Nonuniform Transmission Lines Research Articles

Simple Compact UWB Vivaldi Antenna Arrays for Breast Cancer Detection

In this study, at ultra-wideband (UWB) frequency band (3.1–10.6 GHz), we propose the use of compact 2:1 and 3:1 nonuniform transmission line Wilkinson power dividers (NTL WPDs) as feeding networks for simple 2 × 1 linear UWB Vivaldi tapered and nonuniform slot antenna (VTSA and VNSA) arrays. The 2:1 and 3:1 tapered transmission line (TTL) WPDs are designed and tested in this work as benchmarks for NTL WPDs. The VTSA array provides measured S11 < −10.28 dB at 2.42–11.52 GHz, with a maximum gain of 8.61 dBi, which is 24.39% higher than the single element. Using the VNSA array, we achieve 52% compactness and 6.76% bandwidth enhancement, with good measured results of S11 < −10.2 dB at 3.24–13 GHz and 15.11% improved gain (8.14 dBi) compared to the VNSA single element. The findings show that the NTL and Vivaldi nonuniform slot profile antenna (VNSPA) theories are successful at reducing the size of the UWB WPD and VTSA without sacrificing performance. They also emphasize the Vivaldi antenna’s compatibility with other circuits. These compact arrays are ideal for high-resolution medical applications like breast cancer detection (BCD) because of their high gain, wide bandwidth, directive stable radiation patterns, and low specific absorption rate (SAR). A simple BCD simulation scenario is addressed in this work. Detailed parametric studies are performed on the two arrays for impedance-matching enhancement. The computer simulation technology (CST) software is used for the simulation. Hardware measurement results prove the validity of the proposed arrays.

Inverse Scattering for Coupled Nonuniform Lossless Transmission Lines Based on a State-Space Method and Nonuniform Frequency Sampling

Inverse Scattering for Coupled Nonuniform Lossless Transmission Lines Based on a State-Space Method and Nonuniform Frequency Sampling

A Method to Determine the Appropriate Section Number of Exponential Nonuniform Transmission Lines

A Method to Determine the Appropriate Section Number of Exponential Nonuniform Transmission Lines

Application of stochastic filter to three-phase nonuniform transmission lines

ABSTRACT This paper implements the stochastic filters for state and parameter estimation of nonuniform transmission lines (NTL). In general, transmission line (TL) problem is a continuous time and space problem. By taking the line loading noise into account, the TL equations become a stochastic partial differential equation (PDE) rather than a simple set of coupled finite stochastic differential equations (SDE). By transforming the spatial variables into the Fourier domain, the stochastic PDE can be transformed into an infinite sequence of SDE. After truncation to a finite set of Fourier series coefficients, it becomes a finite set of coupled linear SDE, which is the required domain in which extended Kalman filter (EKF) and unscented Kalman filter (UKF) can be applied. For state space equation of EKF and UKF, the voltage and current of periodic NTL are expanded into an infinite set of spatial harmonics. In this way, the voltage and current measurement of NTL become an eigenvalue problem. The NTL is considered as cascade of small infinite NTL and the four distributed primary parameters of the periodic NTL are expressed using Fourier series expansion. Finally, the Kalman filter (KF)-based state estimation and the EKF- and UKF-based parameter estimation have been compared with recursive least squares (RLS) method. The simulation results present the superiority of the method.

Compact linearly polarized 5G Vivaldi non-uniform slot filtering antenna

This research proposes compact linearly polarized 5G Vivaldi non-uniform slot filtering antennas (VNSFAs) with stable radiation patterns and improved bandwidth (BW) and gain. The 5G third-order uniform transmission line hairpin bandpass filter (UTL HPBF) is first designed, and a 17.17 % size reduction is obtained using the non-uniform transmission line (NTL) theory. Secondly, the Vivaldi non-uniform slot profile antenna (VNSPA) theory is applied to design the UWB compact VNSA with 51.94 % size reduction, 2.91 %, and 5.8 % BW and gain enhancement. Finally, the predesigned compact UWB VNSA’s good performance is exploited in this work to be integrated with the compact 5G UTL and NTL HPBFs using a co-design methodology resulting in novel compact 6.55 GHz VNSFAs. These VNSFAs are compatible with modern wireless system miniaturization requirements. They are also considered good candidates for cognitive radio networks (CRNs) to mitigate spectrum scarcity. In this work, simulations are carried out using computer simulation technology (CST) software and they are validated by comparing them to the measured results. VNSFAs using UTL and NTL HPBFs provide measured S11 of <−10.35 dB and <−10.34 dB at 5.6–7.76 GHz and 6–7.76 GHz with peak realized gains of 4.84 dBi and 5.23 dBi, respectively. The obtained findings prove the effectiveness of using the simple and low-cost compactness techniques of NTL and VNSPA theories in reducing the filtenna size without degrading its performance.

