Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

Analysis of a coupled slotline on a double-layered substratecontaining a magnetized ferrite

Nonreciprocity in the propagation characteristics of the even and odd modes in magnetized-ferrite-loaded double-layered coupled slotlines is studied. The analysis is based on Galerkin's method applied in the Fourier transform domain. Numerical results are presented for various values of structural parameters. As a result, it is found that the waveguide structures studied have sufficient nonreciprocity in propagation constants for isolators and four port circulators     

A mixed spectral-domain approach for dispersion analysis ofsuspended planar transmission lines with pedestals

A mixed spectral-domain analysis is used to derive dispersion characteristics of domain modes in a class of planar transmission lines with a pedestal. Equivalent structures are constructed in which magnetic surface currents are identified as the unknowns at the aperture separating two different regions. Spectral dyadic Green's functions are derived for these structures using the spectral-domain immittance approach. The characteristic equations resulting from the application of the spectral Galerkin method involve mixing two different spectral domains, which exist on the two sides of the pedestal support. The present method allows one to retain the simplicity and numerical efficiency of the conventional spectral-domain immittance approach, which cannot be applied directly to the present structures. Numerical data are provided for the dispersion characteristics of dominant modes in a pedestal-supported stripline and finline     

Printed Circuit Transmission-Line Characteristic Impedance by Transverse Modal Analysis

Dispersion characteristics of printed circuit transmission lines such as finlines, shielded microstrips, slotlines, suspended striplines, coupled slotlines, and coupled striplines computed by the transverse modal analysis were reported in a previous paper. Application of the transverse modal analysis to compute the characteristic impedances of these printed circuit transmission lines is illustrated in this paper. Favorable comparison with various published data demonstrates the outstanding accuracy achieved by this technique. Combining the characteristic impedance computation with the dispersion results, the transverse modal analysis can be employed for solving various problems in printed circuit transmission lines.     

Full-wave analysis and design of a new double-sided branch-linecoupler and its complementary structure

A new double-sided branch-line coupler using microstrip lines as input/output lines and slotlines as branches is analyzed and designed. The even-odd mode theory is first used to analyze the ideally simplified circuit model and to find out the preliminary circuit dimensions. Based on these dimensions, the full-wave spectral domain approach (SDA) is employed to accurately simulate the circuit performance. By the formulation of the exact Green's function in the spectral domain, the effects of surface wave and radiation phenomena are accurately accounted for. Experimental data agree very well with the SDA simulation results. It is found that the even-odd mode theory which neglects discontinuities between lines is not enough to design a coupler. The SDA code can then be used to accurately simulate and optimize the circuit performance. The complementary structure with slotlines as input/output lines and microstrip lines as branches is also investigated both theoretically and experimentally. It is noticed that the radiation and leakage from the two double-ended branches for all structures will deteriorate the circuit performance     

Full-wave spectral analysis and design of annular patch antenna with electromagnetically coupled microstrip feed line

This paper presents a full-wave analysis, and the ensuing design considerations, of the annular patch antenna fed by an electromagnetically coupled microstrip line. The numerical analysis employs the spectral domain version of the integral equation, with the method of moments formulation; the basis functions on the ring patch are the eigenmodes of the corresponding magnetic wall cavity, and subsectional (rooftop) functions are employed on the access line. Both TM and TE modes are used, along with more-efficient "collective" solenoidal modes; mode sorting criteria are given to ensure uniform convergence. Efficient schemes are presented for the calculation of the spectral-domain reaction integrals, along with criteria to avoid calculation of negligible mode-to-mode couplings, based on the spectral analysis of the matrix condition number. Very good agreement is shown with measured data, and design considerations are given for matching the radiator.     

