scholarly journals Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section

2020 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
H. A. Aebischer
Keyword(s):  
Aspect Ratio ◽  
Radio Frequency ◽  
Cross Section ◽  
Radio Frequency Identification ◽  
Maximum Error ◽  
Arithmetic Mean ◽  
Coil Design ◽  
Cross Sectional ◽  
Spiral Coils ◽  
Rfid Antennas

In modern technology, inductors are often shaped in the form of planar spiral coils, as in radio frequency integrated circuits (RFIC’s), 13.56 MHz radio frequency identification (RFID), near field communication (NFC), telemetry, and wireless charging devices, where the coils must be designed to a specified inductance. In many cases, the direct current (DC) inductance is a good approximation. Some approximate formulae for the DC inductance of planar spiral coils with rectangular conductor cross section are known from the literature. They can simplify coil design considerably. But they are almost exclusively limited to square coils. This paper derives a formula for rectangular planar spiral coils with an aspect ratio not exceeding a value between 2.5 and 4.0, depending on the number of turns, and having a cross-sectional aspect ratio of height to width not exceeding unity. It is valid for any dimension and inductance range. The formula lowers the overall maximum error from hitherto 28 % down to 5.6 %. For specific application areas like RFIC’s and RFID antennas, it is possible to reduce the domain of definition, with the result that the formula lowers the maximum error from so far 18 % down to 2.6 %. This was tested systematically on close to 140000 coil designs of exactly known inductance. To reduce the number of dimensions of the parameter space, dimensionless parameters are introduced. The formula was also tested against measurements taken on 16 RFID antennas manufactured as PCB’s. The derivation is based on the idea of treating the conductor segments of all turns as if they were parallel conductors of a single-turn coil. It allows the inductance to be calculated with the help of mean distances between two arbitrary points anywhere within the total cross section of the coil. This leads to compound mean distances that are composed of two types of elementary ones, firstly, between a single rectangle and itself, and secondly, between two displaced congruent rectangles. For these elementary mean distances, exact expressions are derived. Those for the arithmetic mean distance (AMD) and one for the arithmetic mean square distance (AMSD) seem to be new. The paper lists the source code of a MATLAB® function to implement the formula on a computer, together with numerical examples. Further, the code for solving a coil design problem with constraints as it arises in practical engineering is presented, and an example problem is solved.

scholarly journals Inductance Formula for Square Spiral Inductors with Rectangular Conductor Cross Section

2019 ◽  
Vol 8 (4) ◽  
pp. 80-88
Author(s):  
H. A. Aebischer
Keyword(s):  
Integrated Circuits ◽  
Comparative Study ◽  
Radio Frequency ◽  
Cross Section ◽  
Radio Frequency Identification ◽  
Maximum Error ◽  
Maximum Relative Error ◽  
Spiral Inductors ◽  
Spiral Coils ◽  
The Comparative Study

Planar spiral coils are used as inductors in radio frequency (RF) microelectronic integrated circuits (IC’s) and as antennas in both  radio frequency identification (RFID) and telemetry systems. They must be designed to a specified inductance. From the literature, approximate analytical formulae for the inductance of such coils with rectangular conductor cross section are known. They yield the direct current (DC) inductance, which is considered as a good approximation for inductors in RF IC’s up to the GHz range. In principle, these formulae can simplify coil design considerably. But a recent comparative study of the most cited formulae revealed that their maximum relative error is often much larger than claimed by the author, and too large to be useful in circuit design. This paper presents a more accurate formula for the DC inductance of square planar spiral coils than was known so far. It is applicable to any design of such coils with up to  windings. Owing to its scalability, this holds irrespectively of the coil size and the inductance range. It lowers the maximum error over the whole domain of definition from so far  down to . This has been tested by the same method used in the comparative study mentioned above, where the precise reference inductances were computed with the help of the free standard software FastHenry2. A comparison to measurements is included. Moreover, the source code of a MATLAB® function to implement the formula is given in the appendix.

