Frequency-dependent Surface Impedance Research Articles

Effects of frequency-dependent surface impedance on the vacuum electronic terahertz sources

When the working frequency of vacuum electronic device reaches the terahertz frequency, the ohmic loss has a significant impact on the vacuum electronic device. To study the effect of the ohmic loss on the working characteristic of the vacuum electronic terahertz devices, this paper implements the frequency-dependent surface impedance boundary condition (SIBC) in the 3 dimensional particle in cell code UNIPIC-3D. Conformal mesh is adopted in the code to overcome the staircase error in traditional particle in cell method. By using the surface impedance boundary, we eliminate the need to study the field inside the lossy dielectric objects which require extremely small grid cells for numerical stability. In comparison with constant parameter SIBC, the dispersive SIBC is applicable over a very large frequency bandwidth and over a large range of conductivities. The correctness of the implementation is verified by simulating the lossy resonant cavity and circular waveguide, the simulated power loss is comparable with the theoretical predication. High power vacuum electronic devices of terahertz regime are attracting extensive interests due to their potential applications in science and technologies. The impulse-wave relativistic surface wave oscillator (SWO) and low-voltage continuous-wave planar grating backward wave oscillator (BWO) both made of copper are numerically studied by using UNIPIC-3D and dispersive surface impedance boundary condition. Numerical results show that the strongest field is very close to the slow wave structure where the beam-wave interaction occurs and that terahertz wave generates both in these two devices. The distributed wall loss has a considerable effect on the devices: the output power has a significant decrease and the startup time becomes longer, but the working frequencies of the two devices keep unchanged. To improve the efficiency of relativistic SWO, a resonant reflector is proposed between the diode and the slow wave structure. Numerical results show that the working frequency of the device with a resonant reflector keeps unchanged as the original one, but the output power increases to 60 MW from 41 MW of the original one when the ohmic loss is considered.

Spatially dispersive surface impedance in the electrodynamics of conductors without dc dissipation

We derive general frequency dependencies of the surface impedance modulus for conductors without the dc dissipation, i. e. for superconductors or perfect conductors. The frequency-dependent surface impedance was applied for the solutions corresponding to the spatially dispersive eigenvalues of the permittivity operator for conductors. We demonstrate that appropriately taken into account effects of the spatial dispersion can give the general frequency dependence of the surface impedance for the obtained solutions including that for superconductor. It is shown that an incorporation of the spatial dispersion leads to an appearance of the Meissner effect in perfect conductors in the same manner as in superconductors.

SIBC incorporated in conformal FDTD to efficiently simulate the thin conductive layer of periodic structure

In this study, surface impedance boundary condition (SIBC) incorporated in conformal finite-difference time-domain (CFDTD) to efficiently simulate the thin conductive layer of periodic structure is proposed. The method is based on the vector fitting (VF) technique to approximate the frequency-dependent surface impedance of the thin conductive layer by a series of partial fractions in terms of real or complex conjugate pole-residue pairs. A discrete-time equation of SIBC is then derived and incorporated in CFDTD update equations by Laplace transform and time central difference methods. The proposed method takes the following advantages, (i) the time step is no longer bounded by the fine resolution of the thin layer; (ii) The complicated recursive convolution approach is avoided, and the approximation of the frequency-dependent surface impedance of the thin conductive layer can be easy to handle with the VF method. This method is numerically verified for the time- and frequency-dependent scattering characteristics of several periodic structures behaved under normal and oblique incident waves.

Time domain representation of frequency-dependent surface impedance using finite impulse response filters in discrete Huygens’ modeling

In recent years there has been renewed interest in time-domain numerical methods in view of sound synthesis applications and the need to obtain the impulse response of acoustic systems. Discrete Huygens’ Modeling (DHM) is one of the time-domain methods available and it presents interesting characteristics, such as its simple implementation and relatively low computational cost. Although an equivalent method has been widely applied in the field of electromagnetism, its application in the area of acoustics is still limited, especially for describing absorption materials at boundaries. The main aim of this paper is to show the applicability of the Finite Impulse Response (FIR) filters to represent sound absorbing materials in a DHM model, without significantly degrading its computational performance. The DHM have been used to indirectly obtain the frequency response functions of an acoustic cavity, both with and without the presence of absorbing materials on its boundaries. Numerical results and computational times are compared with Finite Element (FE) models of the cavity. While very good agreement between the methods is observed, the computational cost of the DHM models can be orders of magnitude lower than in the case of FE models.