A study of the fields associated with vertical dipole sources in stripline circuits

A prototype, integral-equation-based, full-wave layered interconnect simulator (UA-FWLIS) has recently been developed. In this simulator, the method of moments (MoM) reaction integrals are evaluated analytically, thereby dramatically improving the computational efficiency compared with standard numerical integration techniques. The closed-form representation for the reaction elements takes the form of a modal series expansion. Since the reaction between closely-spaced elements requires the dominant mode and a significant number of higher-order modes, an investigation of the behavior of the fields associated with both the propagating and higher-order evanescent wave modes will be beneficial for the further development of the simulator. The simulator can currently handle homogeneously-filled stripline structures only. In this paper, the electric field analysis is extended to an inhomogeneously-filled stripline structure. The knowledge gained from these studies will allow for the extension of the simulator to the analysis of inhomogeneously-filled stripline structures. The spectral domain technique is first used to obtain the field expressions in the spectral domain.     

Calculating the Characteristic Impedance of Finlines by Transverse Resonance Method

The characteristic impedance of finlines with up to three slots is calculated by a rigorous hybrid-mode analysis which includes the finite metallization thickness and finite depth of the mounting grooves. The transverse resonance principle utilized reduces considerably the order of the involved matrix eigenvalue problem. The propagation constants for the fundamental HE/sub 1/ mode (and EH/sub 0/ mode at related structures), as well as for the higher order modes (up to HE/sub 7/), and the characteristic impedances for the fundamental modes are computed as a function of frequency for the bilateral and unilateral finline, as well as for the unilateral finline with two coupled slots, and an additional slot on the opposite side of the substrate surface. The finite metallization thickness and mounting groove depth considered show significant influence on the behavior of the characteristic impedance.     

The effects of covering on complex wave propagation in gyromagneticslotlines

The evolution of complex leaky waves in partially open gyromagnetic slotlines into complex modes in a shielded slotline is presented. Given a particular stratified gyromagnetic slotline with two sidewalls present, four types (Types I-IV) of guided structures are defined and investigated, depending upon the four possible combinations of top and bottom covers. The behavior of the complex solutions is discussed for the partially open gyromagnetic slotlines. Initially, the slotline of Type I, which lacks both top and bottom covers, shows that no coupling exists among various pairs of leaky waves. By adding only a top cover into Type I, the resultant slotline of Type II exhibits certain coupling between different sets of leaky waves. Similarly, by adding only a bottom cover into Type I, the resultant slotline of Type III shows that certain strong leaky waves of Types I and II now become weak leaky waves. From these numerical experiments, we deduce that the complex modes supported by Type IV, which is completely shielded, can be the result of the mode coupling of the two previously found leaky waves in Types II and III waveguides, respectively. Therefore, the formation of complex modes in shielded slotline is related to the effects of covering on mode coupling of the various leaky waves of the partially open slotlines     

Analysis of a CPW on electric and magnetic biaxial substrate

A formulation of the spectral domain technique (SDT) for the analysis of the general case of uniaxial/biaxial, electric/magnetic anisotropic multilayer planar structures is presented. As an illustration of the capabilities of this formulation it is applied to the analysis of shielded coplanar waveguide (CPW) structures. The dispersive properties of the fundamental and higher-order modes in various cases of electric/magnetic anisotropy as well as the induction electric and magnetic lines are calculated. Such results, and particularly the induction lines, may be used to predict the behavior of the structure studied as well as to point out its sensitive geometrical and electrical parameters. Some general rules which lead to a better understanding of the effect of anisotropy are discussed     

Phase velocity compensation in three-line coupled microstrip structure by using stratified dielectric substrate

A three-line coupled microstrip structure containing stratified dielectric substrate is analysed by the spectral domain technique. It is shown that phase velocities of any two of the guided fundamental modes can be compensated independently by proper choice of substrate composition.     

Computer analysis of the fundamental and higher-order modes in single and coupled microstrip

By means of finite-difference methods, dispersion curves are obtained for the fundamental and higher-order hybrid modes in both single and coupled microstrip. Structures of realistic proportions are investigated by the use of a graded finite-difference mesh. Variational methods are used in deriving the finite-difference equations.     

Analysis of printed transmission lines for monolithic integrated circuits

Planar transmission lines formed with MIS and Schottky barrier contacts are analysed based on the spectral domain technique. Depending on the frequency and the resistivity of the substrates, three different types of fundamental modes are predicted. The calculated slow-wave factors and attenuation constants agree well with experimental results.     

