Equivalent Rectangular Waveguide Research Articles

A new formula for the optimum width of Substrate Integrated Waveguide

A new formula for calculating the optimum width of a Substrate Integrated Waveguide (SIW) corresponding to the first mode is presented in this paper. Finite Difference Frequency Domain (FDFD) method is applied to analyze the waveguide structure where geometrical parameters of the SIW are iteratively varied in order to minimize the gap between cutoff frequencies of SIW structure and that of an equivalent conventional rectangular waveguide. Adequate parameters are used to derive the new formula. To verify the accuracy of the new formula, several waveguides are designed and analyzed using the commercial software HFSS. The calculated propagation constants are compared with experimental measurements from literature, a very good conformity is obtained.

A Formula for Radiation Loss in Substrate Integrated Waveguide

Substrate integrated waveguide, an emerging technology for microwave and millimeter-wave circuits, is affected by three loss mechanisms: ohmic and dielectric losses, standard waveguides, and radiation leakage. While ohmic and dielectric losses can be accurately determined by the analytical formulas of the equivalent rectangular waveguide, no equations are available for radiation leakage. This paper presents the derivation of a formula to calculate the attenuation constant due to radiation leakage in substrate integrated waveguide interconnects.

Scattering loss in optical waveguide with trapezoidal cross section

To get the scattering loss of the trapezoidal core waveguide, a new analysis model is presented based on the perturbation equivalent method and modified effective-index method. Firstly, the trapezoidal core waveguide is successfully equivalent to the rectangular one with both restricting the same optical field energy by adopting the perturbation method. Then, the equivalent rectangular core waveguide is decomposed into two slab waveguides by employing the modified effective-index method. The trapezoidal core waveguide scattering theory model is established based on the slab waveguide scattering theory. With the sidewalls surface roughness in the range from 0 to 100 nm in the single model trapezodial core waveguide, optical simulation shows excellent agreement with the results from the scattering loss model presented. The relationship between the dimension and side-wall roughness with the scattering loss can be determined in the trapezoidal core waveguide by the scattering loss model.

Study on photonic crystal grating slow-wave circuits for millimeter-wave ribbon-beam traveling wave tubes

A kind of photonic crystal grating slow-wave circuit, namely the cross-section distributing two-dimensional photonic crystal slow-wave circuit (CD2DPhSWC), was proposed. And the way of designing CD2DPhSWC was put forward. To simply the design, the process was realized in two steps, firstly the calculation of the photonic band gap (PBG) for the TE polarization, and then the dispersion of the equivalent rectangular waveguide grating. The numerical results show that the bandwidth of the traveling wave tubes (TWTs) based on CS2DPhSWC is wider, and the operating voltage is lower, than that of the rectangular waveguide grating. Correspondingly, the cost of the TWTs is reduced.

Refractive index sensing characteristics of dual resonance long period gratings in bare and metal-coated D-shaped fibers

We present a theoretical study of the ambient refractive index sensing characteristics of long period gratings in bare and metal-coated D-shaped fibers. An equivalent rectangular core waveguide method based on the first-order perturbation theory has been used to study the modal behavior of the waveguide. Power coupling corresponding to dual resonance in both cases has been investigated, and an optimum metal thickness giving maximum sensitivity has been found to exist. The study shows that the dual resonances can be shifted to lower wavelengths by increasing (decreasing) the metal thickness (core to flat surface separation). Further, an optimum combination of metal thickness and core to flat surface separation, corresponding to maximum sensitivity, has been presented for different cladding modes and their relative performance has been discussed. It has been shown theoretically that detection of refractive index changes as small as 1.67x10(-7) RIU in the ambient region is possible using the optimized parameters. The study should find application in realizing highly sensitive biochemical sensors.

Efficient and accurate design of substrate-integrated waveguide circuits synthesised with metallic via-slot arrays

A new class of substrate-integrated waveguides (SIWs) is proposed, which highlights a novel synthesis of waveguide circuits using metallic via-slot arrays instead of via-hole arrays. When the gaps between the slots are small enough, the broadside dimension of equivalent rectangular waveguide is approximately equal to the spacing between the inner walls of slots. Therefore the size of the SIW can directly be used to calculate propagation constants almost without phase bias. This new design is of critical importance in the design of substrate-integrated circuits (SICs) with fine and sensitive geometrical details with respect to circuit response such as filters and resonators. In this way, the design of SICs based on the new SIW structures can greatly be simplified. A finite difference frequency-domain method accelerated by an implicitly restarted Arnoldi method is developed to model the substrate-integrated resonant cavities with leakage. Simulated and measured results have confirmed the fact that conventional waveguide components are very similar to the SIW counterparts of the same structure.

