Nonuniform Transmission Lines Research Articles

A simplified numerical modeling of the transient behavior of grounding systems considering soil ionization

The analysis of the transient performances of grounding systems during a lightning discharge is proposed in the literature by modeling in time or in frequency domain. The frequency modeling makes it generaly possible to take into account the electromagnetic effects observed during the rise time of the pulse while temporal modelling makes it possible to introduce the nonlinear phenomenon (soil ionization) observed following an injection of a very high intensity lightning strike. In this work we propose a modeling with a simplified implementation which takes into account the various electromagnetic couplings which arise after spatial discretization of the grounding system as well as the ionization of the soil. This new formalism is developed from the equations of nonuniform Transmission Lines (nuTL) and the Finite-Difference Time-Domain (FDTD) method. This simplified modeling is carried out solely by spatial discretization of the grounding system conductors, is done without loss of precision and with very low calculation times. Our calculation results are compared to those already published and carried out by simulation or by the measurements.

Theory of Optimum Taper for Distortionless Pulse Transmission

A theory of nonuniform transmission line taper with almost linear transmission phase characteristics has been proposed in this article. The proposed taper provides a preferably flat group delay with optimum time domain characteristics compared to the conventional tapers. Closed-form expressions for the impedance profile of the optimum taper has been discussed here. A stripline and dispersive microstrip line implementation of the taper has been measured to validate the proposed theory.

Surrogate based design optimization of low noise amplifier for ISM band

Design optimization of microwave circuits is a crucial matter for microwave engineers. For the last decades, researchers had been studying surrogate models for a computationally efficient design optimization process. Artificial Intelligence based algorithms had been used for modelling of complex microwave stages such as antenna, amplifiers and frequency selective surfaces. In this study, design optimization of a Low Noise Amplifier (LNA) based on surrogate models for both transistor stage and input & output matching circuits had been presented. Support Vector Regression Machine had been used for creating surrogate models of a microwave transistor and a non-uniform transmission line for having a fast and accurate LNA design optimization process alongside a low profile and high performance LNA using on-uniform transmission lines. By using this methodology, not only designer can create a mapping for missing points in the sparse sample S parameter data points provided by manufacturers but also the overall simulation duration can be significantly reduced thanks to the fast nature of surrogates compared to EM simulators. Here, the proposed surrogate models had been used alongside of Particle Swarm Optimization algorithm to determine optimal geometrical values of input/output matching networks. Then the obtained designs are prototyped and measured. The measured results are also compared with the performance results of counterpart design in literature. As for results, not only the proposed methodology is an effective, fast and reliable method for computationally efficient design optimization process of LNA but also provides better results than the counterpart design in literature.

Realistic modeling of the grounding system transient behavior with frequency dependence

For better protection of electrical networks, modeling the transient behavior of grounding systems is now fundamental before the realization step. In this work we propose a new modeling approach which permits a quick and efficient analysis of the grounding systems.In the proposed approach we solve the transmission lines equations using the Finites Differences (FD) taking into account the different electromagnetic couplings that occur during the spatial discretization of the grounding electrodes. To achieve this objective we complete the general transmission lines equations by introducing the coupling terms between the different parts of the grounding system and we calculate the self and mutual per-unit length parameters according to the geometrical position of the elements (cells). We therefore use rather the term non-uniform Transmission Lines (nuTL). This new modeling offers the advantages of calculating in a single step the currents and voltages at all the points of a grounding system, also taking into account the frequency dependence. Compared to already existing full-wave electromagnetic models our modeling is realistic because its numerical implementation is simple, retains good precision and the calculation times are much reduced.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Artificial intelligence–based design optimization of nonuniform microstrip line band pass filter

