AIM: Adaptive integral method for solving large‐scale electromagnetic scattering and radiation problems

Abstract

Lagrange interpolation, the new formula provides relatively higher accuracy and larger grid step size and also makes it simpler to implement higher-order basis functions in IE-FFT. frequency and the slotline radiation loss. In addition, high radiation loss of a transition is undesired in high density circuits due to that it will cause unwanted crosstalk. Furthermore, for a low characteristic impedance of the slotline and easy matching to a 50 ⍀ microstrip line, they are all fabricated on high dielectric constant substrates ( r Ͼ 10 ). As the high dielectric constant substrates are suitable for circuit design rather than the antenna design, using such transitions to feed antennas will degrade the antenna radiation performance. Recently, the microstrip-to-slotline transitions on low dielectric constant substrates with the slotline stepped circular ring terminations have been reported with a 1-dB back-to-back insertion loss bandwidth covering from 2.9 to 15.2 GHz (1:5.2) and a 3-dB back-to-back insertion loss bandwidth covering from 2.5 to 19.0 GHz (1:7.6) [6]. However, they also increase the design complexity of the transition due to its complex structure. Furthermore, as there are no easy design equations for the slotline stepped circular ring termination, the design of these transitions may only rely on time-consuming full-wave optimization.In this article, an improved version of a broadband microstripto-slotline transition [3] on low dielectric constant substrate is presented. The proposed transition consists of a microstrip multisection matching transformer and a right-angle crossing of a microstrip radial stub and a slot radial stub. Compared to the original designs [3], the geometry of the microstrip radial stub has been adjusted to allow the fabrication of larger angle slot radial stub. By employing the extremely large angle slot radial stub to reduce radiation loss, the proposed transition has a return loss of better than 15 dB while the 1-and 3-dB back-to-back insertion loss bandwidth can cover from 1.04 to 5.13 GHz (1:4.9) and from 1.02 to 13.90 GHz (1:13.6), respectively. The improved transition achieves greater bandwidth and lower loss than the earlier designs [1-6], and besides, does not increase the design complexity in comparison to the original design [3]. To the best of our knowledge, it is the first time that the extremely large angle slot radial stub is used for broadband and low-loss microstrip-to-slotline transition. DESIGN AND FABRICATIONThe geometry of the improved microstrip-to-slotline transition is shown in Figure 1. The microstrip radial stubs and the microstrip multisection matching transformers are at the top layer of a substrate while the ground plane is at the bottom layer. The slotline and the slot radial stubs are in the ground plane. The geometry of the microstrip radial stub is adjusted to allow the fabrication of the extremely large angle slot radial stub, which is used to decrease the insertion loss of the transition in the upper band. In addition, as the characteristic imped...

Resistances and Inductances Extraction Using Surface Integral Equation With the Acceleration of Multilevel Green Function Interpolation Method

“…There exist several fast algorithms for matrix-vector multiplication that can be used to enhance the efficiency of the solution, such as fast multipole method (FMM) [7][8][9], conjugate gradient fast Fourier transform (CGFFT) [10,11], precorrected FFT (PFFT) [12], the sparse matrix/canonical grid (SMCG) method [13], adaptive integral method (AIM) [14], and MLGFIM [15,16] and so on. Among them, FMM is a fast algorithm with O(N ) complexity, CGFFT, PFFT, SMCG, and AIM are FFT based methods with O(N log N ) complexity, while MLGFIM is based on a hierarchical structure which is similar to FMM but using the Green's function matrix interpolation method with QR [17] factorization technique.…”

Numerical Analysis of the Potential Formulation of the Volume Integral Equation for Electromagnetic Scattering

“…The adaptive integral method (AIM) or precorrected-FFT algorithm (pFFT) [Bleszynski et al, 1996;Phillips and White, 1997] separates the computations of the near and far field interactions. The near field interactions are directly computed by using (26) and the far field interactions are approximated with the interpolation and the FFT.…”

Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

“…It can find various applications in geophysics exploring [1], unexploded objects characterizing, and microwave integrated circuit analyzing, etc. This structure can be efficiently and rigorously analyzed by the method of moments (MoM) [2][3][4] and fast algorithms based on MoM, such as the conjugate gradient fast Fourier transform method [5], the adaptive integral method [6], the fast multipole method [7]. Either for the conventional MoM or fast algorithms, dyadic Green's function for layered media should be computed.…”