Simulation of nonuniform transmission lines

PurposeThe purpose of the paper is the simulation of nonuniform transmission lines.Design/methodology/approachThe method involves a Magnus expansion and a numerical Laplace transform. The method involves a judicious arrangement of the governing equations so as to enable efficient simulation.FindingsThe results confirm an effective and efficient numerical solver for inclusion of nonuniform transmission lines in circuit simulation.Originality/valueThe work combines a Magnus expansion and numerical Laplace transform algorithm in a novel manner and applies the resultant algorithm for the effective and efficient simulation of nonuniform transmission lines.

Nonuniform Transmission Line Model for Electromagnetic Radiation in Free Space

An equivalent nonuniform transmission line model for electromagnetic radiation in free space is developed. By properly defining a voltage and a current associated with the transverse component of the mode fields, a kind of telegrapher’s equation is derived for each spherical harmonic mode in frequency domain. Based on the equivalent distribution inductance and capacitance, the local characteristic impedance and phase velocity are derived. For each spherical mode, a cutoff spherical surface and an associated cutoff radius are introduced to separate the space into an evanescent region and a propagating region. A spherical mode field decays approximately exponentially in the evanescent region and experience local reflection in the propagating region. The proposed model may provide an intuitive illustration for the radiation process in free space.

A new method for analyzing non-uniform guiding structures

This paper presents a new technique for analyzing a non-uniform transmission line (NUTL). This method expands the differential equations of voltage and current as the slope functions. Then, differential equations are solved using the explicit Runge–Kutta technique with the fourth-order method with four stages. It is shown that the proposed method can be used not only for analyzing the NUTL but also for analyzing the no-uniform waveguides (NUWG). Additionally, it is shown that the sensitivity of the proposed method concerning the discretization error is suitable. Several theoretical and practical NUTLs and NUWG are investigated to verify the proposed method’s accuracy and advantages. The performance of the proposed method is compared with those obtained by the other popular techniques, such as uniform cascaded sections (UCS).

Influence of High Reflection Order Components on the Transmission Characteristics of Nonuniform Transmission Lines

The high reflection order components are usually ignored when theoretically studying the transmission characteristics of the nonuniform transmission lines (NTLs), but this simplification is reasonable or not still unknown. In this article, the frequency responses of high reflection order components of the NTL are investigated by combining analytical analysis and numerical simulations. Analytical results show that, for arbitrary impedance profile, when the frequency is zero, the value of frequency response only depends on the reflection order and the ratio of output impedance to input impedance. Through numerical simulations, it is found that the frequency responses of high reflection order components decrease as the frequency increases, and the physical meaning of this phenomenon is explained. Based on the above results, a practical method is proposed to determine which high reflection order components should be considered under arbitrary input waveforms. The proposed method is meaningful for correctly choosing the essential components to be considered when studying the NTL analytically.

Compact 5G Vivaldi Tapered Slot Filtering Antenna with Enhanced Bandwidth

Compact fifth-generation (5G) low-frequency band filtering antennas (filtennas) with stable directive radiation patterns, improved bandwidth (BW), and gain are designed, fabricated, and tested in this research. The proposed filtennas are achieved by combining the predesigned compact 5G (5.975 – 7.125 GHz) third-order uniform and non-uniform transmission line hairpin bandpass filters (UTL and NTL HPBFs) with the compact ultrawide band Vivaldi tapered slot antenna (UWB VTSA) in one module. The objective of this integration is to enhance the performance of 5.975 – 7.125 GHz filtennas which will be suitable for modern mobile communication applications by exploiting the benefits of UWB VTSA. Based on NTL HPBF, more space is provided to add the direct current (DC) biassing circuits in cognitive radio networks (CRNs) for frequency reconfigurable applications. To overcome the mismatch between HPBFs and VTSA, detailed parametric studies are presented. Computer simulation technology (CST) software is used for the simulation in this study. Good measured S11 appeared to be < −13 and < −10.54 dB at 5.48 – 7.73 and 5.9 – 7.98 GHz with peak realized gains of 6.37 and 6.27 dBi, for VTSA with UTL and NTL HPBFs, respectively which outperforms the predesigned filters. Validation is carried out by comparing the measured and simulated results.