Design and characterization of novel fabric-based multi-resonators for wearable chipless RFID applications

2021 ◽  
pp. 004051752198978
Author(s):  
Huating Tu ◽  
Yaya Zhang ◽  
Hong Hong ◽  
Jiyong Hu ◽  
Xin Ding
Keyword(s):  
Radio Frequency ◽  
Radio Frequency Identification ◽  
Printed Circuit Boards ◽  
Signal Transmission ◽  
Circuit Boards ◽  
Cross Sectional ◽  
Rfid Tag ◽  
Response Characteristics ◽  
Chipless Rfid ◽  
Screen Printed

Nowadays, the chipless radio frequency identification (RFID) tag is attracting significant attention owing to its immense potential in tracking. However, most of the chipless tags are fabricated on hard printed circuit boards, and the wearable fabric-based chipless tag is still in the research stage. In this paper, a symmetrical 3rd L-shaped multi-resonator wearable chipless RFID tag is designed and screen-printed onto fabric. In order to investigate the influence of the non-uniform conductive layer on the signal transmission at high frequency, the surface and cross-sectional topographies of the printed conductive film are analyzed and the frequency response characteristics are simulated and measured. The obtained results show that the common fabric can be used as the substrate to screen print the L-shaped multi-resonators of the chipless RFID tag, and the quality of the screen printed line, especially a narrow line, significantly affects the radio frequency performance. For the screen-printed 3rd L-shaped stub resonators, the relative frequency shift compared with the simulation results are 0.99%, 0.88% and 2.26%, respectively. Generally, the surface morphology of fabric and screen-printed precision are critical in improving the performance of L-shaped multi-resonators.

Modelling the Acoustical and Airflow Performance of Simple Lined Ventilation Apertures

2005 ◽  
Vol 12 (4) ◽  
pp. 277-292 ◽  
Author(s):  
D J Oldham ◽  
Jian Kang ◽  
M W Brocklesby
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
High Aspect Ratio ◽  
Natural Ventilation ◽  
Ventilation System ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Ventilation Performance ◽  
Acoustic Treatment

The pressure differences that can be used to drive a natural ventilation system are very small and thus large apertures are required to allow sufficient air to enter and leave a building to ensure good air quality or thermal comfort. Large apertures are potential acoustic weak points on a façade and may require some form of acoustic treatment such as absorbent linings, in which case the ventilator is similar to a short section of lined duct. In ducts, the performance of absorbent linings increases with the length of lining and the ratio of the length of lined perimeter to the cross sectional area of the duct. Thus, for a duct of a given cross sectional area, a lining is more effective for a duct with a high aspect ratio than for a duct with a square cross section. However, the high aspect ratio cross section will result in greater flow resistance and impede the airflow performance. In this paper numerical methods are employed to investigate the effect of different configurations of a lined aperture on the acoustical and ventilation performance of the aperture in order to establish the optimum configurations.

scholarly journals The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section

2002 ◽  
Vol 470 ◽  
pp. 91-114 ◽  
Author(s):  
ANDREW L. HAZEL ◽  
MATTHIAS HEIL
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Capillary Number ◽  
Stokes Equations ◽  
Rectangular Cross Section ◽  
Scaling Law ◽  
Propagation Speed ◽  
Cross Sectional ◽  
Steady Propagation ◽  
Rectangular Tubes

This paper investigates the propagation of an air finger into a fluid-filled, axially uniform tube of elliptical or rectangular cross-section with transverse length scale a and aspect ratio α. Gravity is assumed to act parallel to the tube's axis. The problem is studied numerically by a finite-element-based direct solution of the free-surface Stokes equations.In rectangular tubes, our results for the pressure drop across the bubble tip, Δp, are in good agreement with the asymptotic predictions of Wong et al. (1995b) at low values of the capillary number, Ca (ratio of viscous to surface-tension forces). At larger Ca, Wong et al.'s (1995b) predictions are found to underestimate Δp. In both elliptical and rectangular tubes, the ratio Δp(α)/Δp(α = 1) is approximately independent of Ca and thus equal to the ratio of the static meniscus curvatures.In non-axisymmetric tubes, the air-liquid interface develops a noticeable asymmetry near the bubble tip at all values of the capillary number. The tip asymmetry decays with increasing distance from the bubble tip, but the decay rate becomes very small as Ca increases. For example, in a rectangular tube with α = 1.5, when Ca = 10, the maximum and minimum finger radii still differ by more than 10% at a distance 100a behind the finger tip. At large Ca the air finger ultimately becomes axisymmetric with radius r∞. In this regime, we find that r∞ in elliptical and rectangular tubes is related to r∞ in circular and square tubes, respectively, by a simple, empirical scaling law. The scaling has the physical interpretation that for rectangular and elliptical tubes of a given cross-sectional area, the propagation speed of an air finger, which is driven by the injection of air at a constant volumetric rate, is independent of the tube's aspect ratio.For smaller Ca (Ca < Ca), the air finger is always non-axisymmetric and the persisting draining flows in the thin film regions far behind the bubble tip ultimately lead to dry regions on the tube wall. Ca increases with increasing α and for α > αˆ dry spots will develop on the tube walls at all values of Ca.

