Determination of Far Fields of Wire Antennas on a PEC Sphere Using Spherical Harmonic Expansion
TL;DR: In this paper, the far field patterns of wire antennas on a PEC sphere are calculated from quasi-static near fields using spherical harmonic expansion. But the results of the analysis were not considered in this paper.
Abstract: Far-field patterns of wire antennas on a PEC sphere are calculated from quasi-static near fields using spherical harmonic expansion. Three cases of the wire antennas—F-antenna, dipole, and resonant loop on the PEC sphere—are considered. With the assumed sinusoidal current distribution on the antenna, the method of images is employed to obtain currents and charges on the antenna's image against the sphere. Only from the charge density and current distributions of the wire antenna and its image, ignoring the sphere, the quasi-static near fields are calculated using Coulomb's and Biot–Savart's laws. The fields in a source-free region are expressed in spherical harmonic expansion with the coefficients obtained from the radial components of the calculated quasi-static electric and magnetic near fields. The far fields thus obtained from the expansion match well with that of the simulated patterns. Deviations between simulation and theory are discussed and explained.
Citations
More filters
TL;DR: It is illustrated, through a toy example, that spatial-Slepian transform yields a much better estimate of the underlying region of hidden localized variations than scale-discretized wavelet transform.
Abstract: We present spatial-Slepian transform (SST) for the joint spatial-Slepian domain representation of signals on the sphere to support localized signal analysis. We employ well-optimally concentrated Slepian functions, which are obtained as a solution of the Slepian spatial-spectral concentration problem of finding bandlimited and spatially optimally concentrated functions on the sphere, to formulate the proposed transform. Due to optimal energy concentration of Slepian functions in the spatial domain, the proposed spatial-Slepian transform allows us to probe spatially localized content of the signal. Furthermore, we present an inverse transform to recover the signal from its spatial-Slepian coefficients, formulate an algorithm for fast computation of SST, and carry out computational complexity analysis. We compute the spatial variance of spatial-Slepian coefficients and conduct experiments to show that spatial-Slepian coefficients have better spatial localization than scale-discretized wavelet coefficients. We present the formulation of SST for zonal Slepian functions, which are spatially optimally concentrated in the axisymmetric polar cap region, and provide an illustration using a bandlimited Earth topography map. To demonstrate the utility of the proposed transform, we carry out localized variation analysis, in which we employ SST to detect hidden localized variations in the signal. We illustrate, through a toy example, that spatial-Slepian transform yields a much better estimate of the underlying region of hidden localized variations than scale-discretized wavelet transform.
4 citations
Cites background from "Determination of Far Fields of Wire..."
..., signals defined on the sphere, which are naturally encountered in many areas of science and engineering such as computer graphics [1], medical imaging [2]–[4], acoustics [5], [6], planetary sciences [7]–[11], geophysics [12], [13], cosmology [14]–[16], quantum mechanics [17], wireless communications [18]–[20] and antenna design [21], to name a few....
[...]
TL;DR: In this paper, a framework for generalized linear transformations of the joint spatial-Slepian domain representation of signals on the sphere is developed, which is enabled by the spatial-slepians transform on the spheres.
Abstract: We develop a framework for generalized linear transformations of the joint spatial-Slepian domain representation of signals on the sphere. Such a representation is enabled by the spatial-Slepian transform on the sphere. We formulate a least-square signal estimation framework for reconstruction of the spherical signal from the modified (transformed) spatial-Slepian representation specified by the spatial-Slepian transformation kernel. We specialize the form of the kernel to present analytical expressions for the multiplicative and convolutive transformations, and use the latter to present illustrations on a Mars topography map.
4 citations
TL;DR: In this paper, the authors proposed a multipole expansion of the fields radiated from a rectangular microstrip patch antenna on an infinite ground plane to calculate the fields at any distance (near and far fields) from the antenna.
Abstract: In this letter, the multipole expansion of the fields radiated from a rectangular microstrip patch antenna on an infinite ground plane is presented. Such multipole expansion allows calculating the fields at any distance (near and far fields) from the antenna. It is shown that the coefficients of the expansion can be obtained from the quasi-static fields due to the quasi-static currents on the edges of the patch. The static fields are calculated on a spherical surface enclosing the patch and its image in the infinite perfect electric conductor (PEC) ground plane by applying the duals of Coulomb's and Biot–Savart's laws. Using only the radial components of the fields on the enclosing sphere, the multipole coefficients and, hence, the fields outside the sphere are calculated. The field distributions obtained using such multipole expansion match well with the corresponding analytical approximations in the far-field and HFSS simulation results. The spatial evolution of the field components with distance from near field to far field for the patch is presented. The minor deviations of the obtained results from that of simulations and the limitations of the proposed method are discussed.
