Infinite Flange Research Articles

Improved open-ended coaxial probe for temperature-dependent permittivity measurements of foodstuff at radio frequencies

Accurate determination of permittivity is a crucial factor for successfully developing new food processing technologies at radio frequencies. An improved measurement test fixture based on an open-ended coaxial probe was developed to determine the permittivity of lossy food products at radio frequencies as a function of temperature. In order to increase the sensitivity of the permittivity measurements at these frequencies, especially when using a vector network analyzer as a measuring device, the dimensions of the coaxial cell were carefully modeled to consider the range of dielectric losses estimated for food materials. The electromagnetic model was used to retrieve permittivity values from reflection measurements where the entire geometry of the test fixture was considered assuming there was no open radiation or infinite flanges and without the need of reference materials to calibrate the probe. The new cell was validated through permittivity measurements of six saline solutions and then, employed to determine the dielectric properties of cheese sauces and commercial milk samples at 40.68 MHz up to 120 °C. The ionic content and temperature had a limited influence on the dielectric constant but highly determined the loss factor. • A test fixture was developed for improved temperature-dependent permittivity measurements of foodstuffs at radio frequencies. • It used an open-ended coaxial probe achieving more than 6 times the response of previous designs reported in the literature. • Permittivity of milk and cheese food sauces were measured at 40.68 MHz up to 120 °C.

Multimodal radiation impedance of a waveguide with arbitrary cross-sectional shape terminated in an infinite baffle.

Simulations of waveguide acoustics require a description of the boundary condition at the open end. For problems involving higher order transverse modes, it is often described by a multimodal radiation impedance matrix. Expressions for the computation of this matrix for an infinite flange condition are available only for circular and rectangular cross-sectional shapes. Thus, a general expression valid for arbitrary cross-sectional shapes is of interest. Such an expression is proposed, validated against known cases, and applied to an arbitrary cross-section shape. The solution is shown to be computationally efficient.

Re-expansion method for generalized radiation impedance of a circular aperture in an infinite flange.

The paper applies the re-expansion method to analyze the sound radiation from a flanged circular pipe. The axial velocity in the aperture is expressed by means of some orthogonal polynomials combining the properties of Jacobi's polynomials and hypergeometric functions, and also accounting for the velocity singularities at the edge points of the aperture. This makes it possible to reveal the physical parameters of the problem with a very limited number of terms. Besides the classical case when the flange covers the whole plane outside the pipe, the method also permits one to study also the case of the flange extending with zero thickness over a part of the circular pipe. Finally, the paper includes the extension of the results beyond the plane wave region achieving good accuracy and convergence.

Matching of Fundamental Modes at a Junction of a Cylinder and a Truncated Cone; Application to the Calculation of Some Radiation Impedances

The problem of the junction between a cylinder and a truncated cone at frequencies below the first cutoff of the cylinder is investigated, in particular for the case of acute angles. An analytical model of the matching of a cylinder and a truncated cone is derived for the general case of a cone of finite length having a known terminal impedance. When the cone is infinite and the angle is right, the problem is similar to the classical problem of a tube radiating in an infinite baffle. The model is based on a general formulation of the junction of several waveguides at low frequencies (when only the fundamental mode propagates in each guide), and on the assumption that at high frequencies, the radiation impedance of the cylinder is equal to its characteristic impedance. The model has the form of an equivalent circuit, and involves several parameters related to the geometry (the areas of the surfaces defining the matching cavity and the volume of this cavity). In addition, the model requires one supplementary parameter only, i.e., the zero frequency value of the added mass (or length correction), which has to be determined numerically (the Finite Element Method is used). Analytical and numerical results agree very well at low and moderate frequencies, up to the cutoff of the first higher-order mode. For the radiation into an infinite flange, the results improve upon those in a recent publication that were obtained by optimization. The case of obtuse angles is more complicated and is briefly discussed. Finally for the case of infinite cones, the reflection coefficient is compared to that obtained in previous studies.