AbstractDesign optimization of many electromagnetic and multiphysics problems have multiscale issues that require a fast, efficient, and accurate surrogate‐based model to be used. Recently, in microwave engineering field, artificial intelligence–based models are being used for modeling of complex microwave stages. In all the studies, the main aim is to form models inner structure parameters, by using the given data to predict the linear/nonlinear relationships between given inputs and outputs. Herein, a surrogate‐based model of a nonuniform microstrip transmission line (NTL) with a typical application of design optimization of a band‐pass filter for ISM band application using deep learning (DL) and meta‐heuristic optimization has been presented. In order to have a computationally efficient and accurate optimization process, firstly a 3D EM unit element model of NTL has been designed. The training and test data sets are created based on different sampling methods. A DL regression model modified multilayer perceptron M2LP have been used for prediction of scattering parameters (S) of the NTL, with respect to the variation of geometrical design parameters. The proposed S‐parameters will then be used to calculate the equivalent S‐parameters of the cascading NTL to be used to calculate the NTL‐based microstrip band‐pass filter S‐parameter response. The optimal design parameters of each line used in the filter design have been determined using a fast and powerful optimization algorithm differential evolutionary algorithm.

Compact 5G Hairpin Bandpass Filter Using Non-Uniform Transmission Lines Theory

A compact three order 5G low frequency band Hairpin Bandpass Filter (HPBF) is analyzed, designed and fabricated in this paper. The designed filter operates at 5G frequency range (5.975-7.125 GHz). 17.76% compactness in each λ/2 uniform transmission line (UTL) resonator of the filter is achieved by applying Non-Uniform Transmission Lines (NTLs) theory. This compactness will make modern wireless transmitter and receiver designs more compatible. Study on the best reduction size percentage and suitable constraints to design the required NTL resonator is highlighted in this paper. Six samples with different size reductions percentage are fabricated and measured. The simulation is carried out in this study uses High Frequency Structure Simulator (HFSS) software and Computer Simulation Technology (CST) software. The simulated results for UTL HPBF and NTL HPBF with the six cases are verified with measurement. For the best size reduction percentage design, the measured results demonstrated that the 6.55 GHz NTL and UTL HPBF show good impedance matching within the unsilenced 5G frequency band.

Impedance matching system design using non uniform transmission line for 2.4 Ghz antenna system

The Matching Impedance (MI) design method using Non-Uniform Transmission Line (N.U.T.L.) is a design method that offers more advantages over the 1/4 transformer method, the 1/4 multisection method, and the stub method. In this study, the Matching Impedance system is designed to match the WLAN antenna load with a line impedance of 50 Ohm at the 2.4 GHz. The Matching Impedance system is designed using a transmission line with a Characteristic Impedance (Zo) value that is triangular (Triangular Taper) distributed. This study also examines the effect of the number of cutting sections on a transmission line if the line with the Triangle distribution is implemented on a Microtsrip. From the test results, it is found that the number of sections used to form the Non Uniform transmission line has a significant effect on the bandwidth of the system working frequency for the required value of the Reflection Coefficient.

Scattering from Spheres: A New Look into an Old Problem.

In this work, we introduce a theoretical framework to describe the scattering from spheres. In our proposed framework, the total field in the outer medium is decomposed in terms of inward and outward electromagnetic fields, rather than in terms of incident and scattered fields, as in the classical Lorenz–Mie formulation. The fields are expressed as series of spherical harmonics, whose combination weights can be interpreted as reflection and transmission coefficients, which provides an intuitive understanding of the propagation and scattering phenomena. Our formulation extends the previously proposed theory of non-uniform transmission lines by introducing an expression for impedance transfer, which yields a closed-form solution for the fields inside and outside the sphere. The power transmitted in and scattered by the sphere can be also evaluated with a simple closed-form expression and related with the modulus of the reflection coefficient. We showed that our method is fully consistent with the classical Mie scattering theory. We also showed that our method can provide an intuitive physical interpretation of electromagnetic scattering in terms of impedance matching and resonances, and that it is especially useful for the case of inward traveling spherical waves generated by sources surrounding the scatterer.