Analysis of slotlines and microstrip lines on anisotropicsubstrates

The propagation characteristics of the dominant mode in slotlines as well as in microstrip lines on anisotropic substrates are studied. The dielectric tensor in the substrate may have nondiagonal elements which represent misalignment, on the substrate surface, between the material coordinate system and the waveguide coordinate system. The analysis is devoted to the slotline and is based on Galerkin's method applied in the spectral domain. Numerical results are presented for a sapphire substrate and a boron nitride substrate. It is found that the coordinate misalignment on the substrate surface has a significant influence on the propagation characteristics of the slotline     

Frequency-dependent solution of suspended microstrip line with tuning septums

The frequency-dependent effective dielectric permittivity and equivalent characteristic impedances of the technically most relevant modes of the suspended microstrip line with tuning septums are derived using the conventional spectral domain approach. Normalised numerical results are presented in a very large frequency band.     

Exact calculations of scattering parameters of a step slot width discontinuity in a unilateral fin-line

The dominant and the first four higher-order modes in a unilateral fin-line are accurately described from a thorough spectral-domain approach. Then, coupling coefficients between eigenmodes at a step slot width discontinuity to be used in the generalised scattering matrix formulation are directly computed in the spectral domain. Scattering parameters of the dominant mode in the Ka band are presented.     

K-band quasi-planar tapped combline filter and diplexer

Quasi-planar realizations of a combline bandpass filter and diplexer using multiple coupled suspended substrate striplines (MCSSSs) have demonstrated good performance at K-band without any tuning. The N MCSSSs excite N zero-cutoff-frequency quasi-TEM modes. A computer-aided filter design approach employing a rigorous spectral domain approach and 2N-port microwave circuit theory accounts for the effects of the N quasi-TEM modes, the couplings through nonadjacent MCSSSs, and cover height. Two 19.5-20.5 GHz MCSSS combline filters with different cover heights have been built and tested to compare their filter characteristics. The reduction in cover height has been found to decrease the amount of nonadjacent coupling through MCSSSs and to result in better filter stopband performance. An 18.5-19 GHz and 20-20.5 GHz MCSSS diplexer is also presented. All the measured results for the combline filters and diplexers agree well with the theoretic calculations     

Experimental and Numerical Investigation of Crosstalk Effect in Coupled Coplanar Waveguides—Part I: Bi-Mode Coupled-Line Representation

The effect of square-wave propagation along coupled coplanar waveguides (C-CPWs) is presented in this paper. Developed numerical tools combining full-wave calculations of the frequency-dependent guided-mode parameters and the network theory formalism enable the determination of port voltages under specified linear termination conditions. Propagation constants and characteristic impedances of coupled lines have been determined for fundamental guided modes using the spectral domain technique combined with Galerkin's procedure. The scattering matrix of the four-port structure has further been used for the calculation of port voltages. Analysis has been performed by taking into account the bi-mode operation resulting from the assumption of the ideal electrical connection of distributed ground plane conductors. Simulation results have been compared with experimental data, and very good agreement has been found, proving the usefulness of the developed numerical tools     

Analysis of ring launching scheme using hollow optical fibre mode converter for 10 Gbps multimode fibre communication

A ring launching scheme using a mode converter based on hollow optical fibre (HOF) is theoretically investigated for the purpose of increasing bandwidth for multimode Gigabit Ethernet communication. The mode converter based on HOF transforms the fundamental mode of a single-mode fibre (SMF) to a ring-shaped mode. It has the characteristic to improve the bandwidth by exciting higher-order modes of the multimode fibre (MMF) selectively. The HOF launch is studied under various aspects such as induced coupling efficiency, mode power distribution, and bandwidth-length product and is compared to centre and offset launching schemes. It is shown that the ring launching scheme is expected to support 10-Gb Ethernet applications using conventional multimode fibres.     

Circularly symmetric distributed feedback laser: coupled modetreatment of TE vector fields

The vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating is treated. The equations are derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of the laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width