A multiple scattering solution for the effective permittivity of asphere mixture

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N² algorithm rather than the normal N³ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible     

A spectral domain method for multiple scattering in discrete randommedia

In an earlier paper (see ibid., vol.36, p.1114-28, 1988) a spectral-domain method was developed for analyzing multiply scattered scalar wavefields propagating in continuous random media. This method is extended to accommodate vector wavefields propagating in discrete random media. The two-dimensional Fourier spectra of vector wavefields propagating in the forward and backward directions are characterized by a pair of coupled first-order differential equations. Dyadic scattering functions characterize the local interaction of the wavefields with the random medium. The results are restricted to sparse distributions whereby the dyadic scattering functions are easily computed. The first- and second-order moments of the vector wavefields can be computed by invoking an assumption essentially equivalent to the Markov approximation as it is applied to scalar wavefields propagating in continuous random media. A complete solution for the coherent wavefield is derived and compared to known results. The results are essentially equivalent to those obtained by using the effective field approximation     

Experimental characterization of the effective propagation constantof dense random media

A new technique for measuring the effective propagation constant of dense random media is presented. This technique involves two major steps: (1) measurement of the mean bistatic scattered field of a cluster of the random medium confined in a spherical boundary and (2) characterization of the complex permittivity for a homogeneous dielectric sphere having identical radius and bistatic scattered field as those of the spherical cluster of the random medium. Using this measurement technique, not only the effective propagation constant of complex dense random media for which an analytical solution does not exist can be characterized, but it can also be used to establish the validity region of the existing models. The sensitivity analyses of the proposed algorithm show that the imaginary part of the effective propagation constant can be measured very accurately. It is also shown that the effective complex permittivity of media with very low dielectric contrast or volume fractions can be characterized accurately. Measurements of the effective propagation constant of different dense random media comprised of homogeneous spherical particles of different packing densities are reported and compared with the existing analytical models     

液相化学反应介电常数的测量与气泡影响分析

溶液中化学反应的等效介电常数是微波化学研究中的重要内容,等效介电常数的精确测量是研究微波与化学反应系统相互作用的基础.介绍了一种对溶液中化学反应等效介电常数随时间微弱变化跟踪测量的方法并对测量中经常遇到的气泡影响进行了分析.最后制作了一批测量探头,该探头可以有效排除其中的气泡.通过测量得到的反射系数和遗传算法(GA)可以对等效介电常数的微小变化进行精确测量.对稀溶液中的皂化反应测量的结果证实了该测量方法的有效性.     

Numerical method for calculation of complex dielectric permittivity

The letter describes the numerical method used at Istituto di Elettronica dell'Università di Pisa, Italy, for processing experimental data obtained in measuring complex dielectric permittivity by dielectrometer. The letter shows that it is possible to obtain high-precision results without using Von Hippel tables.     

Complex permittivity characterization of benzocyclobutene for terahertz applications

High-quality polymers such as the benzocyclobutene polymer (BCB) provide interesting dielectric feature for terahertz applications. Already used in silicon integrated circuit technologies, this material could become one of the most promising candidates for the realization of future THz waveguides and interconnections on a silicon substrate but also after active devices process on the top of any other technology (GaAs, InP, GaN…). A frequency-dependent complex permittivity of spin-coated thick layers of this low-k dielectric is obtained from transmittance spectra measured with Fourier transform spectroscopy in the frequency range of 0.5-5.4 THz. The dielectric constant and the loss tangent are discussed according to curing conditions of the photosensitive resin used. A low loss tangent value of 7 − 9 × 10^-3 at 1 THz is obtained with polymerisation in oxygen-free atmosphere. An incomplete curing and a high dose UV exposure have a weak impact on losses. These results associated with the high compatibility of this polymer with silicon and metals make BCB layers well suited for the design of microelectronic THz devices and circuits.     

Spread in effective permittivity of alumina substrates

Measured data on the spread in effective permittivity of alumina substrates in the range 1?18 GHz are presented. The data show both the spread from sample to sample and over the area of a single substrate. Effective permittivities were calculated from the resonant frequencies of open-ended straight-line resonators.     

Test for two-dimensional scattering Hurwitz polynomials

Tests for the discrete scattering Hurwitz property of two-dimensional (2-D) polynomials are suggested. Results belonging to two different categories are presented. The first procedure uses a finite number of rational operations and relies on the so-called polynomial resultant algebra. Alternative methods of testing, which are computationally less complex to implement are also developed.The work described in this paper was carried out during a visit of the first named author under the sponsorship of the Alexander von Humboldt Foundation at the Lehrstuhl für Nachrichtentechnik, Ruhr-Universität Bochum. The authors gratefully acknowledge the support received from this foundation.     

Numerical analysis of MOS transistor effective channel width

The effect of modulation of the effective width of a narrow-channel MOST by the gate voltage is demonstrated using a two-dimensional integral MOS process and device similator. The realistic shapes of the `bird's beak? and doping concentrations allow a numerical analysis of this effect to be made for typical enhancement- and depletion-mode devices, as well as a comparison with the experiment.     

