Cutoff Frequencies Of Higher Order Modes Research Articles

Impact of Field Polarization on Radiated Emission Characterization in an Open TEM Cell

This article presents a comprehensive study of the influence of electromagnetic (EM) field polarization on radiated emission characterization in an open transverse EM (TEM) cell, which is usually neither considered in the measurement process nor clearly identified. It also takes into account the influence of the operating frequency with respect to the higher order mode cutoff frequency of the cell, the latter being generally unknown to the experimenter. Commonly used 433-MHz (LoRa) and 2.4-GHz (Wi-Fi) antennas were placed inside an open TEM cell in different orientations in order to investigate the impact of the antenna polarization. For antennas parallel to the septum, a 1.6–8.6-dB difference in power levels collected by the cell (corresponding to a 31%–86% underestimation), for different polarizations, depending on the operating frequency being below or above the higher order mode cutoff frequency, was obtained between orthogonal orientations due to reduction in $E$ - and (mainly) $H$ -field levels, leading to significant uncertainty on power levels. For the 2.4-GHz antenna perpendicular to the septum, the power level was highly dependent on both the antenna orientation and location along the cell’s axes, being more dependent along the main axis. This clearly demonstrates that the physical phenomena due to the polarization of the radiating element and the cell’s dominant mode frequency must be characterized and estimated, in addition to the generally known tangential $H$ -field coupling to integrated circuit pins or printed circuit board (PCB) traces. This leads to an update of best practices of IEC 61000-4-20 or IEC 61967-2 emission testing.

1.1 THz tenth harmonic mixer based on planar GaAs Schottky diode

Here, the tenth harmonic mixing technology based on planar GaAs Schottky diode is first proposed for the 1.1 terahertz (THz) frequency conversion module. The first higher order mode cut-off frequency of the suspended microstrip line has been investigated to determine the appropriate cross-sectional dimension of transmission line shield cavity in the radio frequency (RF) circuit portion. The height of shield cavity of transmission line is designed to be discontinuous in order to facilitate the assembly of the diode. A modelling approach combining field and circuit is used to achieve joint simulation of linear passive structure and diode non-linear characteristics. The simulation results show that the frequency conversion loss of this mixer is <55 dB in the RF frequency range of 1.03–1.154 THz, and the best frequency conversion loss is 50 dB at RF of 1.098 THz.

Simple but accurate method to compute LP11mode cutoff frequency of nonlinear optical fibers by Chebyshev technique

We propose a simple method to compute the first higher order mode cutoff frequency of a single-mode fiber in the presence of optical nonlinearity. We consider optical Kerr-type nonlinearity for these fibers having dispersion-shifted and dispersion-flattened profiles. Our analysis involves the Chebyshev method but introduces a linearization of cubic terms of fields due to Kerr-type nonlinearity. Our results are shown to match excellently with the available exact numerical values. Thus, this formulation and stepwise algorithm should be considered as a simple but accurate alternative to deeply involved numerical technique and used as a guideline in calculating and minimizing the modal noise in single-mode nonlinear fibers.

Bend-insensitive single-mode photonic crystal fiber with ultralarge effective area for dual applications

A novel photonic crystal fiber (PCF) having circular arrangement of cladding air holes has been designed and numerically optimized to obtain a bend insensitive single mode fiber with large mode area for both wavelength division multiplexing (WDM) communication and fiber-to-the-home (FTTH) application. The bending loss of the proposed bent PCF lies in the range of 10 −3 to 10 −4 dB / turn or lower over 1300 to 1700 nm, and 2 × 10 −4 dB/turn at the wavelength of 1550 nm for a 30-mm bend radius with a higher order mode (HOM) cut-off frequency below 1200 nm for WDM application. When the whole structure of the PCF is scaled down, a bending loss of 6.78 × 10 −4 dB / turn at 1550 nm for a 4-mm bend radius is obtained, and the loss remains in the order of 10 −4 dB / turn over the same range of wavelength with an HOM cut-off frequency below 700 nm, and makes the fiber useful for FTTH applications. Furthermore, this structure is also optimized to show a splice loss near zero for fusion-splicing to a conventional single-mode fiber (SMF).

