 180° out of phase from ports 1 and 2 (S41 = −S42 = S14): port 4 behaves as the E-arm.
• S34 = S43 = 0: the E and H arms are isolated; S33 = S44 = 0: those arms are matched.
• The matrix is symmetric, so the device is reciprocal.

These are the features of a magic tee (hybrid tee, E-H tee) with ports 1 and 2 as the collinear arms.

              E-arm (4)
                | |
     -----------+ +-----------
 (1) ===========+ X +=========== (2)
     -----------+ +-----------
               / /
              / /  H-arm (3)

Finding the ideal values (lossless condition)

For a lossless junction, [S]*ᵀ[S] = I.

 Row 3: |S13|² + |S13|² = 1  ->  S13 = 1/√2
 Row 4: |S14|² + |S14|² = 1  ->  S14 = 1/√2
 Row 1: |S11|² + |S12|² + 1/2 + 1/2 = 1
        -> S11 = 0 and S12 = 0
 Row 2: |S12|² + |S22|² + 1/2 + 1/2 = 1  ->  S22 = 0

So matching the E and H arms automatically matches ports 1 and 2 and isolates them:

              | 0   0   1   1 |
 [S] = (1/√2) | 0   0   1  -1 |
              | 1   1   0   0 |
              | 1  -1   0   0 |

Properties

1. Input at H-arm (3): b1 = b2 = a3/√2 – equal in-phase split; b4 = 0.
2. Input at E-arm (4): b1 = a4/√2, b2 = −a4/√2 – equal split, 180° apart; b3 = 0.
3. Input at port 1: b3 = b4 = a1/√2; port 2 gets nothing (S21 = 0), so collinear arms are isolated.
4. Equal in-phase inputs at 1 and 2: b3 = √2·a (all power at H-arm), b4 = 0. Equal anti-phase inputs: all power at E-arm.
5. All ports matched, lossless and reciprocal.

Uses

Balanced mixers, radar duplexers, power combiners/dividers, impedance bridges and monopulse comparators.