Parametric and Structural-Parametric Synthesis of Nonuniform Transmission Line Resonators

This article discusses methods of parametric and structural-parametric synthesis of resonators, which contain transmission line segments of the same length. These methods allow optimizing resonators of various configurations with different segments number $N$ and characteristic impedances $Z_{0i}$ . We will call optimal resonators if they have a minimum ratio $m = Z_{\mathrm {0max}}/Z_{\mathrm {0min}}$ at given ratio between the critical frequencies (poles and zeros of the input impedance). The input impedances of the resonators under consideration at the Richards’ frequency variable $S$ are described by the reactance functions of $N$ degree: $Z^{N}(S)$ . The parametric synthesis refers to stepped impedance resonators (SIRs). The structural-parametric synthesis refers to resonators of a more general form, which contain open- and short-circuited stubs. The methods are based on two states established in this paper: the order of the reactance function $Z^{N}(S)$ should be the minimum possible ( $N = N_{\mathrm {min}}$ ) to implement the required ratio between certain critical frequencies; the characteristic impedances of the composite sections $Z_{0i}$ take only two values $Z_{\mathrm {0min}}$ or $Z_{\mathrm {0max}}$ . These methods were used to synthesize different resonators useful for practical application. With the help of the structural-parametric synthesis, the resonators of a more complex configuration are synthesized, which significantly exceed SIRs. The results of the measurements and simulation are presented.

A Generalized Synthesis Technique for High-Order and Wideband 3-D Frequency-Selective Structures With Chebyshev Functions

A generalized synthesis technique for a new class of high-order and wideband 3-D frequency-selective structures (FSSs) is presented in this article. First, a general circuit model with shunt short-ended stubs and an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> -section nonuniform transmission line is discussed, whose frequency response can be synthesized with Chebyshev functions over a wide frequency range. Following the synthesis procedure, all the circuit parameters can be derived from the specifications of the filtering response, such as filtering order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> (≥4), fractional bandwidth (FBW), and equal-ripple return loss (RL). Then, the general circuit model is applied to design high-order and wideband 3-D bandpass FSS, which is physically realized by using stacked printed circuit board pieces etched with slotlines and microstrip lines. As an example, a fourth-order 3-D FSS with FBW = 80% and equal-ripple RL = 10 dB is designed to show the establishment of good relationship between the circuit model and the physical model. To further improve the frequency selectivity, another two coupling paths independent of the main transmission path are created by simultaneously adjusting the FSS thickness and the separation of slotline sections, thus introducing two transmission zeros at both skirts of the passband. Both design examples are fabricated and measured. Good agreement between measured results and simulated ones indicates that the proposed synthesis method can provide an efficient and accurate solution to design such a class of wideband and high-order 3-D FSSs.

Scattering Parameters Characterization of Periodically Nonuniform Transmission Lines With a Perturbative Technique

In this article, a novel procedure for the frequency-domain solution of nonuniform transmission lines (NUTLs) is presented. The procedure is based on a recently proposed perturbative technique, which is proven to be computationally more efficient than standard solution approaches, which are based on line subdivision into uniform cascaded sections. With respect to the original perturbation technique, the procedure proposed here offers more flexibility, as it provides a representation of the NUTL under analysis in terms of $S$ and/or $T$ parameters at its ports. Moreover, it retains the same prediction accuracy at the price of a slight increase in computational burden, which can be mitigated anyway through parallel computing. Furthermore, even without ad hoc (parallel) implementations, the proposed procedure outperforms other approaches to solve differential lines with partially or fully repetitive geometries. Namely, it assures accurate prediction of output quantities with reduced simulation time. This is proven by three application examples, namely, two differential trapezoidal tabbed lines (one with interdigital tabs and one with facing tabs), and a differential microstrip line with a varying common-mode (CM) impedance (as such reducing CM noise). Comparison with full-wave simulations allows assessing the prediction accuracy of the proposed procedure. Comparison with the aforementioned transmission-line-based solutions allows appreciating the enhanced computational efficiency.

