Analysis of Nonlinearities in Superconducting Microstrip Straight Bends; FDTD Method in Comparison with Nonlinear Circuit Modeling (original) (raw)
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Journal of Superconductivity and Novel Magnetism
This paper presents the prediction of nonlinearities in the superconducting microstrip straight bends in microwave frequencies based on two different methods; FDTD simulation as a numerical approach, and nonlinear circuit modeling as an analytical method. In the FDTD method, the superconducting microstrip structures are simulated with London’s equations. In the simulation, the penetration depth and normal conducting coefficient are considered as functions of current density of superconductor. To simulate the thin strip of superconductor, a non-uniform mesh has been used. For the nonlinear circuit modeling, we use distributed RLGC parameters for superconducting microstrip transmission lines. These parameters are considered as functions of the current distribution. This yields an equivalent nonlinear circuit model for bends. The final equivalent nonlinear circuit is analyzed using the harmonic balance (HB) method. Different straight bend structures have been considered and the two methods’ results are compared.
Modeling of unusual nonlinear behaviors in superconducting microstrip transmission lines
Physica C: Superconductivity, 2013
There are unusual nonlinear behaviors in superconducting materials, especially at low temperatures. This paper describes the procedure to reliably predict this nonlinearity in superconducting microstrip transmission lines (SMTLs). An accurate nonlinear distributed circuit model, based on simultaneously considering of both quadratic and modulus nonlinearity dependences, is proposed. All parameters of the equivalent circuit can be calculated analytically using proposed closed-form expressions. A numerical method based on Harmonic Balance approach is used to predict nonlinear phenomena like intermodulation distortions and third harmonic generations. Nonlinear analyses of the SMTLs at the different temperatures and the input powers have been presented. This proposed model can describe the unusual behaviors of the nonlinearity at low temperatures, which are frequently observed in the SMTLs.
Modeling Unusual Nonlinear Behaviors in Superconducting Microstrip Transmission Lines
Physica C: Superconductivity and its Applications
There are unusual nonlinear behaviors in superconducting materials, especially at low temperatures. This paper describes the procedure to reliably predict this nonlinearity in superconducting microstrip transmission lines (SMTLs). An accurate nonlinear distributed circuit model, based on simultaneously considering of both quadratic and modulus nonlinearity dependences, is proposed. All parameters of the equivalent circuit can be calculated analytically using proposed closed-form expressions. A numerical method based on Harmonic Balance approach is used to predict nonlinear phenomena like intermodulation distortions and third harmonic generations. Nonlinear analyses of the SMTLs at the different temperatures and the input powers have been presented. This proposed model can describe the unusual behaviors of the nonlinearity at low temperatures, which are frequently observed in the SMTLs.► Avoiding of considering just quadratic or modulus nonlinearity. ► Proposing a nonlinear model to predict unusual nonlinear behaviors at low temperatures. ► Description of temperature dependency of nonlinear behaviors in superconducting lines. ► Analytical formulation for each parameter in our proposed model. ► Obtaining very good results which shows this model can predict unusual nonlinear behavior.
Current Distribution and Nonlinearity of Open-ends and Gaps in Superconducting Microstrip Structures
Journal of Superconductivity and Novel Magnetism
Superconducting devices are known to produce nonlinear effects. In planar structures, these nonlinearities depend on the current distribution on the strip, which definitely depends on the structure of device. This paper used a numerical method based on 3D-FEM to obtain the current distribution in the open-ends and gaps in the superconducting microstrip structures. This is used to present the nonlinear distributed circuit modeling of these discontinuities and its impact on the nonlinear phenomenon. This nonlinear circuit model is used in the Harmonic Balance (HB) method to analyze nonlinearity in the superconducting microwave devices. Therefore, this simple accurate enough nonlinear circuit model is warmly welcomed to retire the seemingly inevitable use of time- and memory-consuming numerical techniques for nonlinear analysis of discontinuities in superconducting microwave structures. As an example, we analyze a microstrip superconducting end-coupled band pass filter (BPF). These results are very useful for optimizing the resonators of the superconducting microwave filters in order to minimize its nonlinear distortions.
