Field coupling to nonuniform coupled microstrip transmission lines

An efficient method for frequency‐domain and transient analysis of the nonuniform lossless coupled microstrip transmission lines excited by external electromagnetic waves is presented. The nonuniform coupled microstrip transmission lines system is first decomposed into a large number of uniform sections called steplines. Using the modal decomposition method, each step is modeled as a linear system with matrix coefficients. The effects of the external excitation are then modeled as inputs in the proper positions of the system. Finally, the solution in the frequency domain is obtained, and the fast Fourier transform algorithm is used to find the time‐domain response of the lines. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 215–228, 2003.     

An efficient method for analyzing nonuniformly coupled microstrip lines

This article presents an efficient method for analyzing nonuniformly coupled microstrip lines. By choosing a modal‐transformation matrix, the coupled nonlinear differential equations describing the symmetric nonuniformly coupled microstrip lines are decoupled using even‐ and odd‐mode parameters; the original problem is thus transformed into two single nonuniform transmission lines. A power‐law function of arbitrary order and having two adjustable parameters is chosen to better approximate the equation coefficients. Closed‐form ABCD matrix solutions are obtained and used to calculate the S‐parameters of nonuniformly coupled microstrip lines. Numerical results for two examples are compared with those from a full‐wave commercial package and experimental ones in the literature in order to demonstrate the accuracy and efficiency of this method. This highly efficient method is employed to optimize a cosine‐shape 10‐dB codirectional coupler, which has good return loss and high directivity performance over a wide frequency range. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005.     

Crosstalk analysis of multi‐microstrip coupled lines using transmission line modeling

This article presents a new analytical method to predict crosstalk of a homogeneous terminated two microstrip coupled lines over a ground plane using transmission line theory. The derived formula is frequency and location dependent, which can be used to quickly estimate the crosstalk of a coupled line. Also, the effect of the geometrical parameters of the lines and load are included in the derived formula. Presented method can be used for the other types of coupled lines including lossy or lossless lines. To verify the accuracy of the introduced method, a few microstrip coupled line structures with different geometrical parameters are considered numerically and experimentally. The results of crosstalk based on the proposed analytical methods, simulation study using high frequency structure simulator and those obtained by measurements are reported and compared with each other. It is shown that our proposed method accurately estimates the amount of crosstalk for a two microstrip coupled lines.     

Using linear sections instead of uniform ones to analyze the coupled nonuniform transmission lines

In this article, a new method is introduced to frequency domain analyze arbitrary coupled nonuniform transmission lines (CNTLs). The CNTLs are subdivided into several short linear sections instead of uniform sections. The chain parameter matrix of linear sections is obtained by expressing the voltages and currents by power series expansion. This method is applicable to all arbitrary CNTLs. The accuracy of the proposed method is verified using a comprehensive example. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

Numerical deembedding technique for planar discontinuities with periodically nonuniform feed lines

A numerical short‐open calibration technique is applied to deembedding of planar discontinuities with periodically perturbed nonuniform feed lines in the full‐wave method of moments (MoM) algorithm. Different from the other deembedding techniques that are based on the assumption of uniform feed lines, this proposed technique exhibits an unparalleled capability on modeling of planar circuits with nonuniform feed lines. To demonstrate this feature, the open and gap discontinuities are modeled under periodically nonuniform feed configuration, and the effective per‐unit‐length transmission parameters of slow‐wave and electromagnetic bandgap structures are extracted from the full‐wave MoM simulation. Two periodically nonuniform microstrip‐line resonator circuits are modeled and then confirmed by EM simulators and measurement. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

Nonlinear transient analysis of coupled RLGC lines by the method of characteristics

A computationally efficient numerical technique for the evaluation of the time domain response of coupled lossy uniform and nonuniform transmission lines terminated in general nonlinear elements is presented. The technique is based on the method of characteristics where the original system of coupled transmission line equations is transformed into a system of ordinary differential equations which hold along a family of characteristic curves. An algorithm to solve these equations is presented. The procedure is applicable to both uniform and nonuniform coupled systems and examples of two and three line structures terminated in linear and nonlinear elements are included to demonstrate the versatility and the usefulness of the algorithm.     

