Two-conductor Transmission Line Research Articles

Nondestructive evaluation of grout defect in rock bolt using electromagnetic waves

This study aims to inspect grout defects in rock bolts using electromagnetic (EM) waves. The experiments are conducted using one intact rock bolt and eight defective rock bolts with defect ratios (DR) of 10–50%. A two-conductor transmission line is configured using a pair of rock bolts to transmit EM waves. The EM waves are generated and detected using a time-domain reflectometer. Consequently, the velocity of the EM waves increases with increasing DR. Additionally, almost identical velocities are observed at the same DR, regardless of the defect locations. Moreover, the EM wave reflections are observed at these defects. The defect locations are estimated using the velocity and reflection time of the defects. The estimated location is in good agreement with the actual location. This study demonstrates that EM waves can be an effective tool for evaluating grout defects in rock bolts.

МЕТОД СИНТЕЗУ ВІБРАТОРНИХ АНТЕН З РЕАКТИВНИМИ ВСТАВКАМИ

A new approach is proposed for investigating the electromagnetic properties of a specific class of periodically loaded structures (vibrator antennas with capacitive inserts), which is characterized by relative simplicity and sufficient accuracy. It allows obtaining analytical solutions, thus avoiding the difficulties associated with numerical solutions. At the same time, the obtained solutions can be used in iterative methods for numerical analysis of electromagnetic properties of periodically loaded structures and antenna devices containing these structures. The solution of the problem of electromagnetic energy propagation in a uniform two-conductor transmission line with reactive inclusions is presented. Its solution has revealed new regularities and provided a fresh perspective on the calculation of vibrator antennas with capacitive inserts. Studies on the frequency characteristics of antennas with capacitive inserts have identified three extreme cases of current distribution: exponential, sinusoidal, and linear. Expressions for calculating internal and external characteristics of such antennas have been derived, and dependencies of their electrical characteristics on geometric dimensions have been established. Recommendations for the rational selection of capacitance values and their locations have been formulated. A calculation method for vibrator antennas with capacitive inserts has been developed, which involves the rational use of dispersion properties of such structures in the frequency domain to create wideband antennas with inserts. For the operation of specialized radio equipment, samples of vibrator antennas with two or three capacitive inserts have been manufactured and studied. The results of testing such antennas have shown that their gain at frequencies close to the critical value exceeds the gain of a quarter-wavelength radiator by two or more times, thus increasing the overall efficiency of the developed antennas.

A New Method for Twisted Wire Crosstalk Estimation Based on GA-BP Neural Network Algorithm

Based on the research of genetic algorithm (GA) to optimize the BP neural network algorithm, this paper proposes a method for predicting twisted wire crosstalk based on the algorithm. Firstly, the equivalent circuit model of a multi-conductor transmission line is established, combined with the method of similarity transformation, the second-order differential transmission line equations are decoupled into n groups of independent two-conductor transmission line equations, and the crosstalk is finally solved. Then the mathematical model of the twisted wire is established and its structural characteristics are analyzed, and the GA-BP neural network algorithm is used to realize the mapping of the electromagnetic parameter matrix of the twisted wire and the position of the twisted wire. Finally, the mapping relationship is substituted into the transmission line equation, and the near-end crosstalk (NEXT) and the far-end crosstalk (FEXT) of an example three-core twisted wire are predicted based on the idea of cascade combined. By comparing with the transmission line matrix method (TLM), it can be seen that the method proposed in this paper is in good agreement with the crosstalk results obtained by the electromagnetic field numerical method, which verifies the effectiveness of the algorithm proposed in this paper.

Smart Sensing Using Electromagnetic Waves for Inspection of Defects in Rock Bolts.

The stability of tunnels and rock slopes is adversely affected by defects in rock bolts. This study investigates the suitability of the smart sensing method using electromagnetic waves for inspecting defects in rock bolts. Experiments were performed with one fully grouted and eight defective rock bolts, out of which five have non-grouted parts at the ends with different non-grouted ratios, and three have different types of voids. Electromagnetic waves were generated and detected using a time domain reflectometer by configuring two-conductor transmission lines in the rock bolts. Results show that electromagnetic waves are reflected both at defects and ends of rock bolts. The electromagnetic wave velocity increases with an increase in the non-grouted ratio and decreases when rock bolts are embedded in a concrete block simulating rock mass. The estimated locations of defects found by electromagnetic waves are in good agreement with actual defect locations. This study demonstrates that smart sensing using electromagnetic waves is an effective method for inspecting and determining defect locations and the non-grouted ratio of rock bolts.

