In many electromagnetic field problems, matrix equations were always deduced from using the method of moment. Among these matrix equations, some of them might require a large amount of computer memory storage which made them unrealistic to be solved on a personal computer. Virtually, these matrices might be too large to be solved efficiently. A fast algorithm based on a Toeplitz matrix solution was developed for solving a bordered Toeplitz matrix equation arising in electromagnetic problems applications. The developed matrix solution method can be applied to solve some electromagnetic problems having very large-scale matrices, which are deduced from the moment method procedure. In this paper, a study of a computationally efficient order-recursive algorithm for solving the linear electromagnetic problems [Z]I = V, where [Z] is a Toeplitz matrix, was presented. Upon the described Toeplitz matrix algorithm, this paper derives an efficient recursive algorithm for solving a bordered Toeplitz matrix with the matrix's major portion in the form of a Toeplitz matrix. This algorithm has remarkable advantages in reducing both the number of arithmetic operations and memory storage.

This paper presents the dual-band bandpass filters (BPFs) design composed of λ/2 and symmetrically/asymmetrically paired λ/4 stepped impedance resonators (SIRs) for the WLAN applications. The filters cover both the operating frequencies of 2.45 and 5.2 GHz. The dual-coupling mechanism is used in the filter design to provide alternative routes for signals of selected frequencies. A prototype filter is composed of λ/2 and symmetrical λ/4 SIRs. The enhanced wide-stopband filter is then developed from the filter with the symmetrical λ/4 SIRs replaced by the asymmetrical ones. The asymmetrical λ/4 SIRs have their higher resonances frequencies isolated from the adjacent I/O SIRs and extend the enhanced filter an upper stopband limit beyond ten time the fundamental frequency. Also, the filter might possess a cross-coupling structure which introduces transmission zeros by the passband edges to improve the signal selectivity. The tapped-line feed is adopted in this circuit to create additional attenuation poles for improving the stopband rejection levels. Experiments are conducted to verify the circuit performance.

Two dual-band bandpass filters (BPFs) based on the doubly parallel-coupled stepped impedance resonators (SIRs) structures have been proposed in this paper. The coupled-SIRs with/without open-stub-loads are introduced in the filter design. The dual-band filters exhibiting multiple zeros design operate at 2.45/5.2-GHz for the WLAN applications. Two three-staged filters composed of four SIRs have been proposed with the tapped-line adapted in the I/O sections. A five-staged filter is constructed based on the same design principle to achieve a better band-rejection. The proposed filters have the advantages of a much wider bandwidth in both the passbands without sacrificing the passband's insertion loss and passband flatness. The design procedure for a conventional parallel-coupled microstrip lines model is still suitable to design the proposed filters. The proposed filters have achieved almost twice the bandwidth of a conventional parallel-coupled lines configuration under the same design parameters. The experiments have been conducted to verify filter performance. Measured results are in good agreement with the full-wave simulation results.

In this paper, a dual-band bandpass filter (BPF) of multilayer suspended stripline (SSL) structure and an SSL diplexer composed of a low-pass filter (LPF) and a high-pass filter (HPF) are proposed. Bandstop structure creating transmission zeros is adopted in the BPF and diplexer, enhancing the signal selectivity of the former and increasing the isolation between the diverting ports of the latter. The dual-band BPF possesses two distinct bandpass structures and a bandstop circuit, all laid on different metallic layers. The metallic layers together with the supporting substrates are vertically stacked up to save the circuit dimension. The LPF and HPF used in the diplexer structure are designed by a quasi-lumped approach, which the LC lumped-elements circuit models are developed to analyze filters' characteristics and to emulate their frequency responses. Half-wavelength resonating slots are employed in the diplexer's structure to increase the isolation between its two signal diverting ports. Experiments are conducted to verify the multilayer dual-band BPF and the diplexer design. Agreements are observed between the simulation and the measurement.