Transmission Line Circuit Model Research Articles

Compact Microstrip Bandstop Filter for UWB Application

In this paper, a novel Ultra-Wideband (UWB) Bandstop Filter (BSF) with five Transmission Zeros (TZ) and three Transmission Poles (TP) is presented. This filter is designed with a new type of resonator. Validation of the proposed filter with the lumped model is also investigated. Further, the transmission line circuit model of the filter is proposed, and consequently even and odd mode impedance is calculated analytically. Furthermore, a compact size of 16.8 mm × 14.98 mm (0.2λg × 0.18λg) is achieved by employing folded stubs. The proposed filter offers an Ultra-wide bandwidth of 7.5 GHz (2.9 –10.4 GHz) with a rejection depth of greater than 20 dB over the entire stopband. Moreover, the upper and lower skirt factors of 70 dB per GHz are achieved. A prototype of the proposed UWB BSF is fabricated and measured. Simulated and measured results are in good agreement, which validates the proposed design.

Model of a 5-MA Linear-Transformer-Driver Accelerator: Comparison of MITL Performance for Bremsstrahlung Electron Beam Diodes and Z-Pinch Loads

A transmission line circuit model was conducted to compare the performances of the two-level 2.5 Ω magnetically insulated transmission lines (MITLs) system of a 5-MA linear-transformer-driver (LTD) accelerator for two kinds of typical loads, including bremsstrahlung electron beam diodes and Z-pinch loads. Both the electron current loss in the pulse front during the magnetic insulation setup process and the electron flow distribution in the magnetic insulation steady state were analyzed. When the accelerator drives an electron beam diode load with impedance of 1.20 Ω (a single level), the duration of the magnetic insulation setup is about 12 ns, the current loss is about 130 kA in a single MITL level, the maximum electron flow current is about 50 kA in the end of MITL, and its amplitude decreases gradually after the steady magnetic insulation is established. When the accelerator drives a Z-pinch load with length of 1.5 cm, radius of 1.2 cm, and mass of 0.3 mg/cm, the duration of the magnetic insulation setup is almost zero, the maximum electron flow current in the end of MITL can reach about 55 kA (a single level), and the waveform of the electron flow resembles a saddle shape, which reaches the peak at the pinch stagnation time.

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.

Equivalent Circuit Modeling and Experimental Analysis of Low Frequency Metamaterial for Efficient Wireless Power Transfer

This study proposes a low-frequency metamaterial(MM) coupled with an equivalent circuit model to emulate the behavior of an MM-based Wireless Power Transfer (WPT) system. For this purpose, the electromagnetic simulation and Finite Element Analysis (FEA) of the proposed MM-based WPT system are performed in ANSYS three-dimensional (3D) High-Frequency Structured Simulator (HFSS). In addition, numerical analysis of the circuit design of the proposed structure is performed in a MATLAB simulation environment to evaluate its transfer characteristics. While some methods, including effective medium theory and transmission line circuit model, have been exploited to explain the physical mechanism of MM-based WPT systems, some of the reactive parameters and the fundamental physical interpretation have not been clearly expounded. In contrast to existing theoretical models, the proposed approach focuses on the effect of system parameters of the MM and transfer coils on transfer characteristics, coupled with its effectiveness in analyzing complex circuits. A design prototype is fabricated for experimental measurement of power transfer efficiency and medium parameters using the KeySight ENA 5061 vector network analyzer (VNA), confirming the validity of the proposed design. The excellent efficiency enhancement and mutual coupling make the design an attractive solution for WPT applications. A close agreement of the experimental results and numerical simulation validates the accuracy of the analytical model.