1 citations
Cites methods from "Determination of Far Fields of Wire..."
...A Similar method of calculating the multipole coefficients for wire antennas on a PEC sphere has been validated by Talashila and Ramachandran [9]....
[...]
...[9] R. Talashila and H. Ramachandran, “Determination of far fields of wire antennas on a PEC sphere using spherical harmonic expansion,” IEEE Antennas Wireless Propag....
[...]
24 Jan 2021
TL;DR: In this article, the authors proposed a framework that takes the optimal number of noisy measurements and employs autoencoder (deep learning architecture) to enhance the signal consisting of a finite number of Diracs before estimating the parameters using the annihilating filter method.
Abstract: We propose a method for the accurate reconstruction (recovery of parameters) of non-bandlimited finite rate of innovation (FRI) signals on the sphere from its measurements contaminated by additive isotropic noise. We propose a framework that takes the optimal number of noisy measurements and employs autoencoder (deep learning architecture) to enhance the signal consisting of a finite number of Diracs before estimating the parameters using the annihilating filter method. We use convolutional and fully connected autoencoders for signal enhancement in the spatial and spectral domains respectively. We analyse the denoising performance of both the overcomplete and undercomplete autoencoders and demonstrate the superior performance, measured as a gain in the signal to noise ratio (SNR) of the output signal, of the fully connected overcomplete autoencoder that filters the signal in the spectral domain. Through numerical experiments, we demonstrate the improvement enabled by the proposed framework in the accuracy of recovery of the parameters of the FRI signal.
1 citations
TL;DR: In this paper, a method was derived to obtain an expansion formula for the magnetic field generated by a closed planar wire carrying a steady electric current using Gegenbauer polynomials.
Abstract: A method is derived to obtain an expansion formula for the magnetic field $\boldsymbol{B}(\boldsymbol{r})$ generated by a closed planar wire carrying a steady electric current. The parametric equation of the loop is $\mathcal{R}(\phi)=R+Hf(\phi)$, with $R$ the radius of the circle, $H \in [0,R)$ the radial deformation amplitude, and $f(\phi)\in[-1,1]$ a periodic function. The method is based on the replacement of the $1/|\boldsymbol{r} - \boldsymbol{r}'|^3$ factor by an infinite series in terms of Gegenbauer polynomials, as well as the use of the Taylor series. This approach makes it feasible to write $\boldsymbol{B}(\boldsymbol{r})$ as the circular loop magnetic field contribution plus a sum of powers of $H/R$. Analytic formulas for the magnetic field are obtained from truncated finite expansions outside the neighborhood of the wire. These showed to be computationally less expensive than numerical integration in regions where the dipole approximation is not enough to describe the field properly. Illustrative examples of the magnetic field due to circular wires deformed harmonically are developed in the article, obtaining exact expansion coefficients and accurate descriptions. Error estimates are calculated to identify the regions in $\mathbb{R}^3$ where the analytical expansions perform well. Finally, first-order deformation formulas for the magnetic field are studied for generic even deformation functions $f(\phi)$.
Keywords: Magnetic Field, Gegenbauer Polynomials, Arbitrary current loop, Biot-Savart law.
References
More filters
Book•
13 Oct 2008
TL;DR: In this article, the authors present a short history of antennas and their applications in wireless networks. But they do not discuss their application in the context of wireless communication networks, except for the following:
Abstract: Preface. List of Symbols. 1. Introduction. 1.1 A Short History of Antennas. 1.2 Radio Systems and Antennas. 1.3 Necessary Mathematics. 1.3.1 Complex Numbers. 1.3.2 Vectors and Vector Operation. 1.3.3 Coordinates. 1.4 Basics of Electromagnetics. 1.4.1 Electric Field. 1.4.2 Magnetic Field. 1.4.3 Maxwell's Equations. 1.4.4 Boundary Conditions. Summary. References. Problems. 2. Circuit Concepts and Transmission Lines. 2.1 Circuit Concepts. 2.1.1 Lumped and Distributed Element Systems. 2.2 Transmission Line Theory. 2.2.1 Transmission Line Model. 2.2.2 Solutions and Analysis. 2.2.3 Terminated Transmission Line. 2.3 The Smith Chart and Impedance Matching. 2.3.1 The Smith Chart. 2.3.2 Impedance Matching. 2.3.3 Quality Factor and Bandwidth. 2.4 Various Transmission Lines. 