Unconventional wave reflection due to “resonant surface”

This study deals with the reflection phenomena in an elastic half-space on which lies a “resonant surface”. The resonant surface consists in a 2D periodic repetition of a surface element over which linear oscillators are distributed. Following the homogenization approach developed by Boutin and Roussillon (2006) [1], the periodic distribution of oscillators (1 to 3D sprung-mass) is reduced to a frequency-dependent surface impedance. It is hereby shown that the surface motion comes to zero in the resonating direction around the oscillators’ eigenfrequency. Further, the surface impedance may be isotropic or anisotropic, according to the type of oscillator. Thereby unusual free/rigid mixed boundary condition arises, which in turn induces atypical reflected wave fields. The most notable effects are (i) drastic change of P and SV waves conversion, (ii) depolarization of shear waves, (iii) conversion of SH waves into P and SV waves, and (iv) possibility of vanishment of the whole reflected field. The physical insight of the theoretical results is discussed and numerical illustrations are provided.

Ground effects of space weather investigated by the surface impedance

Abstract The objective of this paper is to provide a discussion of the surface impedance applicable in connection with studies of geomagnetically induced currents (GIC) in technological systems. This viewpoint means that the surface impedance is regarded as a tool to determine the horizontal (geo)electric field at the Earth’s surface, which is the key quantity for GIC. Thus the approach is different from the traditional magnetotelluric viewpoint. The definition of the surface impedance usually involves wavenumber-frequency-domain fields, so inverse Fourier transforming the expression of the electric field in terms of the surface impedance and the geomagnetic field results in convolution integrals in the time and space domains. The frequency-dependent surface impedance has a high-pass filter character whereas the corresponding transfer function between the electric field and the time derivative of the magnetic field is of a low-pass filter type. The relative change of the latter transfer function with frequency is usually smaller than that of the surface impedance, which indicates that the geoelectric field is closer to the time derivative than to the magnetic field itself. An investigation of the surface impedance defined by the space-domain electric and magnetic components indicates that the largest electric fields are not always achieved by the plane wave assumption, which is sometimes regarded as an extreme case for GIC. It is also concluded in this paper that it is often possible to apply the plane wave relation locally between the surface electric and magnetic fields. The absolute value of the surface impedance decreases with an increasing wavenumber although the maximum may also be at a non-zero value of the wavenumber. The imaginary part of the surface impedance usually much exceeds the real part.

Effective microwave surface impedance of a thin type-II superconducting film in the parallel magnetic field

The effective microwave surface impedance for a layered structure made of a thin type-II superconducting film as well as a dielectric substrate is theoretically investigated. We consider the superconducting film with thickness comparable or smaller than the penetration depth in the parallel magnetic field, in which a vortex chain is present in the central plane of film. The total effective microwave surface impedance is shown to consist of two parts, one represents the Meissner state response which can be calculated by the usual impedance transform technique, and the other not obtainable from the impedance transform is the vortex response. The effective surface resistance and reactance due to the vortex chain are specifically numerically investigated as functions of the thicknesses of film and dielectric, static magnetic field and microwave frequency as well. For the frequency-dependent surface impedance, numerical results reveal that there exists a crossover frequency such that the surface resistance is equal to the surface reactance. This crossover frequency is further proven to be equal to the depinning frequency for a vortex system.

A tunable impedance surface performing as a reconfigurable beam steering reflector

We describe a reconfigurable microwave surface that performs as a new kind of beam steering reflector. The surface is textured with an array of tiny resonators, which provide a frequency-dependent surface impedance. By tuning the individual resonators, the surface impedance, and thus the reflection coefficient phase, can be varied as a function of position across the reflector. Using a reflection phase gradient, the surface can steer a reflected beam. As an example, we have built a simple mechanically tuned surface in which physical motion of only 1/100 wavelength generates a sufficient phase gradient to steer a reflected beam by /spl plusmn/16 degrees. To steer to greater angles, the surface can be configured as an artificial microwave grating, capable of /spl plusmn/38 degrees of beam steering. The concept of the tunable impedance surface demonstrated here can be extended to electrically controlled structures, which would permit more elaborate reflection phase patterns, and provide more capabilities, such as the ability to focus or steer multiple beams.

Efficient calculation of surface impedance for rectangular conductors

The Letter presents a new expression for the frequency-dependent surface impedance of a rectangular bar that is easily used, and is numerically efficient. By dividing the metal bar into rectangular and square sections, skin depth-induced current crowding to the surfaces and corners can be accurately modelled. Comparison with measured data shows excellent agreement over a wide frequency range, covering the transition from DC-like behaviour to skin-depth limited behaviour.

High Frequency Characterization of High Temperature Superconducting Thin-Film Lines

ABSTRACT An integral equation approach is applied to calculate the propagation characteristics of high temperature thin-film superconducting lines at high frequencies. To evaluate losses in these lines, the superconducting strips are replaced by frequency-dependent surface impedance boundaries. The values of these surface impedances are measured experimentally by a TE01 cavity technique. Using this method, a parametric study is performed where phase and attenuation constants as well as characteristic impedance are evaluated as functions of frequency, temperature, permittivity and geometry of the structure.