Compact 5G Nonuniform Transmission Line Interdigital Bandpass Filter for 5G/UWB Reconfigurable Antenna

In this study, at two different fifth generation (5G) low-frequency bands (3.7-4.2 GHz and 5.975-7.125 GHz) and based on nonuniform transmission lines (NTLs) theory, a compact three-quarter-wave resonators interdigital bandpass filter (IBPF) is analyzed, designed, and fabricated. The compact proposed filter is considered as a good candidate for reconfigurable 5G low-frequency bands and ultrawide band (UWB) antenna, which will reduce the size of the final RF communication system. Firstly, a uniform transmission line (UTL) IBPF at these two bands is designed and tested; then the NTL concept is applied for compactness. For both UTL and NTL IBPFs, different parametric studies are performed for optimization. At the first frequency band, size reductions of 16.88% and 16.83% are achieved in the first (symmetrical to the third resonator) and second λ/4 resonator of UTL IBPF, respectively, with up to 36.6% reduction in the total area. However, 16.46% and 16.33% size reductions are obtained in the first (symmetrical to the third resonator) and second λ/4 resonator, respectively, at the second frequency band with a 40.53% reduction in the whole circuit area. The performance of the proposed NTL IBPF is compared with the UTL IBPF. The measured reflection coefficient of the proposed NTL IBPF, S11, appears to be less than -10.53 dB and -11.27 dB through 3.7-4.25 GHz and 5.94-7.67 GHz, respectively. However, the transmission coefficient, S12 is around -0.86 dB and-1.7 dB at the center frequencies, fc = 3.98 GHz and 6.81 GHz, respectively. In this study, simulations are carried out using high-frequency structure simulator (HFSS) software based on the finite element method (FEM). The validity of the proposed theoretical schematic of this filter is proved by design simulations and measured results of its prototype.

Transient response of nonparallel frequency-dependent transmission lines due to nearby lightning strikes in the presence of finitely-conducting ground

Overvoltage transients due to lightning strikes is a common occurrence in power transmission lines which can ultimately lead to line outages. Simulation of transmission line networks under the influence of lighting plays a vital and essential role in predicting their transient behaviour . The transient behaviour of uniform transmission lines due to lightning has been studied extensively. However, in modern transmission line networks, nonuniformities and discontinuities such as nonparallel wire, line crossings or bends are becoming increasingly common. Therefore, in such cases, inaccuracies might be present in analysis performed using conventional uniform transmission line approaches. A recent publication by the authors analysed the transient behaviour of nonparallel and crossing transmission lines above perfect electric conductor (PEC) ground. However, the PEC assumption can only be used in a limited scope. In this paper a nonuniform transmission line model with external field coupling is presented to analyse the transient behaviour of a nonuniform wire structure due to the field coupling from a nearby lightning strike in the presence of lossy ground. Simulation results generated by the proposed model is compared with full-wave simulations and results published by other researchers. A case study to compare the results from the proposed model with a conventional uniform transmission line model under various ground-conductivity values and terminating conditions is also performed. The study indicates that the presence of nearby nonparallel lines can cause the transient behaviour of the structure to deviate from the behaviour predicted using uniform approaches. • The transient behaviour of a nonuniform wire structure a nearby lightning strike in the presence of lossy ground is studied. • Simulation results generated by the proposed model is compared with full-wave simulations and results published by other researchers. • Results from the proposed model have been compared with a conventional uniform transmission line model. • The study indicates that the presence of nearby nonparallel lines intensify the transient behaviour.

Port Impedance Measurement and Current Injection Response Analysis for PLCs

Programmable logic controllers (PLCs) are used to control devices throughout the power system since they have fast control capabilities and can utilize multiple types of communication interfaces. Therefore, studying and mitigating their vulnerabilities to electromagnetic pulse is important for the reliability of PLC operations. In this article, an effective impedance measurement scheme is proposed and demonstrated for three PLCs to estimate their susceptibility to an electromagnetic pulse. The equivalent nonuniform transmission line model is established to eliminate the impact of the fixture in the de-embedding process. Then, different parameters of the impedance measurement setup are explored. Based on the measured impedance, the equivalent circuit is established to calculate the response of the device when subjected to the electromagnetic pulse. The voltage and current responses of different interfaces are compared utilizing the developed pulsed current injection (CI) method. Finally, the impedance measurement scheme is verified through testing using three measuring instruments. And the CI simulation experiments reveal the characteristics and susceptibilities of different PLCs interfaces, indicating that some protection measures are required for the reliable operation of the PLC.

Overview of Transient Simulations of Grounding Systems under Surge Conditions

The present paper gives an overview of modelling methods of standard grounding systems under surge conditions, using the non-uniform transmission line approach. The model presented considers the soil ionization and the frequency dependence of the soil parameters during the current transients. Furthermore, the representation of the non-linear response of the soil is made using a shunt time-variable resistance to simulate the behavior of the grounding resistance when a surge current flows through the system. The model development and analysis are made using ATP-EMTP/ATPDraw transient software.