scholarly journals Comparative Study of the Accuracy of Analytical Inductance Formulae for Square Planar Spiral Inductors

2018 ◽  
Vol 7 (5) ◽  
pp. 37-48 ◽  
Author(s):  
H. A. Aebischer
Keyword(s):  
Integrated Circuits ◽  
Radio Frequency ◽  
Radio Frequency Identification ◽  
Short Wave ◽  
Error Statistics ◽  
Four Dimensions ◽  
Spiral Inductors ◽  
Frequency Identification ◽  
Spiral Coils ◽  
Relative Errors

In the design of radio frequency (RF) microelectronic integrated circuits (IC’s) and of antennas for short-wave radio frequency identification (RFID) and telemetry systems, planar spiral coils are important components. Many approximate analytical formulae for calculating the inductance of such coils can be found in the literature. They can simplify the problem of designing inductors to a predefined inductance considerably. But the error statistics given by different authors cannot be compared because they are based on different or unknown domains of definition. Hence, it is not possible to decide which formula is best in a given case by merely studying the literature. This paper compares the maximum relative errors of six of some of the most cited formulae in the literature. To all formulae, the same domains of definition are applied. Each of them spans all four dimensions of the parameter space. Precise inductances are obtained numerically with the help of the free scientific and industrial standard software FastHenry2 and used as reference values to calculate the errors of the formulae. It has been found that the alleged maximum errors reported by some authors are far too optimistic. Only two formulae feature small enough errors to be useful in circuit design. The method and the domains of definition applied in the present study may also prove useful for the assessment of future formulae.

Saint-Venant Decay Rates for the Rectangular Cross Section Rod

2004 ◽  
Vol 71 (3) ◽  
pp. 429-433 ◽  
Author(s):  
N. G. Stephen ◽  
P. J. Wang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Decay Rates ◽  
Elastic Rod ◽  
Cross Sectional ◽  
Element Transfer

A finite element-transfer matrix procedure developed for determination of Saint-Venant decay rates of self-equilibrated loading at one end of a semi-infinite prismatic elastic rod of general cross section, which are the eigenvalues of a single repeating cell transfer matrix, is applied to the case of a rectangular cross section. First, a characteristic length of the rod is modelled within a finite element code; a superelement stiffness matrix relating force and displacement components at the master nodes at the ends of the length is then constructed, and its manipulation provides the transfer matrix, from which the eigenvalues and eigenvectors are determined. Over the range from plane stress to plane strain, which are the extremes of aspect ratio, there are always eigenmodes which decay slower than the generalized Papkovitch-Fadle modes, the latter being largely insensitive to aspect ratio. For compact cross sections, close to square, the slowest decay is for a mode having a distribution of axial displacement reminiscent of that associated with warping during torsion; for less compact cross sections, slowest decay is for a mode characterized by cross-sectional bending, caused by self-equilibrated twisting moment.

scholarly journals Effect of Cross-Sectional Aspect Ratio on Rectangular FRP-Concrete-Steel Double-Skin Tubular Columns under Axial Compression

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Bing Zhang ◽  
Xia-Min Hu ◽  
Wei Wei ◽  
Qian-Biao Zhang ◽  
Ning-Yuan Zhang ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Axial Stress ◽  
Axial Strain ◽  
Steel Tube ◽  
Confined Concrete ◽  
Cross Sectional ◽  
Tubular Columns ◽  
Double Skin ◽  
Frp Tube

