Generalized Transmission Line Research Articles

Analysis of a double step microstrip discontinuity using generalized transmission line equations

In this paper, a new analysis for a double step microstrip discontinuity is presented by using generalized transmission line equations . The new analysis is based on a new concept of a finite-length transmission line integrated with its double step discontinuity so that the double step discontinuity is regarded as a finite-length nonuniform transmission line and the generalized equations could be directly implemented. Since the generalized equation coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the equations are dynamic rather than TEM. The interested discoveries are that the generalized equations for the whole double step structure or a partial double step structure can give us the same results and the generalized equations have broadband frequency characteristics. For the double step structure used in this paper for the analysis, the S-parameters for a frequency band from 0.5 GHz to 10 GHz can be well calculated by using only two separately generalized equations at frequency of 3 GHz and 8 GHz.

Generalized transmission line equations for bianisotropic materials

The generalized transmission line equations for bianisotropic materials are derived in this paper. These equations are obtained in a general orthogonal curvilinear reference system, taking properly into account the metric factors and decomposing the field vectors into two components: a transverse component and a longitudinal one, both with respect to a reference coordinate direction. Such a general formulation is very useful in order to analyze metallic/dielectric uniform bended waveguides. On the other hand, it is very appropriate when studying conformal integrated circuits by using the method of lines (MoL). Finally, the formulation here presented leads to a straightforward derivation of the transmission line equations in the spectral domain when studying conformal integrated antennas. As particular cases of the theory here presented, transmission line equations in orthogonal curvilinear coordinates are also derived for anisotropic, bi-isotropic, and isotropic materials.

Modeling of waveguide circuits based on generalized transmission line equations and impedance/admittance transformation concept

Algorithms for the modeling of waveguide circuits are described. The material parameters can be anisotropic. Starting with generalized transmission line equations, suitable expressions for the analysis are derived. The introduction of the admittance/impedance transformation concept guarantees numerical stable expressions even in case of long devices or high numbers of concatenated sections. The presented algorithm is validated by comparing numerical results with those obtained by measurement and other numerical methods.

Modeling of planar waveguides with anisotropic layers of variable thickness by the method of lines

A new algorithm for the analysis of planar waveguides for optical frequencies with anisotropic layers of nonconstant thicknesses is proposed and substantiated. This algorithm is based on the method of lines with discretization lines of various length. Impedance/admittance transformation formulas between the interfaces of the layers are developed with the help of the generalized transmission line (GTL) equations. The materials are assumed to be biaxial or specific anisotropic. The proposed algorithm is verified by numerical results.

Application of online FDTD on microstrip cross and T‐junction structures

AbstractThe online FDTD method derived from general transmission line equations [1] has been introduced in [2, 3]. Following the research on non‐uniform transmission lines, we further explore the application of online FDTD in the microstrip cross and T‐junction structures. As the theoretic difficulties of modeling the connection of multi‐transmission lines have been solved, many microstrip structures that have cross or stub substructures can be easily simulated by online FDTD. Three examples are presented to test the validity of this application. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 184–187, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10715

Modelling Quantum Mechanics by a Quantumlike Description of Electric Signal Propagation in Transmission Lines

It is shown that transmission line technology can be suitably used for simulating quantum mechanics. Using manageable technology, several quantum mechanical problems can be simulated. The electric signal envelope propagation through the line is shown to be governed by a Schrödinger-like equation for a complex function, representing the low-frequency component of the signal.

The Method of Lines: A Versatile Tool for the Analysis of Waveguide Structures

Algorithms for the determination of eigenmodes and for the analysis of longitudinally varying structures are presented. The media may be anisotropic and the devices may consist of an arbitrary number of layers or waveguide sections, respectively. Starting with generalized transmission line equations, suitable expressions are derived which are implemented in the method of lines, a semianalytical algorithm. To ensure the numerical stability, a transformation of the reflection coefficient is performed. Numerical results are presented for a Bragg-grating with a very high number of periods, for an electro-optical switch, and for an anisotropic groove waveguide. The results prove stability of the algorithm, and comparisons with other methods show the accuracy.