A New Approach Based on MoM-GEC Method to Mutual Coupling Analysis of Symmetric Twin Waveguides for Antenna Applications

In previous modeling works, the waveguide radiation in the free space is modeled using an infinite flange in aperture plan. In this paper, we propose a new formulation to analyze the radiation of twin rectangular waveguides in free space. Our formulation consists firstly in simulating the free space as rectangular waveguide and seeking the appropriate dimensions that do not affect scattering parameters. In the second step, we use the symmetry principle to reduce the coupling problem to single guide radiating in the free space. Moreover, for more simplification, we consider a concentric discontinuity to solve this latter. This approach is based on moments method combined to the generalized equivalent circuit method (MoM-GEC) in order to reduce the number of unknown problems and alleviate their computation. Obtained numerical results are presented and discussed. A good agreement with literature is shown and the boundary conditions are verified.

Modified Waveguide Flange for Evaluation of Stratified Composites

Nondestructive evaluation of stratified (layered) composite structures at microwave and millimeter-wave frequencies is of great interest in many applications where simultaneous determination of the complex dielectric properties and thicknesses of multiple layers is desired. Open-ended rectangular waveguide probes, radiating into such structures, are effective tools for this purpose. The technique utilizes a full-wave electromagnetic model that accurately models the complex reflection coefficient as a function of frequency and material properties. While the electromagnetic model assumes an infinite waveguide flange (or ground plane), the measurements are conducted using a finite-sized flange. Consequently, the results of the electromagnetic model and those from measurements may not be sufficiently alike for accurate dielectric property and thickness evaluation. This paper investigates the effect of using an open-ended waveguide with a standard finite-sized flange on the error in evaluating the complex dielectric properties of a composite structure. Additionally, we present the design of a novel flange that markedly reduces this undesired effect by producing very similar electric field properties, at the flange aperture, to those created by an infinite flange. Finally, the efficacy of the design for evaluating the dielectric properties of a layered composite structure is demonstrated as well.

Approximate expressions for the reflection coefficient of ducts terminated by circular flanges

Estimating the magnitude of the pressure reflection coefficient |R| and the end correction l at the open end of ducts is a critical procedure when designing or predicting the acoustic behavior of acoustical systems, such as exhausts, tailpipes, mufflers, loudspeaker enclosures and so on. For cylindrical ducts and plane waves, exact intricate solutions exist for two distinct open-end boundary conditions, namely for a thin-walled unflanged pipe and for a pipe terminated by an infinite flange. This work provides simple approximate expressions for |R| and l of cylindrical pipes terminated by circular flanges with finite radii. The expressions are obtained from a polynomial fit performed over the numerical results provided by a Boundary Element model, and is valid for Helmholtz numbers in the range 0 < ka < 3.0, as well as for 0 < a/b < 1, where a and b are the pipe and flange radii, respectively. When compared with the exact solutions for both the unflanged and the infinite-flanged pipe, the approximate formulae provide a maximum error of ~2% at the upper frequency limit (ka →3.0).

Improved precision in acoustic impedance measurements by using calibration loads without resonances

Although the input impedance of a one-dimensional waveguide is simply defined by the ratio of pressure to volume flow measured at its input, the deficiencies of available transducers require a more complicated approach for precise measurements. These can involve multiple transducers at points within an impedance head connected to the measured load. However, resonances and/or singularities during calibration and/or measurement often limit the precision of acoustic impedance spectra. This paper reviews and compares several established techniques, and describes a technique that incorporates three features that can considerably improve precision. The first feature involves minimising the problems due to resonances by calibrating the instrument using up to three different acoustic reference impedances that do not themselves exhibit resonances: an acoustically infinite waveguide, an acoustic open circuit and an acoustically infinite flange. The second feature involves using multiple pressure transducers to reduce the effects of measurement singularities. The third involves iteratively tailoring the spectrum of the stimulus signal to control the distribution of errors across the particular measured impedance spectrum. Examples are given of the performance of the technique on simple cylindrical waveguides and some wind instruments, including the saxophone and clarinet.