The bymoment method for two-dimensional electromagnetic scattering

The bymoment method is presented for analyzing two-dimensional electromagnetic wave scattering in an unbounded region. The method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity. The solution in the interior is generated using the standard finite-element solution of an interior Dirichlet boundary-value problem. The interior solution is then coupled to the exterior using Green's theorem in the unbounded exterior region. The validity of the method and the associated computer program is demonstrated by comparing the results to those of other methods for scattering by various cylindrical geometries     

Measurement of the effective relative permittivity of unshielded coplanar waveguides

The dependence of the effective relative permittivity of coplanar waveguides is measured as a function of frequency in the frequency range from 3?12 GHz and is compared with the computed values.     

Numerical analysis of two-dimensional piezoelectric waveguides for surface acoustic waves by finite-element method

A combined approach of the finite-element method and the analytical solutions is described for the analysis of two-dimensional piezoelectric waveguides with semi-infinite media for surface acoustic waves. Agreement between the exact and predicted results is very good.     

Capacitance, inductance and effective relative permittivity of microstrip line

The capacitance and inductance of the open microstrip line are found in explicit form for narrow and wide microstrips and for very large substrate permittivity. For an arbitrary width, the integral equation is transformed into an infinite set of algebraic equations, which can be handled by computer. Hence the effective relative permittivity at low frequencies can be found.     

散射参数反演材料电磁参数的新方法

基于传输反射原理,介绍了一种利用散射参数求复数形式的磁导率和介电常数的计算方法。通过建立同轴线的测试模型并将一个待测的材料放入其中,测试出待测材料的散射参数,从而将它们代入算法进行求解。通过与以前的几种反算电磁参数的方法进行比较,该算法可以在较宽的频带内更加准确地得到电磁参数并消除相位误差,这种方法同样适用于测量左手介质的电磁参数。     

Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method

The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations are performed using the DBIM and the method proposed previously by the authors (Int. J. Imaging Syst. Technol., vol.1, no.1, p.100-8, 1989) called the Born iterative method (BIM) for several cases in which the conditions for the first-order Born approximation are not satisfied. The results show that each method has its advantages; the DBIM shows faster convergence rate compared to the BIM, while the BIM is more robust to noise contamination compared to the DBIM.     

Quasi-static effective permittivity of periodic compositescontaining complex shaped dielectric particles

A methodology is described for computing the quasi-static effective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) lattice of dielectric particles. The particles in this composite material may have complicated shapes. This methodology uses a moment method based technique to determine the electric dipole moments of the particles immersed in a uniform electric field. The effective permittivity is then obtained using an appropriate macroscopic model. With this methodology, the mutual interaction between particles can be accounted for accurately. The computed effective permittivity for round cylinders and spheres suspended in a host are compared with our previous T-matrix method results as well as the Maxwell Garnett (MG) formula predictions. Three additional examples involving square (2-D), rounded square (2-D), and spherical (3-D) dielectric inclusions are also given, illustrating the shape effects on the computation of the quasi-static effective permittivity. While the square- and cubic-shaped particles can possess great mutual interaction, surprisingly their effective permittivity is well predicted for all volume fractions by the simple MG formula in both 2-D and 3-D problems     

A phase matrix for a dense discrete random medium: evaluation ofvolume scattering coefficient

In the derivation of the conventional scattering phase matrix of a discrete random medium, the far-field approximation is usually assumed. In this paper, the phase matrix of a dense discrete random medium is developed by relaxing the far-field approximation and accounting for the effect of volume fraction and randomness properties characterized by the variance and correlation function of scatterer positions within the medium. The final expression for the phase matrix differs from the conventional one in two major aspects: there is an amplitude and a phase correction. The concept used in the derivation is analogous to the antenna array theory. The phase matrix for a collection of scatterers is found to be the Stokes matrix of the single scatterer multiplied by a dense medium phase correction factor. The close spacing amplitude correction appears inside the Stokes matrix. When the scatterers are uncorrelated, the phase correction factor approaches unity. The phase matrix is used to calculate the volume scattering coefficients for a unit volume of spherical scatterers, and the results are compared with calculations from other theories, numerical simulations, and laboratory measurements. Results indicate that there should be a distinction between physically dense medium and electrically dense medium     

Iterative determination of complex permittivity and SAR distribution of two-dimensional biological body

An iterative inversion procedure is presented for noninvasive measurements of the complex permittivity and SAR distribution of two-dimensional biological bodies. The inversion procedure is tested numerically by using a two-layered circular model having high dielectric contrast.<>     

A new space-time integral equation for two-dimensional transient scattering

In this letter a general time-domain integral equation for solving 2-dimensional scattering problems is presented. This new approach improves the integrodifferential equations commonly employed for the transient scattering of plane waves on cylindrical perfectly conducting obstacles. Moreover, this approach solves the problem of circular symmetric scatterers illuminated by transient incident waves that have the same symmetry.