On the inverse variational problem for one class of quasilinear equations

The paper concerns the inverse problem of calculus of variations for one class of elliptic and hyperbolic quasilinear second order equations with two independent variables. The equations of this class have a rather wide range of applications, among which are modeling of a two-conductor transmission line, motion of a hyperelastic homogeneous rod whose cross-sectional area varies along the rod, vibration of a string, wave propagation in a bar of elastic–plastic material, and isentropic flows of a compressible gas with plane symmetry. A constructive solution of the problem in hand is given and the corresponding Lagrangians are explicitly constructed.

Non-destructive Method for Evaluating Grouted Ratio of Soil Nail Using Electromagnetic Wave

Although soil nails have been widely used for stabilizing slopes, they are often only partially grouted. Thus, grouted ratio of soil nails should be evaluated to prevent landslides. The purpose of this study was to investigate the suitability of a non-destructive method using electromagnetic waves for evaluating grouted ratio of soil nails. Experimental studies were performed with steel bars, partially grouted steel bars, and fully grouted steel bars in air. Partially and fully grouted steel bars were also installed in soils to simulate soil nails installed on slopes. Electromagnetic waves were generated and received using a time domain reflectometer by configuring a two-conductor transmission line formed by two parallel steel bars or two parallel grouted steel bars. Results of experiments showed that the respective round-trip travel time of electromagnetic waves increased with increasing length of the steel bar, grouted steel bar in air, and grouted steel bar in soils. The velocity of electromagnetic waves was the greatest in steel bars but the lowest in grouted steel bars in soils. In addition, the velocity of the electromagnetic waves decreased with increasing grouted ratio. This study suggests that electromagnetic waves might be useful for evaluating grouted ratios of soil nails to stabilize slopes.

FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Lossy Two-Conductor Transmission Lines

This paper presents a finite difference time domain formulation incorporating conductor losses due to skin and proximity effects for a uniform lossy two-conductor transmission line. At high frequency the per-unit-length effective internal impedance model is based on a boundary element method formulation enforcing high-order surface impedance boundary conditions. A smooth transition from the low to the high frequency model is obtained using first-order low- and high-pass filters. The effective internal impedance model is implemented into the finite difference time domain method via the discretization of the convolution. Finally, a computationally efficient finite difference time domain discretization of the two-conductor transmission line equation is obtained applying a recursive convolution technique. The proposed formulation is validated by comparison with the conventional inverse fast Fourier transform method and shows an improvement with respect to the well-known Paul's method, which does not consider the proximity effect.

Application of time domain reflectometer for detecting necking defects in bored piles

This paper presents a non-destructive method for detecting necking defects in bored piles using electromagnetic waves. Small-scale laboratory experiments are conducted with a defective model pile with diameter of 0.6 m and length of 1.0 m. Four artificial necking defects are introduced on three different sides of the model pile. One necking defect is introduced at the upper position on one side of the model pile, another one is introduced at the lower position on other side of the model pile, and the other two are introduced at both the upper and lower positions on the same side of the model pile. Electrical wires are installed alongside the main rebars of a reinforcement cage to configure a two-conductor transmission line. Electromagnetic waves are generated and detected using a time domain reflectometer. The experimental results indicate clear detection of the reflected electromagnetic waves at the necking defects and pile end. In addition, the calculated defect locations are similar to the actual locations. This study demonstrates that electromagnetic waves can be effective in detecting necking defects at various positions in bored piles.

A Study on the Development of Scour Monitoring System Using TDR

Scour is a critical factor that affects the stability of a bridge. This paper presents a fundamental study on the development of a Time Domain Reflectometry (TDR) system for monitoring scour around a bridge pier. The laboratory experiments were conducted using a small-scale model pier with inner and outer diameters of 70 and 75 mm, respectively and a height of 200 mm. The model pier was embedded in a soil tank. Electrodes were installed in a circular array alongside the model pier to configure two-conductor transmission lines. Electromagnetic waves were generated and detected using the TDR. The experimental results indicate that the round-trip travel time of the electromagnetic waves increase with an increase in the scour depth. In addition, the estimated scour depth is approximately the same as the actual depth. This study demonstrates that the TDR is an effective tool for monitoring scour. Keywords: Bridge, Electromagnetic Wave, Scour, Time Domain Reflectometry