An accelerating technique for analyzing open‐ended rectangular waveguides

AbstractAn accelerating technique for calculating the reflection coefficient matrix of an open‐ended rectangular waveguide with infinite flange is proposed in this paper. The matrix equation, which contains double surface integrals, is initially established using the mode‐matching method. To improve the computation efficiency, the double surface integral is converted to one surface integral in the spectral domain using the Sommerfeld identity. Then the matrix pencil method and the Gaussian quadrature are employed to accelerate the computation of the matrix elements, which results in the summation of a short series. An open‐ended WR‐90 waveguide model is analyzed to demonstrate the efficiency of the method in the calculation of the reflection coefficients. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1061–1066, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23283

Efficient Analysis of Open-Ended Coaxial Line Using Sommerfeld Identity and Matrix Pencil Method

An efficient method for calculating the reflection coefficient matrix of open-ended coaxial lines with an infinite flange is proposed in this letter. The matrix equation containing double surface integrals on the aperture can be derived using the mode-matching method. These surface integrals are then converted to line integrals in the spectral domain by the Sommerfeld identity. Then the matrix pencil method is employed to fit the integrands with exponential series so that the integrals can be analytically expressed in closed form. An open-ended coaxial line is considered to verify the validity of the formulation. It is shown that the proposed method is very efficient in calculating the reflection coefficient matrix of open-ended coaxial lines.

A coaxial probe for the control of parameters of a multilayer dielectric: Direct and inverse problems

Diffraction of an electromagnetic wave by an open end of a coaxial line with an infinite flange adjoining a piecewise-uniform plane-layered lossy medium is considered. The direct problem is solved on the basis of admittance and impedance algorithms taking into account losses in the flange and the medium. For an infinite conductivity of the flange, a stationary functional for the input admittance is used to find an explicit solution in the form of an integral; numerical results are obtained. The inverse problem consisting in determination of the layer parameters (thickness, permittivity, and permeability) from known (experimental) values of the magnitude of the reflection coefficient at specified frequencies via minimization of the corresponding residual of the least-squares method is considered. It is proposed to increase the amount of experimental data through performance of measurements for several positions of the sample relative to the flange and for different impedance conditions behind the sample. In order to solve the inverse problem, a perceptron neural network is constructed. This approach reduces the solution time by several orders of magnitude.

Radiation from a flanged rectangular waveguide

The radiation from a rectangular waveguide with a perfectly conducting infinite flange is rigorously studied by using the method of the Kobayashi potential (KP). The fields in the waveguide and half-space are expanded in terms of the waveguide modes and the Weber-Schafheitlin discontinuous integrals, respectively. Continuity of the tangential aperture fields yields matrix equations for the expansion coefficients and the matrix elements consist of double infinite integrals and double infinite series of Bessel functions, which are calculated efficiently by applying the asymptotic approximation of the Bessel function. Numerical results are presented for various physical quantities, such as the aperture admittance, reflection coefficient of the incident wave, and magnitudes of higher-order mode waves, as well as the far-radiation pattern and aperture fields. To verify the validity of our method, the results are compared with other methods and excellent agreement is obtained.

Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance

This paper describes an analytical model of finite cylindrical ducts with infinite flanges. This model is used to investigate the sound radiation characteristics of the gradient coil system of a magnetic resonance imaging (MRI) scanner. The sound field in the duct satisfies both the boundary conditions at the wall and at the open ends. The vibrating cylindrical wall of the duct is assumed to be the only sound source. Different acoustic conditions for the wall (rigid and absorptive) are used in the simulations. The wave reflection phenomenon at the open ends of the finite duct is described by general radiation impedance. The analytical model is validated by the comparison with its counterpart in a commercial code based on the boundary element method (BEM). The analytical model shows significant advantages over the BEM model with better numerical efficiency and a direct relation between the design parameters and the sound field inside the duct.

Analyses of radiation impedances of finite cylindrical ducts

To aid in understanding the characteristics of acoustic radiation from finite cylindrical ducts with infinite flanges, mathematical expressions of generalized radiation impedances at the open ends have been developed. Newton's method is used to find the complex wavenumbers of radial modes for the absorption boundary condition. The self-radiation impedances and mutual impedances for some acoustic modes are calculated for the ducts with rigid and absorption walls. The results show that the acoustical conditions of the duct walls have a significant influence on the radiation impedance. The acoustical interaction between the two open ends of the ducts cannot be neglected, especially for plane waves. To increase the wall admittance will reduce this interference effect. This study creates the possibility for simulating the sound field inside finite ducts in future work.