Compact UWB 1:2:1 unequal-split 3-way bagley power divider using non-uniform transmission lines

In this paper, compact Ultra-Wide Band (UWB) 1:2:1 unequal split modified Bagley Power Divider (BPD) using Non-Uniform Transmission Lines (NTLs) theory is designed and tested. Based on this theory, 42.44% and 31.1% size reductions are obtained in the lower and upper λ/4 Uniform Transmission Lines (UTLs) in the first and second sections of the proposed divider. To evaluate the effect of the divider’s compactness on its performance, it is compared with UWB 1:2:1 unequal split BPD using Tapered Transmission Lines (TTLs). Both dividers show good results where the measured return loss is appeared to be S11 < −10.6 dB and < −13.4 dB for NTL and TTL BPDs, respectively. However, the insertion losses S12 = S14 and S13 are around −6 ± 1.5 dB and – 3 ± 1.3 dB, respectively for both dividers. In this study, simulations are carried out using High-Frequency Structure Simulator (HFSS) software. The evaluation of the proposed divider is obtained from the simulation and hardware measurements results.

Wideband complex impedance matching using non-uniform microstrip line based on NMPC for microwave and THz bandwidth

In this paper, a compact wideband non-uniform microstrip line for complex impedance matching at microwave and terahertz (THz) frequency range is proposed. To achieve the favorable form of the non-uniform transmission line, the nonlinear model predictive control (NMPC) has been utilized. The state-space equation is extracted from the transmission line differential equation of the output impedance variations. Using the state space equation, the undetermined coefficients of the non-uniform transmission line which were expanded in cosine form are calculated via NMPC. The minimum length for Γ≤ 0.05 is obtained for the real and complex load in 2−4 GHz and 1−2 THz bandwidth, and consequently, the proposed structure is simulated and the microwave structure fabricated. The dimension of the proposed line is 0.78λg and the simulation results are in acceptable accordance with the measurement results.

A novel UWB printed monopole MIMO antenna with non-uniform transmission line using nonlinear model predictive

A novel ultra wideband (UWB) printed monopole multiple-input multiple-output (MIMO) antenna with non-uniform transmission line using nonlinear model predictive control (NMPC) is presented. The proposed antenna is superior to conventional antennas in terms of dimensions, gain, and efficiency while maintaining the impedance bandwidth. In order to improve the results, a non-uniform transmission line has been used for impedance matching between the radiated patch element and the coaxial cable. For designing the non-uniform transmission line, it has been expanded using cosine terms. Regarding the presence of differential equation for the variation in the impedance of the transmission line and its transformation to the state-space equation, NMPC has been employed to design the transmission line and determine the cosine expansion coefficients. Two base antennas, as MIMO, were simulated configuration and fabricated. The surface area of the proposed MIMO antenna is 0.99 λg2, the wavelength has been obtained for the center frequency of the 3.16 GHz to 10.6 GHz range, and its mutual coupling, peak gain, channel capacity loss (CCL), total active reflection coefficient (TARC), mean effective gain (MEG) and diversity gain (DG), envelope correlation (ECC) are acceptable. The simulation and measurement results are in good agreement, and the proposed antenna is suitable for MIMO applications.

Magnetically insulated transmission lines in the form of cone with ribs: Exploratory design and analysis.

This paper numerically confirms that in the ideal case, the form of cone with 16 ribs benefits the reduction in impedance and the promotion (about 20%-30%) on transmission efficiency of a magnetically insulated transmission line, in comparison with the traditional form of cone. Magnetically insulated transmission lines in the form of cone, cone with 4, 8, 12, and 16 ribs, are first designed by using CREO and then imported to COMSOL for obtainment of their circuit parameters. Two codes based on the wave process and wave process coupled with RLC circuits, respectively, simulating the propagation of external waves through non-uniform transmission lines are analyzed and presented in detail. The obtained parameters are then used in these codes for deriving the designed transmission lines' transmission efficiency of peak power. As a comparison, the obtained data are also employed in PSpice for derivation of the transmission efficiency. These derived results consistently verify that the form cone with ribs may effectively promote the transmission efficiency of magnetically insulated transmission lines.

