Propagation characteristics of inductively-coupled superconducting microstrip

A dispersion relationship is developed for the coupled transmission line case of three arbitrarily thick superconductors separated by two arbitrarily thick dielectric layers. The dispersion equation, which was found by the transverse resonance method, can be used to solve for the propagation characteristics of the two dominant coupled line modes. These results have been used to show that, in the symmetric case, the mode with the lower phase velocity had the same attenuation per wavelength as the mode with the higher phase velocity. In addition, a first-order expansion of the dispersion relationship yields an accurate closed-form expression for the attenuation of the coupled line modes. Using a mutual inductance to describe the coupling, an equivalent circuit has been presented, which accurately models the propagation characteristics of the coupled transmission line modes. The equivalent circuit model facilitates the design of circuits using inductively coupled structures, as has been shown with the design of a 20-dB coupler.<>