Circuit simulation of current loss in magnetically insulated transmission line system in 15- MA Z-pinch driver

In this paper, a transmission line circuit model of a magnetically insulated transmission line(MITL) system is developed for a 15-MA Z-pinch driver. The current loss characteristics of multi-level MITL and the ion emission due to the expansion of anode and cathode plasma in the post hole vacuum convolute(PHC) and inner-MITL region are analyzed. The spatiotemporal distribution of current loss of the outer-MITL and ion current of the PHC and inner-MITL of the 15 MA driver are obtained. The results show that the first electron emission happens at the end of constant-impedance MITL and the beginning of constant-gap MITL, and the end of constant-gap MITL firstly achieves fully magnetic insulation. Electron emission occurs at the start of load current and its duration is about 30 ns, which is short for a single pulse and has little effect on the rising edge nor peak value of the load current. The waveform of the electron flow varying with time resembles a saddle shape, whose amplitude first goes up, then comes down, and increases again. The electron flow current decreases from upstream to downstream in constant-gap MITL in space. The starting time of the loss current of the PHC is synchronized with the gap closing time. The loss current amplitude increases rapidly, reaching 4 MA at the peak load current time and 6.5 MA in the end. In the inner-MITL region, the main positive ion species are protons and oxygen 2+. At the beginning, the ion loss current of protons is larger than that of oxygen 2+, and then the protons are quickly magnetically insulated due to the small charge-to-mass ratio. The ion loss current of the inner-MITL region mainly increases after the peak load current time, and its peak value is 2.1 MA. Given the input conditions, the stack is going to deliver current of about 18 MA, the hold voltage is about 2.3 MV, and the peak load current is about 13.5 MA.

Dual-Polarized Slot Antenna for Full-Duplex Systems With High Isolation

A single-layered slot antenna system working at 5.8 GHz Industrial, Scientific and Medical (ISM) band is proposed for in-band full duplex (IBFD) operation applications without the use of a coupler. First, high isolation is achieved by strong separation of even- and odd-mode feeds. The microstrip-coupled coplanar waveguide (CPW) is used at Port 1 (TX port) to excite a stepped-slot antenna in the CPW odd mode. On the opposite side, a microstrip T-junction power divider is employed at Port 2 (RX port) to feed two offset-fed stepped-slot antennas in even mode. Second, isolation is further improved by 30 dB by using a lumped capacitor at the termination of the CPW. The measured isolation between the two ports is about 50 dB across the bandwidth. The measured −10 dB bandwidth of Port 1 is 0.49 GHz (8.5%), while that of Port 2 is 1.06 GHz (18.3%). The gains of TX and RX antennas are 5.4 and 5.8 dBi at 5.8 GHz. The proposed antenna can also be deployed as a dual-polarized antenna. Mathematical analysis and equivalent transmission line circuit models are provided to give physical insight into the working principals of the antenna with validation from ANSYS HFSS simulation.

Metamaterial‐based, compact, wide beam‐width circularly polarized antenna for 5G indoor application

AbstractThis paper describes a metamaterial‐based miniaturized circularly polarized (CP) antenna with high radiation efficiency and wide beam‐width or coverage for 5G indoor application. A novel meta‐resonator is first proposed, which is investigated by transmission line and equivalent circuit models. By exploring a split‐ring resonator‐like meta‐resonator structure, a high‐Q LC resonator tank is formed. Substantial size reduction and a wide beam‐width are achieved. Owing to a uniform field on these multiple capacitive gaps incorporated on this meta‐resonator surface, enhanced aperture efficiency and gain are obtained. It is partly inspired by the classical metasurface‐based antenna. For validation, a miniaturized CP antenna with a size of 0.29 λ0 × 0.29 λ0 × 0.04 λ0 (where, λ0 is the free‐space wavelength at 3.55 GHz) is fabricated and measured. The fabricated antenna achieves a good bandwidth of 3.30–3.80 GHz that well covers 5G‐N78 band, a peak radiation gain of 5.4 dBic, a high radiation efficiency of 90% and a wide half‐power beam‐width of 91°. It exhibits the merits of compact size, good bandwidth and beam‐width, high efficiency, and low‐cost, demonstrating good potential in miniaturized 5G indoor systems demanding wide‐beam coverage.

