Transmission Line Approximation Research Articles

Lock-in thermographic study of spin-wave propagation in magnonic crystals

We have investigated the spin-wave dynamics in a one-dimensional magnonic crystal (MC) with respect to the heat radiation due to the damping of the spin waves. The spin waves were excited by applying microwaves via a wire antenna. The heat induced by the excitation and propagation of spin waves was measured using the lock-in thermography (LIT) technique by periodically modulating the microwave power. The LIT measurements resolved the heat source distributions inside the MC, which is made of an yttrium iron garnet film and periodic grooves with a sub-mm interval, in the backward volume wave geometry. The temperature distribution induced by the spin-wave excitation notably depends on the frequency or wave number of the spin waves, as a result of the formation of rejection bands in the MC. The observed temperature modulation profiles are complicated, but their behavior is consistent with a calculation based on the microwave transmission line approximation of the MCs, demonstrating the applicability of the LIT measurements to the investigation of the spin-wave dynamics in sub-mm scale MCs.

An Efficient Model of High-Frequency Electromagnetic Field Coupling to Multiconductor Transmission Lines With the Presence of the Lossy Ground

The modeling of the high-frequency electromagnetic field coupling to multiconductor transmission lines (MTLs) is the essential subject for the protection of power lines. When the wavelength of the electromagnetic wave is smaller than the cross sections between MTLs, the response of MTLs cannot be evaluated by the classical transmission line approximation. Even though the full-wave method can deal with this problem, it is time consuming to evaluate the response of long MTLs. This article presents a theory and an efficient method to solve the problem of the high-frequency electromagnetic field coupling to MTLs with the presence of the lossy ground. The asymptotic method, adopted for its high computational efficiency, is extended to obtain the solutions of MTLs above the lossy ground. The problem is solved semianalytically using the proposed method, which is much more computationally efficient in dealing with long MTLs. Several numerical examples are presented to validate the accuracy and efficiency of the proposed method.

A reconfigurable frequency selective structure using plasma arrays

In this paper, a novel structure composed of frequency selective surface and plasma arrays is proposed to control the propagation of the free space electromagnetic wave in the X band of the microwave spectrum. Plasma is hard to be used for controlling the propagation of microwave due to its electron density, electron temperature, spatial volume, and distribution continuity, which are too rigorous to be satisfied for most plasma generation methodologies. The idea of this paper lies in that the impedance characteristics of the plasmas could be effectively tuned by periodic structures so that the wave propagation tuning effects of plasmas could be activated under conditions of restricted dimensions of (0.27–0.41)λ0, where the plasma arrays are shown not to be effective alone. The system is described based on transmission line approximation, and the characteristic lumped units have been analyzed using experimental data fitting. It is argued that the properties and the methodology discussed in this paper could be applied in the design of artificial microwave media, especially in the field of active absorbing frequency selective surfaces.

Calculation of High-Frequency Electromagnetic Field Coupling to Overhead Transmission Line Above a Lossy Ground and Terminated With a Nonlinear Load

High-frequency electromagnetic fields such as those associated with electromagnetic pulse (EMP) and intentional electromagnetic interference (IEMI) can couple to overhead power lines. Since the height of the overhead power lines can be comparable or even larger than the smallest wavelength of typical EMP and IEMI pulses, the classical transmission line approximation might not be suitable for evaluating the line response. On the other hand, a traditional full-wave solver (e.g., method of moments) is computationally inefficient, especially when dealing with long lines. To address these problems, we propose an efficient method to handle the high-frequency electromagnetic field coupling to overhead lines with nonlinear loads above a lossy ground. In the proposed method, the asymptotic approach is adopted and extended to the case of a lossy ground, which handles the problem in a semianalytical way and has a much higher computational efficiency in the case of long lines. Although the proposed method applies to the frequency domain, the case of nonlinear loads can be considered through a combination with the time-marching method. The proposed method is validated with several numerical examples.

Time domain generalized telegrapher’s equations for the electromagnetic field coupling to finite-length wires buried in a lossy half-space

The paper deals with a derivation of a time domain variant of the generalized telegrapher’s equations for transient electromagnetic field coupling to buried wires. The formulation is based on the thin wire antenna theory in the time domain. The influence of a lossy half-space is taken into account by means of the time dependent reflection coefficient approximation arising from the modified image theory (MIT), while the per-unit-length surface impedance accounts for the conductor losses. The obtained space-time integral expressions are handled analytically. The concept of the scattered voltage is naturally included in the full model formulation. Computational examples are given for the induced currents along the buried wire and compared to the results obtained by using the transmission line (TL) approximation.

