3.6. Directional Couplers
Apply even/odd modes analysis,
Since port 1 is matched (Zin = Z0s), by symmetry every other port is also matched.
V1 = Vi/2 by voltage division,
Define a design frequency f0 at which l = λ/4,
V3 = cVi/2, from which, c acquires the meaning:
voltage coupling = c = V3/V1.
Following a similar analysis,
Operating point in practical applications is selected for maximum coupling |V3/V1|2 = c2. The smallest size TL producing this is l = λ/4, which is easily implemented in both PCB and MMIC technologies. For l = λ/4, V3/V1 = c, V2/V1 = -j√(1-c2).