Analysis of polymeric arrayed waveguide grating multiplexers with non-ideal core cross sections modeled by ‘tanh’ function

By employing perturbation theory, a technique called the 'equivalent rectangular waveguide method' is proposed for analyzing the transmission characteristics of polymeric arrayed waveguide grating (AWG) multiplexers with non-ideal core cross sections, which are modeled by the 'tanh' function. Simulation results show that the non-ideal core cross sections cause the shift of the transmission spectrum, and result in the increase of crosstalk compared with the device originally designed with exact rectangular core cross sections. In order to eliminate the shift of the transmission spectrum, reduce the crosstalk and further realize accurate demultiplexing, the redesign of the AWG device is carried out.

A band‐pass filter consisting of two substrate integrated waveguide cavities coupled by an aperture on their common side wall

AbstractIn this article, we present a substrate‐integrated waveguide‐based band‐pass filter with wide stop‐band rejection property. This band‐pass filter is made up of two substrate‐integrated waveguide cavities, which couple to each other by an aperture on their common waveguide side wall. By using the empirical formula [19] for obtaining the equivalent rectangular waveguide dimensions, the substrate integrated waveguide structure could then be properly approximated by a closed rectangular waveguide. We employed the rigorous mode‐matching method to analyze the electromagnetic boundary‐value problem of the structure containing multiple discontinuities. In comparison with the conventional end‐to‐end coupled cavity filters, we found that our new side‐wall‐coupled cavity filter can suppress the second resonance frequency and therefore, provide a considerably wide rejection band. It is interesting to note that the suppression of the second resonance frequency can be achieved by properly shifting the second cavity in lateral direction. To explore its physical insight, the resonant modes in the substrate integrated waveguide cavities are carefully inspected for realizing the physical picture of wave process taking place in the two cavities system. In addition to the theoretical analysis, we have fabricated the filters and measured their scattering parameters. The good agreement between the theoretical and measured results validates the accuracy of numerical computation, and also shows the promising performance of the proposed filters. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1884–1887, 2007; Published online in Wiley Inter‐Science (www.interscience.wiley.com). DOI 10.1002/mop.22570

Investigation on the Ohmic Conductor Losses in Substrate-integrated Waveguide and Equivalent Rectangular Waveguide

The substrate-integrated waveguide (SIW) is an artificial waveguide structure that is fabricated in planar dielectric substrate with periodic metallic cylinders, and can be analyzed as an equivalent rectangular waveguide (RW). In this letter, the formula of the conductor loss in SIW has been derived from the conductor loss formula of conventional RW. In addition, the equality condition at which the conductor losses in SIW and RW are exactly equal has been found. The conductor losses in SIW and RW have been investigated and compared, good agreement has been observed between the theoretical calculations and HFSS numerical simulations.

Equivalence between substrate‐integrated (SIRW) rectangular waveguide short‐circuit load and its equivalent rectangular waveguide short‐circuit load

AbstractSubstrate integrated rectangular waveguide (SIRW) is an artificial rectangular waveguide (RW) constructed in planar substrate with two rows of periodic metallized posts or slots. In this letter, the equivalence formula between the locations of the corresponding short circuits by cylinder walls and by the solid wall was derived, based on the former width equivalence formula of the SIRW and its equivalent RW [(11)]]. The theoretical and simulation results are given for the SIRW short load and RW short load, good agreements have been observed. Such equivalences are convenient for the design of small waveguides, of millimeter wave, in a multilayer circuit structure, such as the LTCC etc. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1694–1698, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21805

Equivalence between substrate-integrated rectangular waveguide (SIRW) bend and rectangular waveguide (RW) bend

The equivalence between substrate-integrated waveguide (SIRW) bend and rectangular waveguide bend is investigated in several bands. The width of the equivalent rectangular waveguide of SIRW can be found from a developed formula. The simulation and experimental results all indicate that good agreement of the propagation characteristics of SIRW and RW bends can be observed. However, some insertion loss discrepancies between these two kinds of bends are observed. In addition, the insertion loss of the SIWR bend exhibits some fluctuation within the frequency band of interest, while the insertion loss of the RW bend remains relatively smooth. Furthermore, an SIRW bend and one straight SIRW section with same length are also investigated; the results indicate that the SIRW bend preserves well the propagation characteristic of the straight SIRW. In addition, the analysis also indicates that the first higher mode appears earlier in the SIRW bend than in the RW bend. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1487–1491, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21739

A new six-port junction based on substrate integrated waveguide technology

A six-port junction based on the substrate integrated waveguide (SIW) technology is proposed and presented. In this design of such a junction, the SIW is first converted to an equivalent rectangular waveguide, then regular rectangular waveguide design techniques are used. In this structure, an SIW power divider and SIW hybrid 3-dB coupler are designed as fundamental building blocks. A six-port junction circuit operating at 24 GHz is fabricated and measured. Good agreement between simulated and measured results is found for the proposed six-port junction.