2.4.1 Two-wire Transmission Line. 2.4.2 Coaxial Cable. 2.4.3 Microstrip Line. 2.4.4 Stripline. 2.4.5 Co-planar Waveguide (CPW). 2.4.6 Waveguide. 2.5 Connectors. Summary. References. Problems. 3. Field Concepts and Radiowaves. 3.1 Wave Equation and Solutions. 3.1.1 Discussion on Wave Solutions. 3.2 Plane Wave, Intrinsic Impedance and Polarisation. 3.2.1 Plane Wave and Intrinsic Impedance. 3.2.2 Polarisation. 3.3 Radiowave Propagation Mechanisms. 3.3.1 Reflection and Transmission. 3.3.2 Diffraction and Huygens' Principle. 3.3.3 Scattering . 3.4 Radiowave Propagation Characteristics in Media. 3.4.1 Media Classification and Attenuation. 3.5 Radiowave Propagation Models. 3.5.1 Free Space Model. 3.5.2 Two-ray Model/Plane Earth Model. 3.5.3 Multipath Models. 3.6 Comparison of Circuit Concepts and Field Concepts. 3.6.1 Skin Depth. Summary. References. Problems. 4. Antenna Basics 125. 4.1 Antennas to Radiowaves. 4.1.1 Near Field and Far Field. 4.1.2 Antenna Parameters from the Field Point of View. 4.2 Antennas to Transmission Lines. 4.2.1 Antenna Parameters from the Circuit Point of View. Summary. References. Problems. 5. Popular Antennas. 5.1 Wire-Type Antennas. 5.1.1 Dipoles. 5.1.2 Monopoles and Image Theory. 5.1.3 Loops and Duality Principle. 5.1.4 Helical Antennas. 5.1.5 Yagi-Uda Antennas. 5.1.6 Log-periodic Antennas and Frequency Independent Antennas. 5.2 Aperture-Type Antennas. 5.2.1 Fourier Transform and Radiated Field. 5.2.2 Horn Antennas. 5.2.3 Reflector and Lens Antennas. 5.2.4 Slot Antennas and Babinet's Principle. 5.2.5 Microstrip Antennas. 5.3 Antenna arrays. 5.3.1 Basic Concept. 5.3.2 Isotropic Linear Arrays. 5.3.3 Pattern Multiplication Principle. 5.3.4 Element Mutual Coupling. 5.4 Some Practical Considerations. 5.4.1 Transmitting and Receiving Antennas: Reciprocity. 5.4.2 Balun and Impedance Matching. 5.4.3 Antenna Polarisation. 5.4.4 Radomes, Housings and Supporting Structures. Summary. References. Problems. 6. Computer Aided Antenna Design and Analysis. 6.1 Introduction. 6.2 Computational Electromagnetics for Antennas. 6.2.1 Method of Moments (MoM). 6.2.2 Finite Element Method (FEM). 6.2.3 Finite Difference Time Domain (FDTD) Method. 6.2.4 Transmission Line Modelling (TLM) Method. 6.2.5 Comparison of Numerical Methods. 6.2.6 High Frequency Methods. 6.3 Examples of Computer Aided Design and Analysis. 6.3.1 Wire-type Antenna Design and Analysis. 6.3.2 General Antenna Design and Analysis. Summary. References. Problems. 7. Antenna Manufacturing and Measurements. 7.1 Antenna Manufacturing. 7.1.1 Conducting Materials. 7.1.2 Dielectric Materials. 7.1.3 New Materials for Antennas. 7.2 Antenna Measurement Basics. 7.2.1 Scattering Parameters. 7.2.2 Network Analysers. 7.3 Impedance, S11, VSWR, and Return Loss. 7.4 Radiation Pattern Measurements. 7.4.1 Open Area Test Sites (OATS). 7.4.2 Anechoic Chambers. 7.4.3 Compact Antenna Test Ranges (CATR). 7.4.4 Planar and Cylindrical Near Field Chambers. 7.4.5 Spherical Near Field Chambers. 7.5 Gain Measurements. 7.5.1 Comparison with a Standard-gain Horn. 7.5.2 Two-antenna Measurement. 7.5.3 Three-antenna Measurement. 7.6 Miscellaneous Topics. 7.6.1 Efficiency Measurements. 7.6.2 Reverberation Chambers. 7.6.3 Impedance De-embedding Techniques. 7.6.4 Probe Array in Near Field Systems. Summary. References. Problems. 8. Special Topics. 8.1 Electrically Small Antennas. 8.1.1 The Basics and Impedance Bandwidth. Introduction. Slope Parameters. Impedance Bandwidth. Fundamental Limits of Antenna Size, Q and Efficiency. The Limits of Bandwidth Broadening. Discussions and Conclusions. 8.1.2 Antenna size reduction techniques. Top Loading. Matching. Reactive Loading. Dielectric Loading. 8.2 Mobile Antennas, Antenna Diversity and Human Body Effects. 8.2.1 Introduction. 8.2.2 Mobile Antennas. The Cellular Frequency Bands. The "Connectivity" Frequency Bands. Typical Antenna Types. a). Monopoles. b). Helical Antennas. c). Monopole-Like Antennas. d). Planar Inverted F Antennas. The Effect of the PCB. Specific Absorption Rate (SAR). Multipath and Mean Effective Gain. 8.2.3 Antenna Diversity. De-correlation Methods. a). Polarisation Diversity. b). Spatial Diversity. c). Radiation Pattern Diversity. Combining Methods. a). Switched Combining (SWC). b). Selection Combining (SC). c). Equal Gain (EGC). d). Maximal Ratio (MRC). The Effect of Branch Correlation. The Effect of Unequal Branch Powers. Examples of Diversity Antennas. MIMO Antennas. 8.2.4 User Interaction. Introduction. Body Materials. Typical Losses. 8.3 Multi-band and Ultra Wideband Antennas. 8.3.1 Introduction. 8.3.2 Multi-band Antennas. Techniques. a). Higher Order Resonances. b). Resonant Traps. c). Combined Resonant Structures. c). Parasitic Resonators. Examples. 8.3.3 Wideband Antennas. 8.4 RFID Antennas. 8.4.1 Introduction. 8.4.2 Near Field Systems. 8.4.3 Far Field Systems. 8.5 Reconfigurable Antennas. 8.5.1 Introduction. 8.5.2 Switch and Variable Component Technologies. 8.5.3 Resonant Mode Switching/Tuning. 8.5.4 Feed Network Switching/tuning. 8.5.5 Mechanical Reconfiguration. Summary. References. 9. Appendix. 9.1 Industry Standard Coaxial Cables. 9.2 Connectors. 9.3 Selection of Antenna Simulation Software on the Market.