Design of wide bandwidth pyramidal microwave absorbers using ferrite composites with broad magnetic loss spectra

Wide bandwidth microwave absorbers with a pyramidal shape and a significantly reduced thickness can be designed using high lossy ferrite materials with broad magnetic loss spectra. The microwave absorbing properties of pyramidal cone absorbers are analyzed using the transmission line approximation, which provides the reflection loss as a function of the material parameters and absorber geometry. Three types of ferrite materials (NiZn spinel ferrite, Co2Z hexaferrite, and RuCoM hexaferrite) are used as the absorbent fillers in a rubber matrix. Among these, Co2Z ferrite is the most suitable material for wide bandwidth pyramidal absorbers, due to its broad magnetic loss spectrum in the GHz frequency range. The optimal geometry of the pyramidal absorber is also determined using the transmission line theory. With the reduced total height of the pyramidal absorber (approximately 60 mm), a wide bandwidth (1.5-18 GHz with respect to the −20 dB reflection loss) can be realized. The proposed absorbers have a thickness advantage over the classical pyramidal ohmic absorbers; thus, they are suitable for small and semi-anechoic chambers.

Wide Bandwidth Microwave Absorbers of Ferrite-Rubber Composites with Square-Rod Structure

As one way of shape control for the wide bandwidth in microwave absorbers, a square-rod structure of ferrite composite is proposed. Microwave absorbance of the square-rod absorber is analyzed by the transmission line approximation which provides the reflection loss as a function of material parameters and dimension of the structure. In particular, the absorption bandwidth is greatly dependent upon the size of the square rod, which has been identified in both composites of Ni-Zn ferrite and Co 2 Z hexagonal ferrites. With a controlled geometry of square rod in those composites, a wide bandwidth (about 6 GHz with respect to – 20 dB reflection loss) has been predicted.

Fractal Model of a Compact Intracloud Discharge. I. Features of the Structure and Evolution

We propose a new model of a compact intracloud discharge considered as the result of interaction between two (or more) bipolar streamer structures formed in a strong large-scale electric field of a thundercloud. The model assumes two stages of the compact discharge development. At the preliminary stage, two or more bipolar streamer structures appear successively in the thundercloud in the region of a strong electric field (at the boundaries between the regions of the main positive and the main negative electric charges or between the main positive charge region and the top negative screening layer). The time of development of such structures is determined by the characteristics of the conducting channels that form them and can reach tens of milliseconds. Spatiotemporal synchronization of the bipolar streamer structures is provided by the altitude modulation of the electric field, which, in particular, can originate from a large-scale turbulence of the cloud medium or the stream instability. It is shown that a single bipolar streamer structure accumulates significant electric charges of different signs at its ends as it develops. The start of the main stage of a compact intracloud discharge corresponds to the occurrence of the conducting channel (breakdown of the gap) between the mature streamer structures. The electric charge accumulated at the adjacent ends of the structures at this stage is neutralized over a time much shorter than the duration of the preliminary stage. The parameters of the current pulse are in good agreement with the estimates of the current of a compact intracloud discharge which were obtained in the transmission-line approximation.

High-Frequency Electromagnetic Coupling to Multiconductor Transmission Lines of Finite Length

This paper presents a theory and an efficient solution approach for the problem of electromagnetic field coupling to a long multiconductor line with arbitrary terminations. The theory is applicable for a high-frequency plane wave electromagnetic field excitation, when the transmission line approximation conditions are no longer satisfied.

Physical mechanism of initial breakdown pulses and narrow bipolar events in lightning discharges

AbstractTo date the true nature of initial breakdown pulses (IBPs) and narrow bipolar events (NBEs) in lightning discharges remains a mystery. Recent experimental evidence has correlated IBPs to the initial development of lightning leaders inside the thundercloud. NBE wideband waveforms resemble classic IBPs in both amplitude and duration. Most NBEs are quite peculiar in the sense that very frequently they occur in isolation from other lightning processes. The remaining fraction, 16% of positive polarity NBEs, according to Wu et al. (2014), happens as the first event in an otherwise regular intracloud lightning discharge. These authors point out that the initiator type of NBEs has no difference with other NBEs that did not start lightning, except for the fact that they occur deeper inside the thunderstorm (i.e., at lower altitudes). In this paper, we propose a new physical mechanism to explain the source of both IBPs and NBEs. We propose that IBPs and NBEs are the electromagnetic transients associated with the sudden (i.e., stepwise) elongation of the initial negative leader extremity in the thunderstorm electric field. To demonstrate our hypothesis a novel computational/numerical model of the bidirectional lightning leader tree is developed, consisting of a generalization of electrostatic and transmission line approximations found in the literature. Finally, we show how the IBP and NBE waveform characteristics directly reflect the properties of the bidirectional lightning leader (such as step length, for example) and amplitude of the thunderstorm electric field.

