Short note: Directional coupler

A directional coupler is a four-port passive device that samples a known small fraction of the power travelling in one direction in the main line, while ignoring power travelling in the opposite direction. Port 1 is the input, port 2 the through (direct) port, port 3 the coupled port and port 4 the isolated port. A two-hole waveguide coupler is a common example.

 Input (1) ===================== Through (2)
                 o      o        main guide
             <-- λg/4 -->        (two holes)
 Isolated (4) ------------------ Coupled (3)
                                 auxiliary guide

Two-hole principle: waves coupled through the two holes, spaced λg/4 apart, travel the same distance to port 3 and add in phase, but differ by λg/2 (180°) on the way to port 4 and cancel. So power reaches port 3 only.

Performance parameters (P1 = input power, P2 through, P3 coupled, P4 isolated):

• Coupling factor: C = 10 log(P1/P3) dB (e.g. 3, 10, 20 dB)
• Directivity: D = 10 log(P3/P4) dB (ideally infinite, typically 30–40 dB)
• Isolation: I = 10 log(P1/P4) dB = C + D
• Insertion loss: IL = 10 log(P1/P2) dB

S-matrix of an ideal symmetric coupler (α² + β² = 1):

       | 0   α   jβ  0  |
 [S] = | α   0   0   jβ |
       | jβ  0   0   α  |
       | 0   jβ  α   0  |

All ports matched, ports 1 and 4 (and 2 and 3) isolated.

Types: two-hole and multi-hole waveguide couplers, Bethe-hole coupler, branch-line (90° hybrid) coupler, coupled-line microstrip coupler, rat-race (180° hybrid).

Applications: power monitoring and sampling, reflectometers for VSWR and reflection coefficient measurement, signal injection, power splitting/combining and balanced amplifiers.