Coupled Wave Theory and Waveguide Applications

Some theory describing the behavior of two coupled waves is presented, and it is shown that this theory applies to coupled transmission lines. A loose-coupling theory, applicable when very little power is transferred between the coupled waves, shows how to taper the coupling distribution to minimize the length of the coupling region. A tight-coupling theory, applicable when the coupling is uniform along the direction of wave propagation, shows that a periodic exchange of energy between coupled waves takes place provided that the attenuation and phase constants (α 1 and β respectively) are both equal, or provided that the phase constants are equal and the difference between the attenuation constants (α 1 — α 2 ) is small compared to the coefficient of coupling c. Either (α 1 — α 2 )/c or (β 1 — β 2 )/c being large compared to unity is sufficient to prevent appreciable energy exchange between the coupled waves. Experimental work has confirmed the theory. Applications include highly efficient pure-mode transducers in multi-mode systems, and frequency-selective filters.