Yaowu Liu

Interpolation, extrapolation, and application of the measured equation of invariance to scattering by very large cylinders

Using the conventional method of moment (MoM) calculations, a cylinder of circumferential dimension of 100 wavelengths is considered to be large. Using the measured equation of invariance (MEI) approach, a cylinder of 10000 wavelengths is within the storage capacity and numerical tolerance of a workstation. Although, the MEI has greatly reduced the storage and solution time of the matrix, its overhead to generate the matrix elements is about the same order as that of the MoM. When the target is very large, that overhead can be very time consuming. This paper presents an interpolation and extrapolation technique such that the boundary equations of the MEI for high frequencies may be predicted from those of low frequencies. It is demonstrated that in the optical limit the same set of coefficients may be used for all frequencies, which is consistent with the concept of geometric optics where the same rule is applied to all frequencies.

Analysis of a double step microstrip discontinuity using generalized transmission line equations

In this paper, a new analysis for a double step microstrip discontinuity is presented by using generalized transmission line equations . The new analysis is based on a new concept of a finite-length transmission line integrated with its double step discontinuity so that the double step discontinuity is regarded as a finite-length nonuniform transmission line and the generalized equations could be directly implemented. Since the generalized equation coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the equations are dynamic rather than TEM. The interested discoveries are that the generalized equations for the whole double step structure or a partial double step structure can give us the same results and the generalized equations have broadband frequency characteristics. For the double step structure used in this paper for the analysis, the S-parameters for a frequency band from 0.5 GHz to 10 GHz can be well calculated by using only two separately generalized equations at frequency of 3 GHz and 8 GHz.

Implement the theory of Maxwellian circuits to spiral antennas

The main idea of Maxwellian circuits is that any wire structure, such as a thin wire antenna or a microstrip structure, can be represented by equivalent distributed circuits, the solution of which is identical to the solution of Maxwells equations of that structure. Such circuits are said to be Maxwellian . In this paper, the Maxwellian circuits are implemented into a curved structure, i.e., spiral antennas. Since a spiral antenna has much stronger dispersion and mutual couplings than a straight antenna, the most challenging thing for the spiral antenna is how to realize the broadband equivalent circuits. Numerical results for the two-arm Archimedian spiral antenna show that the solutions of its Maxwellian circuits over a quite wide frequency band are the same as those obtained by the conventional integral equations, but solving the circuits represented by the differential equations is much more efficient than solving the integral equations.

Application of on-surface MEI method on wire antennas

The formulas of the on-surface measured equation of invariance (OSMEI) for wire antennas are derived. The unknowns of each node on the antenna surface are expressed by the vector potential function and surface current density. The unknowns in the vicinity of each node are coupled in a linear equation and the coefficients of the linear equation are determined by the measured equation of invariance (MEI) method. The final impedance matrix obtained by the OSMEI is a highly sparse matrix. It demonstrates that the currents on thin wire antennas may also be solved by a differential equation-based formulation in addition to the conventional integral equations.

Applications of the Maxwellian Circuits to Linear Wire Antennas and Scatterers

The recently proposed theory of Maxwellian circuits is demonstrated for applications to linear wire scatterers as well as to linear antennas. It is shown that for each integral equation of thin wire type, there exist coupled linear ordinary differential equations of currents and voltages, the solutions of which are identical to the integral equation, if the same boundary conditions of the integral equation are applied. The subsequence is that the coupled differential equations can be interpreted as equivalent circuit of new type named Maxwellian circuit. The equivalent circuit can provide physical insights to design engineers and computational advantages for broadband calculations. The highlight of this paper is to show both theoretically and numerically that the Maxwellian circuit components depend only on the geometry of the problem, not on the excitation or boundary conditions at the terminals

A new iterative technique for large and dense linear systems from the MEI method in electromagnetics

In this paper we present a new iterative technique for large and dense linear systems. This technique originally came from the MEI method in electromagnetic fields. The effectiveness of the new technique is safeguarded by a convergence theorem given here. Numerical experiments illustrate that the computed errors for the first approximation with initial guess zero (i.e., the known MEI equation) are within 0.09-0.26%.

Application of discrete periodic wavelets to measured equation of invariance

Recently, the wavelet expansions have been applied in field computations. In the frequency domain, the application is focused on the thinning of matrices arising from the method of moment (MoM). The thinning of matrices can best be done by the measured equation of invariance (MEI), which provides sparsity almost without sacrificing accuracy in that the boundary equation it entails is convertible to that of the MoM. The real power of the wavelet expansions is to give high resolution in convolution integrals. High resolution is also needed in the process of finding the MEI coefficients, which are obtained via an integration process almost identical to that of the MoM. In this paper, it is shown that when the fast discrete periodic wavelets (FDPW) are used as metron currents in the MEI method, the resolutions of the MEI coefficients are improved at high-frequency computations or at geometric extremities. The level of sparsity of the MEI is much more favorable than that achievable by the thinning of MoM matrix using the wavelet expansions. The role of FDPW in the MEI happens to be more fitting than its place in the MoM.

Domain-decomposed MEI method for field computation in single and multiple regions

The domain-decomposed measured equation of invariance (DDMEI) method is proposed for field computation in single and multiple regions. The whole computing domain is partitioned into a cluster of subdomains. For single region problems, this partition splits the computing domain into many subdomains artificially. For multiple regions problems, these subdomains can be taken as those regions separated geometrically. The contribution of sources residing in a subdomain is approximated by a set of sources selected out of these original sources with greatly reduced amounts. The approximation is implemented numerically by the MEI method. The resultant MEI matrices are blocked matrices and each submatrix is highly sparse. Approaches and numerical results are given respectively for the applications of the DDMEI to the scattering of single conducting cylinders, radiation of wire arrays, and capacitance matrix computation for multiconductor transmission lines. The DDMEI proposed in this paper is an improved version of the surface current MEI method (SCMEI). Compared with the SCMEI, the DDMEI improves the sparsity of the MEI matrices and the feasibility of measuring out the MEI coefficients. Furthermore, the DDMEI makes it possible to apply the kind of on-surface MEI methods (OSMEI) to multiple region problems for the first time.