Modeling of optical waveguide structures with general anisotropy in arbitrary orthogonal coordinate systems

An extended algorithm for the analysis of arbitrary waveguide structures with general anisotropic materials is proposed and substantiated. This algorithm is based on generalized transmission line (GTL) equations which are developed here for numerical algorithms. For the purpose of analysis, a general modal matrix for the discretized transverse electric and magnetic fields is calculated. Furthermore, impedance/admittance transformation formulas are developed with the help of the GTL equations for longitudinal sections. The proposed algorithm is verified by numerical results.

Efficient and accurate modeling of planar anisotropic microwave structures by the method of lines

A new algorithm for the analysis of planar microwave structures with anisotropic substrates is proposed and substantiated. This algorithm is based on generalized transmission-line (GTL) equations, which are developed here for numerical algorithms. For the purpose of analysis, two different modal matrices for the discretized transverse electric and magnetic fields are calculated. Furthermore, impedance/admittance transformation formulas are developed with the help of the GTL equations for longitudinal sections and general junctions. Crossed discretization lines are used in the latter case. The materials are assumed to be biaxial or specific anisotropic. Special algorithms are developed for junctions consisting of more than two waveguides in the cross section and for bends. The proposed algorithm is verified by numerical results.

Recovering lossy multiconductor transmission line parameters from impedance or scattering representations

In this paper, we present a generalization of the simultaneous diagonalization technique by means of congruence transformations to the general reciprocal lossy multiconductor transmission line case. The method paves the way to solving the inverse problem, i.e., given a lossy multiconductor transmission line system of a given length, recover the transmission line parameters from the impedance or scattering descriptions.

Broadband property and time‐domain application of general transmission‐line equations on microstrip low‐pass filter

AbstractGeneral transmission‐line equations based on the theory of differential equations [1] were introduced in [2] and [3]. The equations' dispersion characteristic of a microstrip low‐pass filter is studied. The parameters L, C, α, and β of general transmission‐line equations are found to be almost invariant to frequency in the passband of the microstrip low‐pass filter. By restoring current and voltage distributions with the use of equations in both frequency and time domains, the broadband property of these equations on the microstrip low‐pass filter is evident. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 123–126, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10250

Model of a microwave beam coupling to CO 2 laser plasma

We have designed a transmission line model of the microwave coupling mechanism for a microwave pumped CO 2 laser. The model is a total loss ridge waveguide transmission line having nonuniform impedance. The laser plasma is modeled as a frequency-dependent lossy dielectric and acts as a distributed resistance in the length of the microwave cavity. The coupling structure of the microwaves is designed not to be resonant at the microwave source frequency of 2.45 GHz at 1 kW and propagating the total microwave field energy to be absorbed without internal reflection. An exact solution to this general transmission line propagation constant for a shunt resistance along length of the guide is found. The measurements and predictions of the parameters of the plasma conductivity as a function of the attenuation constant agree closely.

Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length

A novel way of approaching wave propagation in two-dimensional (2-D) photonic crystal guides with finite length is presented. It is shown that the main propagation features can be captured by borrowing simple concepts of propagation in transmission lines and combining them with other concepts taken from the theory of periodic structures.

Generalized Telegraphers' and Helmholtz Equations for Conformal Structures With Bi-Anisotropic Loading Materials

This paper introduces a proper set of rotations and variable changing in order to write Maxwell's equations in the generalized orthogonal curvilinear reference system just as in the Cartesian case. These transformations are very useful to strongly minimize the analytical difficulties that arise when handling equations involved in the solution of electromagnetic fields for conformal structures. First, a new set of telegrapher-like equations, called the "Generalized Transmission Line (GTL) equations", is obtained, relating the transverse field components in general conformal structures loaded with bi-anisotropic materials. Then, new Helmholtz equations formally identical to the Cartesian ones, but effective in the generalized curvilinear reference system, are also derived.

Dispersion Characteristic and It's Application of General Transmission Line Equations On Microstrip Step Structures

The differential equations invariant of termination conditions of thin wire structures and transmission line have been derived. New transmission line equations we called general transmission line equations based on the theory of differential equation are described. The dispersion characteristics of the general transmission line equations on microstrip step structures are studied. We found the general transmission line equations on some of microstrip step structures such as cascade double step structures and low-pass filters have the property of broadband in frequency-domain. Using an equivalent circuit modal, we can restore current and voltage distribution in frequency-domain.

