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Journal of Applied Physics

Simple formulae for kinetic inductance of coupled superconducting microstrip lines

Jinfeng Kang, Ruqi Han, Guangcheng Xiong, Xiaoyan Liu, Yangyuan Wang

Published Feb 15, 1997• 1 citation
Publisher

Abstract

Simple formulae for the kinetic inductance of coupled superconducting microstrip lines in odd mode and even mode have been derived by using the conformal mapping technique. Based on the simple formulae, the geometrical effects of kinetic inductance in odd mode and even mode are analyzed and compared with those of magnetic inductance. The coupling effects of two proximity microstrip lines caused by the kinetic inductance are also studied. The kinetic inductance is dominant for smaller geometrical sizes but is less important than the magnetic inductance for larger geometrical sizes.

DOI
10.1063/1.364040

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Simple formulae for the kinetic inductance of coupled superconducting microstrip lines in odd mode and even mode have been derived by using the conformal mapping technique. Based on the simple formulae, the geometrical effects of kinetic inductance in odd mode and even mode are analyzed and compared with those of magnetic inductance. The coupling effects of two proximity microstrip lines caused by the kinetic inductance are also studied. The kinetic inductance is dominant for smaller geometrical sizes but is less important than the magnetic inductance for larger geometrical sizes.
It is pointed out that superconducting microstrip transmission lines operating in the kinetic-inductance limit have the potential to reduce the size and weight of microwave circuits by several orders of magnitude. Since the phase velocity of these guided wave structures is up to a hundred times less than in free space, the electrical length of distributed elements is similarly reduced. Simple transmission lines have been fabricated from both low- and high-transition-temperature superconductors while more complicated circuits, such as filters, with a good match to 50- Omega coax have been fabricated with the low-transition-temperature superconductors. Also, a novel coupled-line topology, compatible with these structures, has been studied analytically.>
Superconducting microstrip, with phase velocities of about 0.01c, employing kinetic inductance have been fabricated using niobium nitride and a silicon dielectric. Delay lines using this phenomenon have several advantages for analog signal processing, including low loss and very compact size. Measurements of kinetic inductance microstrip delay lines were made in the frequency domain and the time domain. The results were compared to theoretical predictions and an accurate circuit model was developed. The circuit model was used to determine the frequency- and temperature-dependent losses of the delay line.
An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.
This paper investigates linear and nonlinear microwave propagation in a periodic superconductor-normal conductor microstrip transmission line (S-N muTL). We derive closed-form equations for complex propagation constant, input impedance and complex resonant frequencies for linear infinite and finite periodic S-N muTL. Jumps on the curves of attenuation constants, input impedances and eigenfrequencies occur exactly at the Bragg frequencies. We demonstrate that the finite S-N muTL shows the same behavior as infinite periodic SmuTL, when there is enough number of unit cells. Furthermore, nonlinear microwave signal propagation analyses are carried out based on the self-consistent method, when the kinetic inductance of the superconducting segments is in the nonlinear regime.
A theoretical study is made of the inductive coupling of two superconducting striplines. The study takes advantage of the kinetic inductance, which is remarkable in superconducting films where the thickness is less than the London penetration depth. In the case of weak coupling where the coupled-mode description is most effective, it has been found that the forward-wave coupling leads to power exchange between two striplines with the efficiency of m= kappa 2 /( kappa 2 + Delta 2 ) at a distance of I= pi /2( kappa 2 + Delta 2 ) 1 2/. Here kappa 2 = beta 1 beta 2 M 2 /4L 1 L 2 is the coupling coefficient and delta =(1/2)(B 1 -B 2 ) is the phase mismatch parameter, where beta i , L i (i=1,2) and M are propagation constants, self-inductances and the mutual inductance of the two striplines, respectively. Numerical studies are also made for new types of kinetic inductance devices for microwave components, i.e. a directional coupler and microwave switch using the scattering coefficients in the general case.