Neural network method for lossless two-conductor transmission line equations based on the IELM algorithm

With the increasing demands for vast amounts of data and high-speed signal transmission, the use of multi-conductor transmission lines is becoming more common. The impact of transmission lines on signal transmission is thus a key issue affecting the performance of high-speed digital systems. To solve the problem of lossless two-conductor transmission line equations (LTTLEs), a neural network model and algorithm are explored in this paper. By selecting the product of two triangular basis functions as the activation function of hidden layer neurons, we can guarantee the separation of time, space, and phase orthogonality. By adding the initial condition to the neural network, an improved extreme learning machine (IELM) algorithm for solving the network weight is obtained. This is different to the traditional method for converting the initial condition into the iterative constraint condition. Calculation software for solving the LTTLEs based on the IELM algorithm is developed. Numerical experiments show that the results are consistent with those of the traditional method. The proposed neural network algorithm can find the terminal voltage of the transmission line and also the voltage of any observation point. It is possible to calculate the value at any given point by using the neural network model to solve the transmission line equation.

Propagation Along Overhead Transmission Lines with Multiply Grounded Shield Wires

Simple, closed-form expressions have been derived for the propagation constants and currents for a two-conductor transmission line over earth with a single shield wire centered above it and periodically grounded through an impedance. Each conductor is driven by a voltage source at $\mathrm{z}=$ 0. The expressions are valid as long as all transverse dimensions are small compared to a free-space wavelength, are in agreement with the known low-frequency expressions, and can be used to establish the validity of low-frequency expressions. In addition, well-known microwave phenomena, such as stop and pass bands, have been identified at frequencies as low as 500 kHz.

Design of a printed non‐planar dual‐polarised log‐periodic dipole array

An efficient and low cost approach to realise a non-planar dual-polarised log-periodic dipole array antenna (LPDA) using printed circuit board technology is proposed which achieves a high bandwidth and operational frequency. The proposed antenna utilises a very short transition from a coaxial cable to a balanced four-conductor transmission line to realise an ultra-wide bandwidth balun and input impedance matching. An analysis of the utilised four-conductor transmission line alongside its comparison to two-conductor transmission line of a planar LPDA is also presented. Two prototypes of the antenna operating over the frequency ranges of 1–13 GHz and 1–18 GHz were designed, fabricated, and tested. An average gain of 6.7 dBi is obtained. Measured voltage standing wave ratio, cross-polarisation and front-to-back ratio of both prototypes are better than 2.6, −14, and 22 dB respectively.

Analytical Formulation for Electromagnetic Leakage Field to Transmission Line Coupling through Covered Apertures of Multiple Enclosures

An efficient analytical model has been developed for predicting the electromagnetic leakage field coupling with a lossless two-conductor transmission line (TL) through covered apertures of multiple enclosures. The analytical results have been successfully compared with those from the full-wave simulation software CST over a broad frequency range. The analytical model can be employed to analyze the effect of different factors including the position and the direction of the electric dipole, the conductivity of the conductive sheet, the quantity of the aperture, and the direction of the TL on the induced currents. Besides, it can also deal with apertures in multiple sides of the enclosures.

Compact SIW dual‐band bandpass filter using novel dual‐resonance quasi‐SIW‐transmission‐line‐structure resonators

A compact substrate integrated waveguide (SIW) dual-band bandpass filter (DBSF) using novel quasi-SIW-transmission-line-structure resonators is proposed in this study. This dual-resonance SIW resonator which works in TE100 mode and TE201 mode can be evolved from a conventional SIW-transmission line or a two-conductor transmission line. Multiple signals transmission paths bring extra transmission zeros (TZs) and improve the selectivity and out-band rejection of the DBSF. This filter works at 4.75 GHz/4.82 GHz, 5.38 GHz/5.51 GHz with 3 dB fractional bandwidths of 3.8 and 3.9%, respectively, and has six TZs. The measured results agree with the simulation results well.

