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Design of a coplanar waveguide branch-line coupler for superconductive circuits

A.A. Omar, Malcolm G. Stubbs

Published Aug 1, 1994• 1 citation
OpenAlex

Abstract

A coplanar waveguide (CPW) is an attractive transmission line for superconducting applications because the presence of the CPW ground and centre strip in the same plane eliminates the need for via holes. These via holes may break the fragile substrate, lanthanum aluminate, most often used with superconductors.

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Several studies have been conducted on field solutions of superconducting planar transmission lines; however, no study has been performed on superconducting grounded coplanar waveguides (GCPWs) which is a promising element, from the viewpoint of immunity to electromagnetic interference, in superconducting circuits. The purpose of this article is to analyze the superconducting GCPW to achieve the electrical parameters of the transmission line. In this regard, first, the magnetic field within the superconducting film is described through a 2-D wave equation. By introducing the proper boundary conditions acquired through the field solution of the structure, the proposed wave equation is solved and the magnetic field is obtained. Accordingly, the current distribution and the inductance of the line are evaluated which are of interest in the superconducting community. Compared with conventional coplanar waveguide (CPW), the GCPW structure experiences less current density at the edges. Hence, it supports a much more sustainable current. Further, it is shown that the GCPW exhibits less kinetic inductance during data transmission.
Superconducting coplanar waveguide (CPW) can be widely used as two-dimensional (2D) resonator, transmission line or feedline, providing an important component for superconducting quantum circuit which is a promising candidate for quantum information processing. Due to the discontinuities and asymmetries in the ground planes, CPW usually exhibits the spurious resonance, which is a common source of decoherence in circuit quantum electrodynamics experiments. To mitigate the spurious resonance, we fabricated superconducting aluminum air-bridges on Nb CPW. The fabricated air-bridges are approximately 3 μm high and up to 120 μm long. Compared with other methods, the fabrication procedures of our air-bridges are simpler, and the air-bridge can withstand strong ultrasound.
This paper presents the design and simulation of a thin-film on-chip superconducting rat-race and quadrature branch-line coupler for circuit quantum electrodynamics. These couplers are designed at a center frequency of 6GHz using coplanar waveguide technology using a thin film of niobium or aluminum on sapphire substrates. The electrical connections are made between the ground using aluminum air bridges. The insertion losses to the through and coupled ports of rat-race and quadrature coupler are 3.1dB. The quadrature and rat-race couplers offer a wide bandwidth of 2GHz and 3GHz, respectively. A spectral shift of around 400MHz is observed in these couplers when operation is shifted from room temperature to the cryogenic regime. The simulated results have been discussed and analyzed.
In terahertz radio astronomy, superconducting coplanar waveguide resonators have been commonly applied in Kinetic Inductance Detectors (KIDs) to measure the absorption of photon energy in the millimeter and submillimeter bands. Here, we present an analysis on the performance of superconducting niobium coplanar waveguides (CPWs). To compute the loss in a superconducting CPW, we have incorporated the complex conductivity developed by Matis and Bardeen based on the superconducting BCS theory, into the CPW loss equation. We have made a comparison between the loss in a CPW at room temperature with that below the critical temperature Tc of the superconductor. It can be observed that at frequencies below the gap frequency fg, the low in the superconducting CPW is significantly lower than that in a normal CPW. Above fg, however, the material loses its superconductivity and the loss in both temperatures becomes comparable. In our analysi, we have also shown that the loss decreases as the gap bewteen the strip and groundplane becomes wider. Hence, with careful design, the loss in a CPW can actually be minimized.
We successfully designed and fabricated an absorption-type of superconducting coplanar waveguide (CPW) resonators. The resonators are made from a niobium film (about 160 nm thick) on a high-resistance Si substrate, and each resonator is fabricated as a meandered quarter-wavelength transmission line (one end is short to the ground and another end is capacitively coupled to a through feedline). With a vector network analyzer we measured the transmissions of the applied microwave through the resonators at ultra-low temperature. The obtained loaded quality factors are significantly high, i.e. up to ∼10 6 . When the temperature increases slowly from the base temperature (20 mK), the resonance frequencies of the resonators are blue shifted and the quality factors are lowered slightly. In principle, this type of device can integrate a series of CPW resonators with a common feedline, making it a promising candidate as the data bus for coupling distant solid-state qubits and the sensitive detector of single photons.
We present calculations of the properties of the first coplanar waveguide transmission line resonators patterned from high-Tc superconducting films at 8.8 and 6.5 GHz [1, 2]. Based on field calculations of the corresponding coplanar waveguides with infinite conductivity, performed by a partial wave synthesis (mode-matching method) [3], we obtain the superconductor losses subsequently using London's theory. Due to the high conductivity of the superconductive material both the electric and magnetic fields within the superconductor may be assumed to be parallel to the surface planes. For the small conductor thickness the tangential electrical field on each surface plane depends on the tangential magnetic fields on both surface planes. This relation is modelled by the surface impedance matrix Zs. The substrate losses are treated in the field calculations and are also taken into account. The calculated overall Q values are compared with the measured values and it has to be pointed out, that the superconducting thin films are due to the available material datas of the YBaCuO superconductor and the used substrate materials of a very good quality, because they reach nearly their upper limit given by the known material datas.