State and Parameter Estimation of Non-Uniform Transmission Line Using Kronecker Product Based Modeling

The distributed parameters of a non-uniform transmission line (NTL) are assumed to depend on a finite set of unknown parameters, for example, their spatial Fourier series coefficients. The line equations are set up taking random voltage and current line loading into account with the random loading being assumed to be white Gaussian noise in the time and spatial variables. Bypassing over to the spatial Fourier series domain, these line stochastic differential equations (SDEs) are expressed as a truncated sequence of coupled stochastic differential equations for the spatial Fourier series components of the line voltage and current. The coefficients that appear in these stochastic differential equations are the spatial Fourier series coefficients of the distributed line parameters and these coefficients in turn are linear functions of the unknown parameters. By separating these complex stochastic differential equations into their real and imaginary part, the line equations become a finite set of SDEs for the extended state defined to be the real and imaginary components of the line voltage and current as well as the parameters on which the distributed parameters depend. The measurement model is assumed to be white Gaussian noise corrupted versions of the line voltage and current sampled at a discrete set of spatial points on the line and this measurement model can be expressed as a linear transformation of the state variables, i.e, of the spatial Fourier series components of the line voltage and current plus a white measurement noise vector. This work uses sparse matrix factorization using Kronecker product to implement the Fourier unitary transform. This work implements perturbation theory for non-uniform transmission line. The extended Kalman filter (EKF) equations are derived for this state and measurement model and our real timeline voltage and current and distributed parameter estimates show excellent agreement with the true values based on MATLAB simulations. The use of sparse matrix factorization using Kronecker product ease the mathematical complexity and provides compact representation.

Novel Compact UWB Vivaldi Nonuniform Slot Antenna With Enhanced Bandwidth

A new theory called Vivaldi nonuniform slot profile antenna (VNSPA) is developed based on the nonuniform transmission lines (NTLs) theory and applied to reduce the size of the predesigned compact ultrawide band (UWB) Vivaldi-tapered slot antenna (VTSA) without affecting its performance in terms of matching and bandwidth. Using this theory, 33% of the taper slot length is reduced, resulting in a novel compact UWB Vivaldi nonuniform slot antenna (VNSA). Furthermore, compactness is achieved by performing parametric studies on VNSA with a final 51.94% size reduction. MATLAB optimization codes, CST simulation, and prototype manufacturing and measurement are used to validate the new theory. The proposed antenna provides a measured S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> < −10.89 dB through 2.9–13.55 GHz with 2.91% and 5.8% bandwidth and maximum realized gain enhancement, respectively, as compared with VTSA’s results. The effectiveness of VNSPA theory is proven by comparing the simulated and measured findings of VNSA and VTSA.

Time-Domain Coupling Model for Nonparallel Frequency-Dependent Overhead Multiconductor Transmission Lines Above Lossy Ground

Expansion of power grids has resulted in the construction of multiple transmission lines within constrained spaces inevitably making them nonuniform in nature. Existing transmission line models available in electromagnetic transient (EMT) simulators are based on classical multiconductor transmission line (MTL) theory with the assumption that the transmission lines are infinitely long and have uniform cross-sectional dimensions. This paper develops a time-domain model, namely dispersive scattered field transmission line (DSFTL) model, for multiconductor dispersive nonuniform overhead transmission lines above lossy, frequency-dependent ground. The proposed model which consists of closed-form equations in the time-domain has been implemented using a modified finite-difference time-domain (MFDTD) algorithm and integrated into an EMT simulator (PSCAD/EMTDC). Results have been compared with and verified by those obtained using a full-wave approach and measured data available in the literature. Simulations of nonuniform structures that include nonlinear components (such as breakers) have also been carried out under fault conditions.

Expanding Functionality of Dual-Mode Resonators and Filters Using Nonuniform Transmission Line Structural Elements

The article provides an optimal synthesis of nonuniform transmission line structural elements, where resonant frequencies have a special placement. It is possible to improve the functionality of dual-mode resonators, which use these transmission segments. The optimal synthesis means that we obtain the special ratio between resonance frequencies of structural elements and have the minimum of parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}={Z}_{\text {0max}}/{Z}_{\text {0min}}$ </tex-math></inline-formula> . We used the parametric synthesis for optimize proposed structure. It leads to stepped-impedance transmission line segments (SILS) which have the resonant frequencies with required placement and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}= {m}_{\text {min}}$ </tex-math></inline-formula> . Two SILS pairs are synthesized. Two ends of one pair are open-circuited and the other pair is short-circuited. We added different stubs to the middle of proposed SILS. As result, four new dual-mode resonators with enhanced functions are designed. All dual-mode resonators have an extended stopband. The dual-mode resonators have reduced length relative to a half-wave resonator. The resonators allow increasing their operating frequencies. These resonators are very promising for use in dual-band BPF, so we can change the placement of one passband to another in the range <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.46 \le {f}_{2}/{f}_{1} \le 6.47$ </tex-math></inline-formula> . The measured and simulated results of two microstrip filters with new structural elements are offered.

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.