Characteristics comparison of substrate-integrated rectangular waveguide (SIRW) and its equivalent rectangular waveguide

The propagation and loss characteristics of the substrate-integrated rectangular waveguide (SIRW) at microwave and millimeter-wave bands are investigated. The results further verify that the substrate-integrated rectangular waveguide has nearly the same waveguide characteristics as conventional rectangular waveguides, and it can be analyzed as a rectangular waveguide with effective width of the SIRW. The insertion loss of SIRW and its equivalent rectangular waveguide agree well with each other. However, it is observed that the derivation of the propagation characteristics of the SIRW and its equivalent rectangular waveguide indicates the frequency dependency. At the X-, K-, and Ka-bands, the effective width of the equivalent rectangular waveguide given by the empirical formula [7] should be slightly increased in order to obtain the propagation characteristic that agrees better with that of the SIRW, about 2%. In addition, at the U-band, when the effective width of the equivalent rectangular waveguide is increased 5% or so, the propagation constant of the rectangular waveguide in the whole band agrees well with that of the rectangular waveguide. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 588–592, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21059

Effects of trapezoid core cross-sections on transmission characteristics of polymer arrayed waveguide grating multiplexers

Based on the perturbation theory, a technique named “equivalent rectangular waveguide method” is presented for analyzing the transmission characteristics of arrayed waveguide grating (AWG) multiplexers with trapezoid core cross-sections. As an example, by using this technique, effects of the trapezoid core cross-section on transmission characteristics are performed for a 33×33 polymer AWG multiplexer around the central wavelength of 1.550918 μm with the wavelength spacing of 0.8 nm. Computed results show that the trapezoid core cross-sections result in the shift of the transmission spectrum, and lead to the increase of the crosstalk compared with the device originally designed with exact rectangular core cross-sections. In order to eliminate the shift of the transmission spectrum, decrease the crosstalk, and further realize the accurate demultiplexing, the redesign of the AWG device is carried out.

Resonant frequencies of post–wall waveguide cavities

A new method is presented for predicting the resonant frequencies of post–wall rectangular waveguide cavities, in which the narrow walls of the guide are composed of rows of vias. By interpreting the fields inside the guide as a superposition of plane waves, the surface impedance of a row of wires, when illuminated by a plane wave, is used to model the narrow walls of the waveguide. The derivation leads to equivalent rectangular waveguide dimensions that are then used to calculate the resonant frequencies of the cavity. Theoretical results are compared with the observed TE10m resonant frequencies of several post–wall waveguide cavities fabricated in low temperature cofired ceramic (LTCC). The results confirm that the method improves the resonant frequency prediction when the pitch of the vias is at least ten times greater than their radius.

An analysis of the folded waveguide: a compact waveguide launcher for ICRF heating

Theoretical and experimental investigations of the folded waveguide launcher as proposed for use in the ion-cyclotron range of frequencies (ICRF) heating of tokamak plasmas are presented. Theoretical results include an analysis of the folded waveguide using Ritz's method to obtain various field quantities. The cutoff wavenumbers from this analysis are within 10% of those calculated using an unfolded equivalent rectangular waveguide model. Measurements of cavity resonances for a scale-model ICRF-folded waveguide with a cutoff frequency of 2.4 GHz also agree closely with those calculated using an unfolded equivalent model. An unfolded equivalent waveguide model is used to evaluate the properties of an inductive strip placed in the folded waveguide. Applying variational analyses provides upper and lower bounds to the reflection magnitude mod S/sub 11/ mod that are in good agreement with measured values. Polarizing plates (which have been proposed to increase the on-axis directivity of the radiated power) are modeled using an unfolded equivalent waveguide. A variational analysis is used to determine an upper-bound value of mod S/sub 11/ mod in air due to a polarizing plate inside a matched folded waveguide. Measured values are found to be within 3% of the calculated values, with mod S/sub 11/ mod >0.95 for frequencies between 2.5 and 4.5 GHz. >

Simple method for analyzing the birefringence of an elliptical-core fiber by an equivalent rectangular waveguide

We present details of a simple method, incorporating first-order perturbation theory, to analyze the birefringence exhibited by elliptical-core fibers by using an equivalent rectangular-core waveguide. The results from this method are compared with those obtained from the finite-element and another approximate technique to demonstrate the accuracy of this simple method. The method may be extended to analyze waveguides of arbitrary geometry.

Method for analysing trapezoidal optical waveguides by an equivalent rectangular rib waveguide

We present a simple analysis, using first-order perturbation theory, to determine an equivalent rectangular rib optical waveguide that will model the propagation characteristics of a trapezoidal rib optical waveguide. The results obtained from our method show excellent agreement with the results from the more accurate finite element method.

Analysis of finite parallel-plate waveguide arrays

The radiation and phase scanning properties of a planar array are investigated using wedge diffraction theory. The TEM and TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> radiation patterns are determined assuming that each guide is excited with equal amplitude but variable phase which is specified by the desired scan angle. Since the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> pattern can be used directly as the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -plane radiation pattern of an equivalent rectangular waveguide array, the analysis for this instance is extended to consideration of aperture reflection coefficients