Dispersion relations and modes of wave propagation in inclusion-reinforced composite plates

This paper is intended to examine the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness on the dispersion relations and modes of wave propagation in inclusion-reinforced composite plates. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Mori–Tanaka mean-field theory is used to predict the effective elastic moduli of the composite plate explicitly. The effective elastic moduli are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior. The resulting moduli are then used to determine the dispersion relations and the modal patterns of Lamb waves using the dynamic stiffness matrix method. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions are symmetrical or antisymmetric about the midplane of the plate. Classifying the wave type in an anisotropic plate is not as simple as that in an isotropic plate, and has not received proper attention in the literature. The wave types and orders are identified by analyzing the dispersion curves and inspecting the calculated modal patterns, and the results indicate that the Lamb waves in an orthotropic composite plate can also be classified as either symmetric or antisymmetric waves. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns. Propagation speed is generally increased with the aspect ratio, e.g., using longer fibers generally results in a higher propagation speed.

A variational calculation for higher order mode cutoff frequencies of a symmetrical strip line by conformal mapping

AbstractThe cutoff frequencies of higher order modes in a symmetrical strip line are calculated using the variational finite‐element method combined with conformal mapping. Conformal mapping is used to improve the modeling of the infinite transverse extents of a strip line. Then the finite‐element method is employed to solve the variational equation in the transformed finite region. Comparisons with numerical results found in the literature validate the presented method. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 32: 449–452, 2002.

Numerical solution of higher order mode cutoff frequencies in asymmetric TEM cells by Galerkin method

The authors describe a Galerkin method (GM), which determines efficiently the basis functions satisfying the edge conditions and the size of the elements on the Neumann boundaries in this paper. The calculated higher order mode cutoff frequencies in both symmetric and asymmetric TEM cells by the GM are presented. The authors could then solve the technical debate for TE/sub 12/-, TE/sub 03/-, TM/sub 11/-, and TM/sub 12/-mode cutoff frequencies in the symmetric TEM cell. It is also shown that the measured resonant frequencies of a designed asymmetric TEM cell agree well with the predicted data by the GM.

Interesting effect of optical Kerr nonlinearity in expanding single-mode regime of optical fibers using dispersion-flattened profiles

An interesting effect of optical Kerr nonlinearity is reported from theoretical investigation on the fundamental and first higher mode cutoff frequencies in single-mode fibers doped with highly nonlinear materials like CdS x Se 1− x with W-type dispersion-flattened profiles. It is observed that whereas the single-mode regime decreases absolutely for dispersion-shifted profiles due to reduction of the first higher order mode cutoff frequency as is evident from earlier studies, it increases for W-type profiles for such nonlinearity taking its effect on the nonzero fundamental mode cutoff frequency into consideration. Thus, one can go further down below the fundamental mode cutoff frequency while using W-fibers in single mode nonlinear fiber devices involving evanescent field coupling in the low V region.

Effect of optical Kerr effect nonlinearity on LP 11 mode cutoff frequency of single-mode dispersion-shifted and dispersion-flattened fibers

A theoretical investigation of the effect of the optical Kerr effect in the refractive index distribution on the first higher-order mode cutoff frequency is carried out for single-mode fibers having dispersion-shifted and dispersion-flattened profiles. It is observed that the effect is the least in the case of step and W-profiles and pronounced for fibers having imperfections like a dip in the profiles. Although the nonlinearity-induced cutoff frequency change is negligible in a practical nonlinear optical fiber which operates at levels of several watts, our analysis includes a single-mode fiber with weakly nonlinear materials like silica under high optical fields or highly nonlinear materials under weak fields. These results should be useful as guidelines in minimising the modal noise in single-mode nonlinear fibers of wide interest.

Cutoff frequencies of transmission lines consisting of pair of cylinders

The paper presents a method of evaluation of cutoff frequencies of higher-order modes of transmission line of parallel cylinders by transforming them into a parallel plate configuration using cotangent hyperbolic transformation. Application of the method of finite difference to the weighted Helmholtz equation leads to a set of simultaneous equations. The eigenvalues related to cutoff frequencies are determined from the characteristic equation expressed in terms of matrices obtained from the simultaneous equations. Numerical data are presented.

