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.

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 considers replacement and maintenance policies for an operating unit which works at random times for jobs. The unit undergoes minimal repairs at failures and is replaced at a planned time T or at a number N of working times, whichever occurs first. The expected cost rate is obtained, and an optimal policy which minimizes it is derived analytically. The imperfect preventive maintenance (PM) model, where the unit is improved by PM after the completion of each working time, is analyzed. Furthermore, when the work of a job incurs some damage to the unit, the replacement model with number N is proposed. The expected cost rate is obtained by using theory of cumulative processes. Two modified models, where the unit is replaced at number N or at the first completion of the working time over time T, and it is replaced at T or number N, whichever occurs last, are also proposed. Finally, when the unit is replaced at time T, number N or Kth failure, whichever occurs first, the expected cost rate is also obtained.