Fast and low complexity frequency domain analysis of nonuniform substrate integrated waveguide‐based structures

A novel, low complexity approach for the analysis of nonuniform lossy substrate-integrated waveguide transmission lines based on the method of moments is proposed. The approach uses frequency-dependent basis functions derived from the structure's propagation characteristics. Two tapered structures are analyzed, fabricated, and measured to validate the proposed approach. The analytical results of the proposed approach for both structures are compared to those obtained by measurement and by three-dimensional field simulation. Excellent agreement is observed between the three sets of results with simulation time savings on more than 98% and memory requirement reduction of more than 97%.

The Transfer Matrix Method: Analysis of Nonuniform Multiport Systems

A ubiquitous tool in science, physics, and engineering at large, the transfer matrix method (TMM) is particularly suited to deal with complex nonuniform systems (NUS). In the field of electrical engineering, the method is employed in a variety of disciplines that span the electromagnetic spectrum, from power frequencies through RF, millimeter-waves, and terahertz. In this work, three nested goals are pursued. The first is to present a general comprehensive review of the transfer matrix method utilizing two distinct languages: the state space (via the matricant) and the modal analysis (via matrix diagonalization). The second goal, focused on electrical engineering issues, is the application of TMM to the interdisciplinary theme of nonuniform multiconductor transmission lines (MTL) –a good example of a complex reciprocal multiport system. The third goal is to offer the reader novel research results in the context of MTL analysis. Making use of a simple microwave stripline-coupler structure new theoretical results are presented showing that, in some cases, load impedance matching of nonuniform MTLs, using only passive components, may not be physically possible (negative resistors being required), even if the global NUS is longitudinally and transversally symmetric, with or without losses.

General Analysis of Coupled Nonuniform Transmission Lines Based on State Transition Matrix

This letter presents an equation-based solution for the analysis of coupled nonuniform transmission lines (CNUTLs) in the frequency domain. The proposed methodology, which is based on state-transition matrix, models the Telegrapher's equations in form of linear position varying (LPV) system. Solving these equations with the Peano-Baker series (PBSs) provides the sought for closed-form far-end/near-end voltages and currents in the CNUTLs. Unlike the previous methods, due to the unique advantages of PBSs, such as versatility, performing with low-order terms, and subsequently, the high convergence rate, the proposed method is very fast and reliable. In order to validate the method, two practical CNUTLs of relevance in electromagnetic compatibility applications, namely, lossy/lossless exponentially and linearly tapered microstrips, are analyzed. Simulation results show that the proposed method is very accurate and fast in comparison to traditional methods.

Nonuniform compact Ultra-Wide Band Wilkinson power divider with different unequal split ratios

ABSTRACTA compact Ultra-Wide Band (UWB) Wilkinson power divider with different unequal split ratios of 2:1 and 3:1 using three optimized resistors is analyzed, designed and fabricated in this study. A 31.1% size reduction in each λ/4 uniform transmission line (UTL) of the divider is achieved by applying non-uniform transmission lines (NTLs) theory. The proposed divider is contributed to be suitable as a feeder to currently used wireless communication networks such as cognitive radios (CR), resulting in good impedance matching to its entire ports. In addition, the optimized resistors used provided good isolation between the output ports. The simulation is carried out in this study uses High Frequency Structure Simulator (HFSS) software. The simulation results are compared with the hardware measurements to validate the results. It was observed that there was approximately 5% of the difference between simulated and hardware measurements which is within the acceptable limit.