389 citations
"Determination of Far Fields of Wire..." refers background in this paper
...A resonant loop antenna is considered to have a circumference of one wavelength [11]....
[...]
...1(c), assumed to be sinusoidal [11], are given by...
[...]
Book•
01 Jan 1965
TL;DR: Theory of electromagnetic wave propagation, Theory of electromagnetic Wave Propagation, and Theory of Wave propagation (TWP) as discussed by the authors, is a theory of wave propagation and propagation theory.
Abstract: Theory of electromagnetic wave propagation , Theory of electromagnetic wave propagation , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
315 citations
"Determination of Far Fields of Wire..." refers methods in this paper
...The detailed expression of this method and examples are given in [6] and [7]....
[...]
TL;DR: In this paper, the electromagnetic field of radiating charges and currents in multipole components is represented in terms of Debye potentials which are shown to be closely related to the radial components of the electric and magnetic vectors.
108 citations
"Determination of Far Fields of Wire..." refers background in this paper
...Similar representation of the field using only two scalar aspects is dealt in [3], [5], and [8]....
[...]
...2900291 and magnetic vectors, on any sphere encompassing the sources is presented in [5]....
[...]
TL;DR: In this article, a theoretical formulation in terms of combined magnetic and electric field integral equations is presented for the class of electromagnetic problems in which one or more wire antennas are connected to a conducting body of arbitrary shape.
Abstract: A theoretical formulation, in terms of combined magnetic and electric field integral equations, is presented for the class of electromagnetic problems in which one or more wire antennas are connected to a conducting body of arbitrary shape. The formulation is suitable for numerical computation provided that the overall dimensions of the structure are not large compared to the wavelength. A computer program is described, and test runs on various configurations involving a cylindrical body with one or more straight wires are presented. The results obtained agree well with experimental data.
63 citations
"Determination of Far Fields of Wire..." refers background in this paper
...Similar to the examples presented in [1], [2], and [9] having antennas near perfect electric conductor (PEC) objects, the far-field calculation from the radial components of the near field [3]–[7] is applied for nontrivial examples of wire antennas on a PEC sphere....
[...]
...A theoretical formulation for radiation from wire antennas on cylindrical conducting body is presented in [2]....
[...]
TL;DR: In this paper, the problem of an arbitrarily oriented thin-wire antenna located near a body of revolution was analyzed and the usual integrodifferential equation for a thin wire in unbounded space was generalized to account for scattering from the nearby body.
Abstract: The problem of an arbitrarily oriented thin-wire antenna located near a body of revolution is analyzed. The usual integrodifferential equation for a thin wire in unbounded space is generalized to account for scattering from the nearby body. The presence of the body is accounted for by a numerical dyadic Green's function. The modified wire equation is solved by standard numerical techniques to obtain the current distribution on the wire. The effects of various bodies on input admittance are compared with results for an isolated antenna. Measured and theoretical input admittance data for a monopole near several different bodies of revolution are found to be in good agreement.
39 citations
Additional excerpts
...Similar to the examples presented in [1], [2], and [9] having antennas near perfect electric conductor (PEC) objects, the far-field calculation from the radial components of the near field [3]–[7] is applied for nontrivial examples of wire antennas on a PEC sphere....
[...]