Time-Domain Finite Element Method Analysis of Frequency-Dependent Transmission Lines

This paper presents the finite element (FE) time-domain model for numerical solution of frequency-dependent transmission lines (TLs) problem. Based on the finite element method (FEM) and the generalized trapezoidal rule applied to frequency-dependent TL equations, a novel numerical procedure for a solution of a system of the telegraph equations in time domain is presented. The principles of the proposed method, for the sake of simplicity, have been shown to the case of two-conductor TL where frequency-dependent per-unit length TL parameters have been incorporated into the FE local system of equations by the direct convolution algorithm. The proposed numerical method has been tested and compared to the solutions available in the literature, and a good correlation has been demonstrated.

Multiresolution Time-Domain Scheme for Terminal Response of Two-Conductor Transmission Lines

This paper derives a multiresolution time-domain (MRTD) scheme for the two-conductor lossless transmission line equations based on Daubechies’ scaling functions. And a method is proposed to generate the scheme at the terminal and near the terminal of the lines. The stability and numerical dispersion of this scheme are studied, and the proposed scheme shows a better dispersion property than the conventional FDTD method. Then the MRTD scheme is extended to the two-conductor lossy transmission line equations. The MRTD scheme is implemented with different basis functions for both lossless and lossy transmission lines. Numerical results show that the MRTD schemes which use the scaling functions with high vanishing moment obtain more accurate results.

Fast and efficient calculation of lightning-induced voltages in frequency-dependent transmission lines over lossy ground

This paper presents a fast and efficient algorithm for the calculation of electromagnetic fields radiated from lightning return-stroke channel as well as lightning-induced voltages in frequency-dependent transmission lines. The algorithm developed in this paper employs a mixed time-frequency macro-model that is based on tracing the poles and residues of the transfer function of the lightning-transmission-line system. Accurate and fast calculation of electromagnetic field data along the excited transmission line is critical to obtain the source terms (or forcing functions) in field-to-transmission-line coupling equations. Using the proposed method, we are able to obtain a closed form solution for the lumped sources required for the analysis of a two-conductor transmission line exposed to nonuniform electromagnetic fields. The algorithm provides high accuracy as well as significant speed gain for multiconductor transmission lines (MTL) as well. To demonstrate the application of the proposed method, we will compare our results with those obtained using other methods or measurements.

ELECTROMAGNETIC RADIATION FROM UNBALANCED TRANSMISSION LINES

Abstract—A theory for the electromagnetic radiation from unbalanced transmission lines is developed. It is shown that radiation results from the convection current that develops in unbalanced transmission lines where the resistances of the lines are unequal. The process that leads to the generation of the nonlinear convection current in unbalanced transmission lines is explained. It is proved that the classical transmission line theory is not valid for unbalanced lines. The convection current and the radiation forces are included in the transmission line equations to develop a generalized model valid for all two-conductor transmission lines. The generalized model is validated via comparisons of its numerical solutions with laboratory measurements.

Simulation of resistive microwave resonator probe for high-pressure plasma diagnostics

A U-shape probe for microwave resonance in plasma was investigated in a range of high pressure (10–760 Torr). The electromagnetic field finite difference time domain-simulation of the probe revealed that, in the resistive resonance at high pressure, the resonant frequency fr approaches the dipole-antenna resonance frequency in vacuum, with almost no dependence on the electron density ne. However, the resonance width Δf is sensitive to the pressure, showing the maximum value at ∼20 Torr. The normalized resonance width (Δf/fr) corrected by the one of vacuum value (no plasma) is linearly proportional to ne, and inversely proportional to νm (electron–molecule collision frequency) for high-pressure plasmas. These simulation results are successfully explained in a model of two-conductor transmission line in cold collisional plasma. According to the resonance analysis, the methods for measuring the electron density and the electron collision frequency at high pressures (, ) were proposed.

A Simple Line Charge Technique for Electrostatic Simulations of Two-conductor Open Transmission Lines

A simple electrostatic-simulation technique based on the boundary integral method is presented. Conduction boundaries are formed by using an arrangement of line charges. The technique is well suited to analyze two-conductor open transmission lines complying or satisfying the Laplace equation. Three examples of the application of the technique are shown. The examples are originated from a slotted coaxial line structure converted to a mirror circular arc-strip line via the image theory. The numerical approach is validated by comparing the results to those obtained using variational expressions. One example considers a mirror convex circular arc-strip line with different angular slots, another treats its dual, i. e., a mirror concave circular arc-strip line and the last one deals with a twin circular arc-strip line considered as a circular version of the twin flat-strip line. A graphical procedure for generating field maps for uniform two-conductor circular geometries is also included.