Shielding Effectiveness of Periodic Screens Against Finite High-Impedance Near-Field Sources

The shielding effectiveness of artificial periodic screens is investigated with reference to high-frequency high-impedance near fields produced by arbitrarily oriented electric dipoles. The screens are formed by metallic objects of arbitrary shape displaced in a 2-D lattice. The problem is first studied through a full-wave approach, using the array scanning method in conjunction with a periodic method of moments in the spatial domain. Next, the shielding problem is solved analytically in some characteristic electromagnetic compatibility configurations through the use of approximate low-frequency homogeneous models together with a classical analysis in the spectral domain. Finally, the solutions are compared with those deriving from the use of the so-called transmission-line approximation. The provided results show the suitability of the analytical approaches in dealing with finite sources different from standard plane-wave excitations and give a useful tool for the design of periodic shields.

Electromagnetic Coupling of Lightning to Power Lines: Transmission-Line Approximation versus Full-Wave Solution

The problem of accurate prediction of lightning-induced overvoltages on power lines still attracts considerable attention. A variety of approaches of different levels of sophistication have been proposed. In particular, transmission-line (TL) approximation is widely used for describing electromagnetic coupling of lightning with power lines. In this paper, validity of this approach for lossless lines is demonstrated by analytically demonstrating that, under the assumptions that are typically justified for practical power distribution lines, the TL approximation and the more rigorous full-wave analysis lead to identical results.

An Efficient SPICE-Compatible Cavity Resonant Model for Microstrip Lines

A SPICE-compatible cavity resonant transmission line (CTL) model for a single-ended microstrip line is first presented by reducing 2-D cavity resonator to 1-D cavity resonator. This model has low efficiency since it consists of infinite higher-order components included inductors, capacitors, resistors, and ideal transformers. A modified CTL model is developed by using a fast algorithm to improve the simulation efficiency, which results in an accurate SPICE model in finite elements. Because the improved cavity resonant model uses higher-order (a little more complicated) elements in finite components, it has high efficiency in the time and frequency domain simulation. The model accuracy and simulation efficiency are validated by comparison with multiconductor transmission line and matrix rational approximation modeled methods.

The Charge Transport in Organic Field-Effect Transistor as an Interface Charge Propagation: The Maxwell–Wagner Effect Model and Transmission Line Approximation

By analyzing electric field migration in the pentacene organic field-effect transistor channel (OFET), visualized using the time-resolved microscopic optical second harmonic generation (TRM-SHG) is analyzed the propagation of injected carriers. We find that the accumulated charge propagation on the pentacene–gate insulator interface of the three-electrode system is clearly different from the drift in electric field of the two-electrode system. The propagation of injected carriers is evaluated on the basis of the Maxwell–Wagner effect model and the transmission line approximation. We show that the interface charge accumulation has a significant contribution to the charge transport in OFET. Proposed model for the transient state is beyond the limits of common used impedance spectroscopy models and represents extension of the small-signal analysis. Found relation between mobility and transit time helps in analysis of OFET transit time sensitive experiments such as the time-of-flight technique (TOF) or TRM-SHG.

Transient Response of Straight Thin Wires Located at Different Heights Above a Ground Plane Using Antenna Theory and Transmission Line Approach

Transient electromagnetic field coupling to straight thin wires parallel to each other and located at different heights above a perfectly conducting or dielectric ground plane is analyzed using wire antenna theory and a transmission line method. The time-domain antenna theory formulation is based on a set of the space-time Hallen integral equations. The transmission line approximation is based on the corresponding time-domain Telegrapher's equations. The space-time integral equations arising from the wire antenna theory are handled by the time-domain Galerkin-Bubnov scheme of the indirect boundary element method. The time-domain Telegrapher's equations are solved using the finite-difference time-domain method. Time-domain numerical results obtained with both approaches are compared to the results computed via NEC 2 code combined with an inverse Fourier transform procedure. Some illustrative comparisons of results obtained by means of antenna theory and transmission line approach are presented throughout the paper.