Acoustic analysis of a gradient coil winding in an MRI scanner

An analytical model for the acoustic radiation from finite cylindrical ducts with infinite flanges is presented in this article. This model will be used for the design of low-noise gradient coils for MRI scanners. The expression of the sound field inside the duct satisfies the boundary conditions at the wall and at the open ends. The wave reflection phenomenon at the open ends of finite ducts is described by the general radiation impedance, which links the model pressure and axial velocity at the interface using an infinite matrix expression. The results obtained from the analytical model are compared with those calculated using the commercial code based on the Boundary Element Method (BEM) and good agreement is achieved. The results reveal that the noise peaks are closely related to the resonant (cut-off) frequencies of the duct. This discovery will be useful for MRI scanner designers to avoid inherently noisy gradient coil designs. The analytical model also displays significant advantages over the BEM model with its much better numerical efficiency and direct relationship between the design parameters and the sound field inside the MRI scanner. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 24B: 15–27, 2005

Improvement of the Permittivity Measurement by a 3d Full-wave Analysis of a Finite Flanged Coaxial Probe

OPen-ended coaxial probes are commonly employed for the dielectric characterization of materials due to several well-known advantages. This measurement technique, consisting in measuring a reflection coefficient, Γ involves an inversion procedure: given the measured Γ the unknown complex permittivity, ε M of the material under test (MUT) is computed by means of an electromagnetic (EM) model of the probe contacting the MUT. For this purpose, a mixed analytical/empirical/full-wave optimization to permittivity measurement is here proposed. The experimental results obtained by a 3D full-wave model of the finite-flanged coaxial probe in the 2-3GHz range, are discussed by comparing with those computed according to an analytical EM model involving an infinite flange \\[1]. The effect of the flange size on the permittivity measurement precision is also analyzed.

Characteristics of spherical shock wave and circular pulse jet generated by discharge of propagating shock wave at open end of tube

When the shock wave propagating in the straight circular tube reaches at the open end, the impulsive wave is generated by the emission of a shock wave from an open end, and unsteady pulse jet is formed near the open end behind the impulsive wave under the specific condition. The pulse jet transits to spherical shock wave with the increase in the strength of shock wave. The strength is dependent on the Mach number of shock wave, which attenuates by propagation distance from the open end. In this study, the mechanism of generating the unsteady pulse jet, the characteristics of the pressure distribution in the flow field and the emission of shock wave from straight circular tube which has the infinite flange at open end are analyzed numerically by the TVD method. Strength of spherical shock wave, relation of shock wave Mach number, distance decay of spherical shock wave and directional characteristics are clarified.

Acoustics of a flanged cylindrical pipe using singular basis functions

The problem of acoustic radiation from a cylindrical pipe with an infinite flange has been discussed in a number of papers. The most common approach is to decompose the field inside the pipe over a basis of Bessel functions. A very large number of basis functions is usually required, with a large degree of ripple appearing as an artifact in the solution. In this paper it is shown that a close analysis of the velocity field near the corner yields a new family of functions, which are called "edge functions." Using this set of functions as test functions and applying the moment method on the boundary between the waveguide and free space, a solution is obtained with greatly improved convergence properties and no ripple.

Moment method calculation of radiation from a cylindrical tube with an infinite flange

This work addresses the calculation of acoustic radiation from a cylindrical tube with an infinite flange, using the moment method. Expressions for the acoustic variables are presented in three separate regions: inside the tube, outside the tube, and on the boundary between them. Examination of the velocity field on this boundary shows that a singularity is present at the corner where the tube and flange meet. A set of basis functions is then developed, which can model this singularity efficiently, resulting in a solution that converges very rapidly. This is demonstrated by a comparison to a solution of the same problem, using the normal modes of the tube as basis functions. The present results are compared with those for the radiation from an unflanged tube, as given in the classic paper by Lewin and Schwinger.

Radiation of Transient Localized Waves from an Open-Ended Coaxial Waveguide with Infinite Flange

Radiation of Transient Localized Waves from an Open-Ended Coaxial Waveguide with Infinite Flange