Rigorous analysis of the higher order modes, impedance and attenuation factor of coupled striplines

The paper presents a rigorous and computationally efficient analysis of coupled striplines of arbitrary dimensions based on the transverse resonance diffraction (TRD) technique. The calculated higher order mode cutoff frequencies, impedance, coupling factors and attenuation factor are shown to give improved accuracy over a wide range of dimensions when compared with purely analytical and numerical approaches. The TRD results are also in excellent agreement with measured values for the higher order mode cutoff frequencies. The design parameters can be computed in a fraction of the time required for numerical based techniques such as finite elements.

Numerical solution of higher order mode cut-off frequencies in symmetric TEM cells using finite element method (EMI measurement applications)

The higher-order-mode cut-off frequencies in symmetric transverse electromagnetic cells are computed with the finite-element method. Transverse electric and transverse magnetic modes are considered. For symmetry, only one-quarter of the cross section is analyzed. Electric and magnetic walls are introduced in the cross section, which includes the effect of the gap between the center conductor and the sidewalls. This arrangement enhances the accuracy of the solution. The results obtained by this method are compared with those of other methods. Discrepancies observed in the results of other methods are explained. The present method is the more powerful one; with this method, mode identification can easily be made using an eigenvector solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On higher order mode cutoff frequencies in elliptical step index fibers

Cutoff frequencies of the first 12 odd and even higher-order modes in a two-layer elliptical fiber are computed from a rigorous analysis of the boundary value problem. Cutoff characteristics of modes in rectangular and elliptical fibers in the literature are reviewed. Mode correspondence, field symmetries, and physical considerations are invoked to establish confidence in previously published results on the first higher-order mode cut off in elliptical fibers. Very large birefringence fibers are shown to have low values for the first higher-order mode cut off; hence, their usefulness in single-mode applications is limited. >

The propagation constant in lossy circular tubes near the cutoff frequencies of higher-order modes

The propagation constants of higher-order modes in lossy circular ducts are investigated with particular interest to the frequency range around the corresponding cutoff frequencies. The analytic expressions for the propagation constants published up to now contain poles at each cutoff frequency. In this article, it is shown that no poles exist. The transition between the frequency range of evanescent and propagating modes is rapid but continuous. An explicit formula for the propagation constant is derived. The theory is experimentally checked with an indirect measuring method that is able to give results in close vicinity to the cutoff frequencies. The measured attenuation due to the transmission line losses is partially somewhat higher than theoretically expected. The deviations are less than about 30%.

Higher order mode cutoff frequencies in TEM cells calculated with TLM method

The higher order mode cutoff frequencies in various symmetric TEM cells are calculated with the TLM method and some comments are made on comparisons between these results obtained by this method and other methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Accurate analysis of latching phase s.hifters

Ferrite-latching phase shifters in a generalised waveguide geometry (grooved rectangular guide with lateral ridges) are analysed using a combination of mode-matching and perturbation techniques. By this method, the double transverse inhomogeneities of the waveguide configuration and of the toroid corner magnetisation are both considered exactly, leading to accurate predictions of differential phase shift and of cutoff frequencies of higher-order modes.

The proximity of coincidence and acoustic cut-off frequencies in relation to acoustic radiation from pipes with disturbed internal turbulent flow

Spectral measurements showing the effects of various pipe fittings (radiused bends, mitred bends, and gate and butterfly valves) on wall pressure fluctuations, wall acceleration, and acoustic radiation due to turbulent air flow in a pipe are presented. In general the fitting is responsible for the creation of a flow disturbance and sound generation. At some distance downstream undisturbed flow conditions are re-established; the internal wall pressure field then consists of the turbulent pressure field due to undisturbed, fully developed, turbulent pipe flow with a superimposed acoustic field. The latter gives rise to enhanced vibrational response and external radiation compared with that for undisturbed flow in a straight pipe. The effects, which are quite dramatic in the case of the stronger disturbances, for which the acoustic field dominates the internal wall pressure field, result primarily from coincidence of higher order acoustic modes and resonant vibrational modes of the pipe wall. The proximity of coincidence frequencies and higher order mode cut-off frequencies is demonstrated; because of it, the effects are in general greatest at and essentially confined to frequencies close to the cut-off frequencies of the higher order modes.