A new time‐domain method based on the general transmission‐line equations

AbstractGeneral transmission‐line equations that can describe both uniform and nonuniform transmission line are derived in brief. By using the algorithm analogous with a one‐dimensional FDTD in the time domain, we obtain a new time‐domain method we call the on‐line FDTD method. Frequency‐domain results are compared with those computed by the MoM to show the validity of our new method. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 46–51, 2002.

P- and n-doping processes in polythiophene with reduced bandgap. An electrochemical impedance spectroscopy study

Electrochemical impedance spectroscopy has been used for the characterisation of electrodes modified with different polythiophenes, namely poly[4,4′-bis(butylsulfanyl)-2,2′-bithiophene], poly[4,4′-bis(methylsulfanyl)-2,2′-bithiophene] and poly(3-methylthiophene), at different applied potentials, using different supporting electrolytes. By comparison of the results obtained under experimental conditions in which n-doping is prevented and those obtained from tests where it does occur, some general features have been deduced, all of them being coherently described by a recently proposed ‘generalised transmission line circuit’ model: impedance plots at different applied potentials exhibit progressive changes which are well accounted for by the ‘evolving’ model. The results obtained on the n-doping process of S-alkyl substituted polymers suggest a behaviour interestingly similar to that exhibited in the p-doping; this supports a symmetry that was also found by us in a previous work, with respect to the incorporation and release of counterions during the n- and p-charge–discharge processes.

Simple model to study soliton wave propagation in periodic-loaded nonlinear transmission lines

A model to study soliton propagation characteristics in nonlinear transmission lines (NLTLs) periodically loaded with voltage dependent capacitances is presented. This is based on the LC ladder equivalent network of the NLTL, and can be applied to structures where the Korteweg–de Vries approach does not hold. Specifically, the model allows to numerically obtain soliton waveforms under arbitrary capacitance non linearity. To demonstrate its validity, it has been applied to structures loaded with symmetric capacitances, similar to those exhibited by actual heterostructure barrier varactors. The model can be of help to understand harmonic generation in monolithic NLTL-based frequency multipliers.

Effects of Line Parameters on Soliton-Like Propagation in Nonlinear Transmission Lines: Application to the Optimization of Frequency Triplers

In this paper, soliton propagation in nonlinear transmission lines (NLTLs) periodically loaded with heterostructure barrier varactors is studied. From the lumped element equivalent circuit of the line we have analyzed the influence of transmission line parameters (i.e, per-section inductance and capacitance) on soliton propagation characteristics. It is shown that by increasing these parameters, a faster separation of input signals into solitons is achieved. From the point of view of NLTL harmonic generation, this gives additional flexibility to optimize multiplier performance by appropriate circuit design. These conclusions are supported from the analysis of a frequency tripler, where device losses are included.

Understanding soliton wave propagation in nonlinear transmission lines for millimeter wave multiplication

It is well known that frequency multipliers based on monolithic nonlinear transmission lines (NLTLs) provide high conversion efficiency as well as broadband operation. Nonlinearity and dispersion (which is introduced by periodically charging the line with voltage variable capacitors) give rise to the possibility of soliton propagation; i.e. travelling wave pulses with permanent profile. The multiplication process in these circuits has been previously interpreted as due to the decomposition of the input signal wavecycle into a set of solitons of different amplitudes and velocities. According to it, to understand harmonic generation in NLTLs and to have design guidelines, it is important to study soliton behaviour and analyse the effects of NLTL parameters on soliton characteristics. In this work we use a very simple model to obtain soliton propagation characteristics in a NLTL with electrical parameters which are typical for actual structures. Since the origin of solitons (and hence frequency multiplication) is the periodic disposal of nonlinear capacitances in the line (usually HBVs), we present some results showing the effects of device nonlinearity variation (i.e. modifying the equilibrium capacitance of an HBV) on soliton characteristics.