Circuit Model of an Overhead Transmission Line Considering the TEM‐Mode Formation Delay

When lightning strikes a transmission tower or overhead line, the lightning current generates a spherically expanding electromagnetic field. The propagation mode of an expanding electromagnetic wave is different from that of a transverse electromagnetic (TEM) wave, which is applied to the modeling of transmission lines. This paper presents an equivalent circuit model of an overhead transmission line that considers the TEM‐mode formation delay. The TEM‐mode formation delay is approximately represented by the first‐order delay functions in surge impedances and time delays in the mutual coupling from one line to the others. The proposed circuit model of the overhead line is introduced to the Alternative Transients Program version of Electromagnetic Transients Program using the MODELS language through a formulation in the phase domain based on Dommel's method. The results of the proposed model are validated through a comparison with the results of a three‐dimensional numerical electromagnetic analysis. Furthermore, the effect of the delay of the TEM‐mode formation on the voltages across the insulator strings of a lightning‐struck tower is described by referencing a previous experimental study conducted using an actual 500 kV transmission tower. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Ka‐band distributed microelectromechanical systems transmission line phase shifter using metal air metal switch

AbstractA new approach for designing a two‐state unit cell for a six‐bit distributed coplanar waveguide microelectromechanical systems (MEMS) phase shifter is proposed in this study. The proposed structure includes metal air metal (MAM) capacitors as switches and consists of a unit cell with one MEMS and two MAM switches to produce two phase shifts per unit cell. In the first state, the MAM switches are pulled down and a 5.625° phase shift is achieved, and in the second state, the MEMS switch is actuated to yield a phase shift of 11.25°. The designed structure is modeled using equivalent transmission line circuit model and simulated in the Ka‐band at 34 GHz, employing advanced design system (ADS), ANSOFT HFSS and COMSOL software. Based on the modeling and simulation results, the root‐mean‐square (RMS) phase error is 1.4°, and maximum return loss and minimum insertion loss for all 64 states are better than −10.1 and −1.45 dB, respectively. The main advantages of the designed structure are its small size, low loss, low phase error and a simple phase shift mechanism. A fabrication process is also proposed for the distributed MEMS transmission line (DMTL) phase shifter that shows the feasibility of the proposed design. The proposed structure can be easily scaled to other bands and used in applications with more bits as complex as phased array antennas.

Design and analysis of ultrathin X‐band frequency selective surface structure for gain enhancement of hybrid antenna

A wideband ultrathin frequency selective surface (FSS) structure is designed and developed for the complete X-band. The design employs a metallic tetra-arrow (two bidirectional arrows placed diagonally) and a circular split structure (metallic) in the top side and bottom side of RT duroid 5880LZ low-loss substrate respectively. The proposed design has novel contribution in terms of significant reduction in electrical thickness (0.007λ0 which is corresponding to lowest operating frequency, 8.3 GHz) and wider transmission (S21) bandwidth (measured: S21 ≤ − 10 dB, 8.15-13.2 GHz, 47.3%), covering entire X-band due to cumulative loading of surface mount chip resistors in the top layer. The principle of operation of the proposed FSS further can be justified with its equivalent transmission line circuit model, which is based on microwave filter (band-stop and band-pass) topology for anticipating the desired characteristics. The FSS structure is further integrated with dielectric resonator (DR)-slot hybrid antenna for enhancing the gain (measured: peak gain of 4.5 dBi without FSS and 7.8 dBi with FSS) of the antenna. The proposed FSS structure is fabricated and measured performance has very similar responses as simulated ones.

Electromagnetic and circuit modelling of a modified design of bulk current injection probe calibration jig

In this study, a wideband rounded-shield calibration fixture or jig used to calibrate in-band injection probe is implemented based on 3D electromagnetic modelling in CST Microwave Studio; the Electromagnetic (EM) model is validated and then used in studying the effect of the jig layout parameters on its bandwidth. The impact of a rounded instead of the typical flat shield is studied too, and showed an improvement of about 15% in the bandwidth at Voltage Standing Wave Ratio (VSWR) level of 3. A new systematic rules procedure for extracting the circuit model of transmission lines based structures is proposed and applied in deriving a circuital model for the jig. The EM and developed circuital models are validated versus vectorial scattering parameters and VSWR. The estimation of the uncertainty shows small values at the band of measurement. The developed prototype meets DO-160 and MIL-STD-461E requirements and shows an improved high frequency performance when compared with reliable products. An application is presented in measuring the insertion loss of bulk current injection probe and in illustrating the effect of the shield slot distance on the probe High Frequency (HF) performance.