Analysis and design of an efficient, fully integrated 1–8 GHz traveling wave power amplifier in 180 nm CMOS

Traveling wave amplifiers (TWAs) offer the advantage of broadband amplification and a closed set of equations that allow deriving the RF gain by means of treating TWAs as discrete transmission line approximations. Up to now, however, the significant losses associated with CMOS integrated inductors have been neglected. This work presents a new approach for determining the transmission line losses and phase constants that will bring about an enhanced gain prediction accuracy. The theory is verified by means of a realized design example. The working principle of the integrated DC supply inductor is discussed, whose performance is based on the inductors self-resonance effect. When applying a supply voltage Vdd of 2.4 V, the measured compression point P1 dB and the power added efficiency PAE at 2.4 GHz amount to 16.9 dBm and 19.6%, respectively. At 5.5 GHz, a value of 16.6 dBm for P1 dB and an associated PAE of 13.9% are achieved. The peak RF gain for these output power values reaches 11 dB, and values greater than 8 dB are obtained up to 7 GHz.

Analytical Formulas for Induced Surges on a Long Overhead Line Caused by Lightning With an Arbitrary Channel Inclination

This paper presents analytical formulas for lightning-induced surges (voltage and current) on an infinite length of overhead line, which are generated by a nearby lightning stroke with arbitrary striking angle. The formulas are derived using the Rusck model, which is one of the electromagnetic coupling models based on a transmission-line approximation of a return stroke. The return-stroke current is approximated by piecewise linearly varying characteristics. The formulas are simple and convenient for lightning-induced effect analysis. The analytical formulas are validated by the comparison with a finite-difference method. The paper proposes approximate formulas of peak value and time to peak value of the lightning-induced voltages for a vertical lightning channel.

Eigenmode analysis of the ITER ICRF antenna plug and electrical solution to the grounding of the antenna

The excitation of non-TEM modes around the ITER ICRF (ion cyclotron range of frequency) antenna plug can considerably increase the level of RF currents and voltages on the ITER plug. We report on a study of these modes and a solution to avoid them in the ITER ion cyclotron range of frequencies. From a transmission line approach we show that resonances can be avoided if the distance between the mouth of the line and an added short-circuit is sufficiently small. We therefore propose to position short-circuits at about 1 m from the antenna mouth, constituted by rows of closely spaced non-capacitive contacts all around the plug. These conclusions are further validated with Microwave Studio® simulations. A simplified model of the ITER ICRF array is used for comparing various grounding solutions and it is proved that the solution already inferred from transmission line approximation suppresses the resonances from the frequency domain relevant for ICRH in ITER. The MWS calculations predict that the proposed solution also avoids large RF currents in the blanket modules and in their connectors. Their amplitude barely exceeds 5% of the strap RF currents. This solution avoids perturbation of the antenna array impedance matrix by the coaxial gap. We also discuss resonances appearing at harmonic frequencies which could be excited by various non-linear effects due to the plasma or the generator. This kind of excitation should not lead to large voltage build-up.

Design of high power radio frequency radial combiner for proton accelerator

A simplified design method has been proposed for systematic design of novel radio frequency (rf) power combiner and divider, incorporating radial slab-line structure, without using isolation resistor and external tuning mechanism. Due to low insertion loss, high power capability, and rigid mechanical configuration, this structure is advantageous for modern solid state rf power source used for feeding rf energy to superconducting accelerating structures. Analysis, based on equivalent circuit and radial transmission line approximation, provides simple design formula for calculating combiner parameters. Based on this method, novel 8-way and 16-way power combiners, with power handling capability of 4 kW, have been designed, as part of high power solid state rf amplifier development. Detailed experiments showed good performance in accordance with theory.

High-Efficiency Class-FE Tuned Power Amplifiers

The results of exact time domain analysis of the novel switched-mode tuned Class-FE power amplifiers with a parallel quarterwave transmission line are presented with analytical derivation of the optimum load network parameters. Effects of the quarterwave transmission line and collector capacitance on the current and voltage waveforms are discussed. A Class-FE power amplifier is based on the combination of a class-F operating mode with Class-E switching conditions, thus extending the Class-F operation to higher frequencies for driving signals with duty cycles D < 0.5. The ideal collector voltage and current waveforms demonstrate a possibility of 100% efficiency without overlapping between each other. A possibility of alternative load network implementation including a series quarterwave transmission line or lumped-element approximation is also considered. The switched-mode Class-FE power amplifiers with a quarterwave transmission line offer a new challenge for RF and microwave power amplification providing high-efficiency operation conditions.