A novel method for crosstalk reduction in coupled pair microstrip lines

This article demonstrates novel ideas for mitigation of far‐end as well as near‐end crosstalk in coupled pair microstrip lines (CPMLs) by means of defected microstrip structure (DMS). Simple equations and models for analysis and design of a DMS are presented and extracted. Different configurations of DMS‐CPMLs are introduced, and their performances in crosstalk reduction are compared. Finally, the best configuration for far‐end crosstalk reduction is fabricated and tested. A maximum of 35 dB reduction in far‐end and 38 dB reduction in near‐end crosstalk are achieved. The signal integrity performance of the structure is also verified by eye‐diagrams. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Design and analysis of multifrequency Wilkinson power dividers using nonuniform transmission lines

In this article, based on nonuniform transmission lines, the design of compact multifrequency Wilkinson power dividers (WPDs) is presented. This is accomplished by replacing the quarter‐wave uniform transmission lines in the conventional WPD by multiband nonuniform transmission line transformers (NTLTs). The design of these NTLTs is performed under the even mode analysis of the WPD. A single isolation resistor is used between the two output ports whose value is determined using the simple odd mode analysis of the WPD. For verification purposes, a triple‐frequency WPD and a quad‐frequency WPD are designed, simulated, fabricated, and measured. The results of the full‐wave simulations and the measurements verify the validity of the design procedure. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

One high-efficiency analysis method for high-speed circuit networks containing distributed parameter elements

In the field of high-speed circuits,the analysis of mixed circuit networks containing both distributed parameter elements and lumped parameter elements becomes ever important.This paper presents a new method for analyzing mixed circuit networks.It adds transmission line end currents to the circuit variables of the classical modified nodal approach and can be applied directly to the mixed circuit networks.We also introduce a frequency-domain technique without requiring decoupling for multiconductor transmission lines.The two methods are combined together to efficiently analyze high-speed circuit networks containing uniform,nonuniform,and frequency-dependent transmission lines.Numerical experiment is presented and the results are compared with that computed by PSPICE.     

Analysis of coupled or single nonuniform transmission lines using the method of moments

A method is proposed for the analysis of arbitrarily loaded lossy and dispersive single or coupled nonuniform transmission lines (NTLs). In this method, the integral equations of the NTLs, converted from their differential equations, are solved using the method of moments. It is assumed that per‐unit‐length matrices are known at all or even some points along the length of the coupled NTLs. The validity of the method is verified using a comprehensive example. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

One high-efficiency analysis method for high-speed circuit networks contaning distributed parameter elements

1Introduction With the increasing signal speed and decreasing featuresize of modern high_speed integrated circuits,theinterconnection effects suchas delay,crosstalkand distortionbecome the dominant factors limiting the overallperformance of microelectronic systems[1].At highfrequencies,the length of transmission lines becomes asignificant fraction of the operating wavelength;conventional lumped impedance models are inadequate fordescribing the interconnection performance,and distributedparamet…     

One high- efficiency analysis method f or high- speed circuit networks containing dist ributed parameter elements

In the field of high-speed circuits , the analysis of mixed circuit networks containing both distributed parameter elements and lumped parameter elements becomes ever important . This paper presents a new method for analyzing mixed circuit networks. It adds transmission line end currents to the circuit variables of the classical modified nodal approach and can be applied directly to the mixed circuit networks. We also introduce a frequency- domain technique without requiring decoupling for multiconductor transmission lines. The two methods are combined together to efficiently analyze high-speed circuit networks containing uniform , nonuniform ,and frequency- dependent transmission lines. Numerical experiment is presented and the results are compared with that computed by PSPICE.     

Miniaturized multi‐frequency Wilkinson power dividers based on nonuniform coplanar waveguide

In this work, the design of miniaturized dual‐ and triple‐ frequency Wilkinson power dividers using nonuniform coplanar waveguides is presented. The miniaturized configurations are achieved by replacing the conventional uniform arms with their equivalent multi‐frequency nonuniform transmission lines. The nonuniform width variation is governed by a truncated Fourier series expansion with coefficients optimized to obtain the desired multi‐frequency operation. The optimization process is carried out through the analysis of the even/odd mode circuits. The proposed dividers are simulated, fabricated, and measured to validate the design methodology. Simulated and measured results agree very well, and show input/output ports return loss and isolation better than 14.4 dB and transmission parameters in the range of ?3 ± 2 dB at the design frequencies. Size reduction of 16.7% and 17.6% are achieved for the fabricated dual‐ and triple‐frequency dividers, respectively.     

Miniaturized wide‐band rat‐race coupler

New designs of wide‐band rat‐race couplers are proposed. The wide‐band operation is achieved with the use of the microstrip nonuniform transmission line sections for the branches of the conventional rat‐race coupler. The design formulas are developed using ABCD matrix and the even‐ and odd‐mode analysis. The theoretical analysis has been verified by measurements of the two manufactured wideband rat‐race couplers, one operate within 0.85–1.92 GHz and other within 1.55–3.55 GHz frequency range with the equal normalized characteristic impedance functions. For both fabricated couplers, the isolation parameter is better than 15 dB over a 77% relative bandwidth. Also, it is shown that the designed wide‐band rat‐race coupler can be realized in higher frequency bands with the fixed fractional bandwidth. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 23: 675–681, 2013.     