IEEE Transaction on Applied Superconductivity
Superconducting materials are known to exhibit nonlinear effects and to produce harmonic generation and intermodulation distortion in superconductive circuits. In planar structures, these nonlinearities depend on the current distribution on the strip which is mainly determined by the structure of the device. This paper investigates the current distribution at the step-in-width discontinuity in superconducting microstrip transmission lines, which is computed by a numerical approach based on a 3-D finite-element method. This current distribution is used to obtain the parameters of the nonlinear circuit model for the superconducting microstrip step-in-width discontinuity. The proposed equivalent nonlinear circuit can be solved using the harmonic balance method. Examples of two superconducting structures which contain the steps in width are given and validated by comparison with electromagnetic full-wave results. The proposed model can be used for effective optimization of the superconducting microwave filter resonators in order to minimize their nonlinear distortions.
Nonlinearity in Symmetric and Asymmetric Superconducting Parallel-Coupled Microstrip Lines
IET Microwaves, Antennas and Propagation
Superconducting materials are known to produce intermodulation distortion and other non-linear effects. In microstrip structures, the non-linearity depends on the current distribution on the strip which is mainly determined by the geometrical structure of the device. The current distribution in superconducting parallel-coupled microstrip lines is computed by a numerical approach based on a three-dimensional finite element method. This computed current distribution is used to produce a non-linear circuit model for parallel-coupled superconducting lines. A numerical technique based on the harmonic balance approach is used for non-linear analysis of the proposed equivalent circuit. To validate the accuracy of the proposed model, the results of analysis of hairpin resonator superconducting band pass filters are compared with measured results. This proposed technique is useful for fast and efficient non-linear analysis of the superconducting microstrip coupled lines.
Modeling Superconducting Transmission Line Bends and Their Impact on Nonlinear Effects
IEEE Transactions on Microwave Theory and Techniques, 2000
This paper reports on a numerical technique to obtain the current distribution in the annular bent sections of planar layouts. This is used to obtain the linear and nonlinear circuit distributed parameters modeling a superconducting strip bend and its impact on intermodulation distortion. As an example, we analyze a superconductive open-loop resonator and assess the linear and nonlinear contribution of its bends in its overall linear and nonlinear performance. These simulations are very useful for optimizing the resonators of a filter in order to minimize its nonlinear distortion.
Physics Procedia, Elsevier.
Superconducting passive microwave devices unlike routine normal conductor ones, due to dependence of superfluid density (ns) to current distribution, have a nonlinear behavior called Nonlinear Meissner Effect (NME). In this paper, a nonlinear distributed circuit model for HTS transmission lines with sub-wavelength longitudinal non-uniformity in the case of weak nonlinearity is proposed. This model is based on the quasi-TEM approximation of sub-wavelength non-uniform transmission lines (SW-NUTLs) that proposes closed form formulas for effective characteristic impedance and complex propagation constant of SW-NUTLs. Any NUTLs can be modeled with the mentioned method through dividing it into adequately small subsections to fulfill sub-wavelength condition. Regarding these propagation parameters relations, some effective equations for RLGC parameters are inferred. Because of dependence of the penetration depth and the real part of conductivity on ns, the proposed effective resistance and inductance depend on current distribution that in case of weak nonlinearity, follow a square-law form. As such the nonlinear microwave effects such as Intermodulation distortion (IMD) and harmonic generation can be calculated with harmonic balance (HB) Analysis. This semi-analytical approach shows great accuracy in different test cases.
IEEE Transactions on Applied Superconductivity, 2005
This paper presents a comprehensive study of microwave nonlinearities in superconductors, with an emphasis on intermodulation distortion and third-harmonic generation. It contains the analysis of various resonant and nonresonant test devices and its validation using numerical simulations based on harmonic balance (HB). The HB simulations made on test devices show that the closed-form equations for intermodulation and third-harmonic generation are only valid at low power levels. The paper also contains examples of application of HB to illustrate that this technique is useful to simulate superconductive devices other than simple test devices, and that the validity of the simulations is not restricted to low drive power levels. Most of the analyses and simulations of this paper are based on electrical parameters that describe the nonlinearities in the superconducting material. These parameters are compatible with many existing models of microwave nonlinearities in superconductors. We discuss the particulars on how to relate these electrical parameters with one of the existing models that postulates that the nonlinear effects are due to a dependence of the penetration depth on the current density in the superconductor.
In this study, an equivalent linear and non-linear circuit model of superconducting microstrip T-junction (SMT) structures is proposed. Two types of SMT structures are analysed using suggested model and their scattering behaviour is compared using both the method of moment and the finite-element method (FEM). The fundamental and third-order harmonic outputs are obtained using harmonic balance method to observe the non-linear behaviour in SMT structures. A linear and non-linear model for enhanced SMT structures is also suggested and verified by S-parameters comparison between the model and FEM method. The non-linearity in enhanced structures is modelled similarly and compared with results of normal structures.