Circuit Model of Vertical Double-Circuit Transmission Tower and Line for Lightning Surge Analysis Considering TEM-mode Formation

The electromagnetic fields, which are produced by lightning currents flowing into a transmission tower and into overhead ground wires, spherically expand with time, and propagate as non-transverse electromagnetic (TEM) waves at least within the round trip time of the traveling wave along the tower. In this paper, a distributed-parameter line model of a vertical double-circuit transmission tower with an overhead line struck by lightning is composed considering the non-TEM characteristics. The surge impedances of the tower, ground wires, and phase conductors increase with time and reach their TEM-mode or steady state values with time constants determined from the configuration. In addition, the significant wave attenuation along the tower is included in the circuit model according to the propagation characteristic determined by the tower configuration. The virtual inductive grounding impedance or damping circuits for approximately representing the wave attenuation is no longer needed. The proposed model is applied to four types of transmission towers. Waveforms of voltages across insulator strings computed by the finite-difference time-domain method, which are regarded as the reference, are well reproduced by the proposed model. Computation efficiency is drastically improved by the proposed model comparing to the numerical electromagnetic field analysis.

Alternative analysis method of lumped‐element circuit model for transmission lines

This Letter presents an alternative analysis method to derive the voltage–current transmission matrix of transmission line sections. By contrast with the approach usually adopted in many microwave engineering textbooks, the proposed method, instead of coping with the telegrapher's equations and their solutions, computes efficiently the relationship between the voltages and currents at the input and output of a circuit modelled through N identical cascaded two-port reciprocal networks. This is implemented through the eigendecomposition of the transmission matrix of the two-port networks which are subsequently synthesised with L-sections. Assuming N as being very large, one obtains the desired transmission matrix, and additionally, it is depicted that the circuit supports forward and backward waves.

Ka-Band Passive Phased-Array Antenna With Substrate Integrated Waveguide Tunable Phase Shifter

A low-cost and low-profile Ka-band passive phased-array antenna (PAA) using continuously tunable substrate-integrated waveguide (SIW) phase shifter is presented in this article. The phase shifting mechanism is based on perturbing the electric field of the slotted SIW (SSIW) line by putting a high dielectric constant slab over the slot of SIW. A systematic approach based on a simple transmission line (TL) circuit model which can support different modes is developed as a fast method for design optimization. It provides insightful physical understanding of the operating mechanism of the proposed phase shifter. In addition, a fully verified TL model of the 1 x 4 SIW PAA is presented and used to predict and optimize the overall reflection coefficients and radiation patterns at different scanning angles. The TL circuit model is verified by full-wave simulations. As a design example, a 1 x 4 SIW-based phased-array is designed, fabricated, and measured to validate phase shifter performance and capabilities. The prototype exhibits a continuous beam scanning range from -20° to +20° covering the whole operating band of 29-31 GHz.

A Broadband, Wide-Angle Scanning, Linear-to-Circular Polarization Converter Based on Standard Jerusalem Cross Frequency Selective Surfaces

A broadband and wide-angle scanning linear polarization (LP)-to-circular polarization (CP) converter based on a dual-layer structure is presented. The elementary cell is composed of conventional Jerusalem crosses (JCs). The design procedure is based on transmission line circuit model and on full-wave simulations. The proposed equivalent circuit has been generalized to include the oblique incidence in the model. Simulated results demonstrate a 24% axial ratio bandwidth for an incidence angle θ = ±50° in both xz and yz planes. The proposed converter provides a unique combination of wide bandwidth, thin profile, and stable response with respect to the angle of incidence. It can be integrated into any LP antenna system to generate CP without significantly affecting the antenna performances.

Regulating the Direction That Power Flows in Microwave Transmission Line Systems With Huygens Sources

An innovative method based on Huygens sources to regulate the direction that power flows in microwave transmission line systems is developed and confirmed with measurements. The phase difference between the electric and magnetic currents in the Huygens source is utilized to finely control the ratio of the wave propagation amplitudes and, hence, power flows along the transmission line in opposite directions. The operating principles are elucidated with both the field distributions in a rectangular waveguide as the transmission line system and the voltages and currents in a transmission line circuit model driven by Huygens sources. The transmission line circuit models excited with electric and magnetic current sources separately and with their balanced combination provide a precise means to quantitatively demonstrate the tunability of the power flow with the Huygens source. A proof-of-concept experiment was implemented in a microwave rectangular waveguide to validate the theoretical analysis. The measured results, in good agreement with their simulated values, demonstrate that the reported approach leads to a wideband operation and large dynamic directional power ratios that are advantageous in the design of multifunctional electromagnetic devices and systems.