Multimode resonator based on composite right‐/left‐handed transmission line for UWB bandpass filter application

A new multimode resonator (MMR) using composite right‐/left‐handed transmission line (CRLH TL) is proposed and discussed. The CRLH TL structure is constructed by cascading interdigital coupled microstrip line sections on which short‐ended stepped impedance stubs are loaded. Dispersion characteristic of the transmission line structure is obtained using the Bloch–Floquet theory. The resonator, which has multiresonances electrical behaviors, is especially suitable in ultrawideband (UWB) applications. An UWB filter is presented as an illustration. With transmission zeros introduced at upper stopband, the filter has a sharp skirt performance. In addition, rejection level at lower stopband also gets enhanced due to direct current suppression effects of the multimode resonator. The filter prototype is implemented and measured. The measured results validate the theoretical analysis and show that the filter has a sharp skirt and an out‐of‐band rejection level as good as 38 dB. Meanwhile, return loss is better than 16 dB. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:815–824, 2015.     

Analysis of nonuniform transmission lines using Taylor's series expansion

A new method is introduced for the frequency‐domain analysis of arbitrarily loaded lossy and dispersive nonuniform transmission lines. In this method, all distributed primary parameters of the line and also the voltage and current distribution along the line are considered as a Taylor's series. The solutions of voltage and current are obtained after finding unknown coefficients of their series. The validity of the method is verified using analysis of some special types of lines. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

矩形谐振腔串扰抑制方法研究

在高速数字系统中,信号完整性问题越来越突出,信号速率和设计密度的不断提高使得串扰上升为主要因素之一。先研究了基于矩形谐振腔的串扰抑制方法;然后与三倍线宽方法(3W方法)和有过孔接地的防护线方法的对比分析表明,矩形谐振腔方法对微带线间近端串扰的抑制能力不理想,但对远端串扰的抑制非常有效,在频域仿真中远端串扰幅度可提高12 dB和8 dB,在时域仿真中远端串扰峰值分别为前两种方法的18.2%和23.1%;最后进一步研究了矩形谐振腔的结构参数（间距、长度和宽度）对远端串扰的影响,发现这三个参数存在一组最优值,能最大程度地减小远端串扰。     

Dual‐band bandpass filters with multiple transmission zeros using λ/4 stepped‐impedance resonators

Two novel dual‐band microstrip bandpass filters (BPFs) with multiple transmission zeros are proposed in this article. The dual‐band BPFs with second‐order bandpass responses are due to two λ/4 stepped‐impedance resonators (SIRs). Two passbands (center frequency ratio f _s/f₀ is 2.36) are realized based on the asymmetric SIRs. The transmission zeros near the passbands can be adjusted conveniently using the stopband transmission characteristic of the open/shorted coupled lines. Two planar microstrip dual‐band BPFs (ε _r = 2.65, h = 0.5 mm) with four and six transmission zeros are designed and fabricated. High selectivity and good in‐band performances can be achieved in the proposed filters.     

Full‐wave analysis of circular guiding structures using the finite difference frequency domain method

In this article, a general full‐wave two dimensional finite difference frequency domain (2D‐FDFD) method is presented that could be used to analyze general circular multi‐layered multi‐conductor guiding structures. The FDFD method is mainly used to get the dispersion curves for these structures. The results which are obtained using the FDFD equations come through solving an eigen‐value problem, where the obtained eigen‐values and eigen‐vectors are used to produce the propagation constants, distribution of the fields and the characteristic impedances for these structures. Several examples ranging from simple coaxial lines to coupled circular microstrip lines are presented. The FDFD results are compared with those obtained through other analytical and numerical techniques. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

Microstrip dual‐band bandpass filters using parallel‐connected open‐loop ring resonators

This article proposes a microstrip dual‐band bandpass filter that uses parallel‐connected open‐loop ring resonators. Compared to many microstrip dual‐band filters, the advantages of using microstrip open‐loop ring resonators are easy calculation (half‐guided‐wavelength), easy fabrication (equal width for all 50‐Ω lines and without grounding holes), and direct connection to external feed lines (reducing insertion loss caused by gap couplings). Another advantage of the filter is an asymmetrical feed on the ring resonator that provides sharp rejections at its adjacent bands. The input and output matches of resonators to the external feed lines are derived using a simple transmission‐line theory. The results of the derivation provide a simple design rule for filter designers. Simulated and measured results are presented with good agreement. The filter has minimum insertion loss of 1.25 dB at 1.85 GHz and 1.6 dB at 2.33 GHz. The 3‐dB fractional bandwidths are 5.9% for the 1.9‐GHz bandpass filter and 4.7% for the 2.4‐GHz bandpass filter, respectively. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.