Hybrid FRP-concrete-steel double-skin tubular columns (hybrid DSTCs) are novel hollow columns consisting of an outer FRP tube, an inner steel tube, and the concrete between the two tubes. Hybrid DSTCs possess important advantages, such as excellent corrosion resistance as well as remarkable seismic resistance. However, existing studies are mainly focused on hybrid DSTCs with a circular cross section or a square cross section. When a column is subjected to different load levels in the two horizontal directions, a rectangular column is preferred as it can provide different bending stiffness and moment capacity around its two axes of symmetry. This paper presents an experimental study on rectangular DSTCs with a particular focus on the effect of the cross-sectional aspect ratio (i.e., the ratio of the breadth to the width of the rectangular cross section). The effect of the cross-sectional shape of the inner steel tube (i.e., both elliptical and rectangular inner steel tubes were used) and the effect of FRP tube thickness were also investigated experimentally. Experimental results show that a larger aspect ratio will have no negative effect on the confinement effect in rectangular DSTCs; a rectangular DSTC with a larger aspect ratio generally has a larger ultimate axial strain and a higher axial stress at the ultimate axial strain; rectangular DSTCs with an elliptical steel tube generally have better performance than corresponding specimens with a rectangular steel tube. An existing model, which was developed based on a model for rectangular FRP-confined concrete columns and a model for circular DSTCs, is verified using the test results of the present study. The model generally provides close predictions for the peak axial stress of the confined concrete but yields conservative predictions for the ultimate axial strain for rectangular DSTCs.

Heat Transfer and Pressure Loss in a Two-Pass, Rectangular Channel Featuring a Reduced Cross-Sectional Area After the 180- Degree Tip Turn with Different Turning Vane Configurations

2021 ◽  
pp. 1-44
Author(s):  
Sulaiman Alsaleem ◽  
Lesley Wright ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Cross Section ◽  
Pressure Loss ◽  
Guide Vane ◽  
Circular Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Number Range

Abstract Serpentine, multi-pass cooling passages, are used in cooling advanced gas turbine blades. In open literature, most internal cooling studies use a fixed cross-sectional area for multi-pass channels. Studies that use varying aspect ratio channels, along with a guide vane to direct the flow with turning, are scarce. Therefore, this study investigates the effect of using different guide vane designs on both detailed heat transfer distribution and pressure loss in a multi-pass channel with an aspect ratio of (4:1) in the entry passage and (2:1) in the second passage downstream of the vane (s). The first vane configuration is one solid-vane with a semi-circular cross-section connecting the two flow passages. The second configuration has three broken-vanes with a quarter-circular cross-section; two broken vanes are located downstream in the first passage, and one broken vane is upstream in the second passage. Detailed heat transfer distributions were obtained on all surfaces within the flow passages by using a transient liquid crystal method. Results show that including the semi-circular vane in the turning region enhanced the overall heat transfer by around 29% with a reduction in pressure loss by around 20%. Moreover, results show the quarter-circular vane design provides higher overall averaged heat transfer enhancement than the semi-circular vane design by around 9% with penalty of higher pressure drop by 6%, which yields higher thermal performance by 7%, over a Reynolds number range from 15,000 to 45,000.

EFFECT OF RADIO FREQUENCY IDENTIFICATION ON RECORDING HEAD IN WRITING PROCESS AT 125 KHZ LOW FREQUENCY

2009 ◽  
Vol 23 (17) ◽  
pp. 3619-3624
Author(s):  
APHAIPHAK PRATOOMTHIP ◽  
ANAN KRUESUBTHAWORN ◽  
CHIRANUT SA-NGIAMSAK ◽  
APIRAT SIRITARATIWAT ◽  
PONCHAI PAKPONGSIRI
Keyword(s):  
Radio Frequency ◽  
Radio Frequency Identification ◽  
Writing Process ◽  
Low Frequency ◽  
Maximum Error ◽  
Recording Head ◽  
Recording Heads ◽  
Frequency Identification ◽  
Current Error

This article presents the effect of Radio Frequency Identification (RFID) at 125 kHz on GMR recording heads. The study is mainly concerned with the RFID effect on recording heads in terms of the distance (r) between the antenna reader of the RFID and the recording head, the coil radius (a) of the antenna reader, and the angle (θ) between antenna reader and recording head. The maximum error of the writing current is found in this experiment of about 2.5% (where r < a). An increase of angle affects the writing current error when the radius increases. It is found that the writing current error decreases when r > a. SEM result shows that radiated fields of RFID do not visibly degrade the writer part but only disturbance to recording heads in testing is found.

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