Two-Way Tunable Phase Shifter With Arbitrary Phase Shift Ratio at Two Different Frequencies

This article presents a new class of tunable passive two-way phase shifters, which can provide an arbitrary phase shift ratio at two different transmit and receive frequencies ( $f_{T}$ and $f_{R}$ ) simultaneously. The proposed phase shifter uses one control element to control both paths. This architecture consists of two transmit and receive paths and a high dielectric constant slab over the paths. By properly setting the length ratio between transmit and receive lines under the dielectric slab, the proposed phase shifters can realize any arbitrary phase shift ratio. For fast and accurate modeling of the proposed phase shifter, a simple Transmission Line (TL) circuit model is presented in this article and verified by full-wave simulations and measurement. The model can be used for calculating the reflection coefficient and phase shift. In order to prove the concept, two phase shifters, one with equal phase shift ( $\Phi _{T}/\Phi _{R}=1$ ) and the other with the phase shift is equal to the ratio transmit frequency and receive frequency ( $\Phi _{T}/\Phi _{R}=f_{T}/f_{R}$ ), are designed, fabricated, and measured. All results show very good agreement between the proposed TL model, the full-wave solver, and measurement results. This type of phase shifter can be used for many beam-forming antenna systems, such as interleaved arrays, full-duplex arrays, and multiband arrays.

The antireflective properties of DMSO-doped-PEDOT:PSS films at THz frequencies

The antireflective properties of DMSO-doped poly (3,4-ethylenedioxythiophene):poly (4-styrenesulfonate) (PEDOT:PSS) thin films produced by spin coating at THz frequencies is reported. The reflected pulses from the silicon substrate are observed to change with the doping concentrate and the thickness of the DMSO-doped-PEDOT:PSS films. Theoretical analysis based on an equivalent transmission line circuit model has been used to understand the experimental results. Excellent antireflective properties is achieved by 10 vol% DMOS-doped-PEDOT:PSS films. The normalized main pulse transmittance remains as high as 70%, and the minimum reflected pulse transmittance is only 3% at 0.52 THz. This work paves the way for PEDOT:PSS-based THz antireflection coating.

Analysis of wireless power transfer based on metamaterial using equivalent circuit

The metamaterial (MA) has been proved to enhance the efficiency of the wireless power transfer (WPT) system considerably in many studies. This study presents an equivalent circuit model using a qualitative and even quantitative simple explanation for the behaviour of MA in WPT. For this purpose, the electromagnetic field simulation of WPT system with MA is carried out by the high-frequency structure simulation three-dimensional electromagnetic simulator. Also, the authors propose the circuit structure of the WPT system based on MA and explore its characteristics by numerical calculation and advanced design system simulation. The transmission efficiency of the simulator is characterised by reflection coefficient here. Although some methods, such as interference theory, transmission line circuit model, and effective medium theory, have been put forward to explain the physics mechanism of WPT system with MA, some of reactive parameters and the basic physical interpretation have not been expounded clearly so far. Differ from the existing theoretical model, the proposed approach focuses on the effect of the system parameters of MA and transfer coils on the transfer characteristics and is beneficial to the analysis of the complicated system.

Plasma modification of spoof plasmon propagation along metamaterial-air interfaces

We report on measurements of the shift in resonance frequency of “spoof” surface plasmon polariton propagation along a 2-D metamaterial slow-wave structure induced by a gaseous plasma near the metamaterial/air interface. A transmission line circuit model for the metamaterial structure interprets the introduction of a plasma as a decrease in unit cell capacitance, causing a shift in the plasmon dispersion to higher frequency. We show through simulations and experiments that the effects of this shift at the resonance frequency and attenuation below and above resonance depend on the plasma density. The shifts recorded experimentally are small owing to the low plasma densities generated near the structure, ∼1011 cm−3, but simulations show that a shift of ∼3% of the resonance frequency can be generated at plasma densities of ∼1012 cm−3.