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Selected asymptotic methods with applications to electromagnetics and antennas /

Bibliographic Details
Main Authors: Fikioris, George J., 1962- (Author), Bakas, Odysseas N. (Author), Tastsoglou, Ioannis (Author)
Format: eBook
Language:English
Published: San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2014.
Series:Synthesis lectures on computational electromagnetics ; # 31.
Subjects:
Antennas (Electronics) > Mathematics.
Asymptotic expansions.
Electromagnetism > Mathematics.
antenna theory
asymptotics
complex variables
electromagnetic theory
special functions
wire antennas
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Introduction: simple asymptotic approximations
  • 1.1 Far field of linear antenna
  • 1.2 Period of simple pendulum: small oscillations
  • 1.3 A differential equation
  • 1.3.1 "Series solution"
  • 1.3.2 The solution as an integral: integration by parts
  • 1.4 Asymptotic approximations for high-SWR transmission lines
  • 1.4.1 Exact formulas
  • 1.4.2 Further exact formulas: large- and small- g regions
  • 1.4.3 Asymptotic formulas for the large-g region
  • 1.4.4 Asymptotic formulas for the small-g region
  • 1.5 Supplementary remarks and further reading
  • 1.6 Problems
  • References
  • 2. Asymptotic approximations defined
  • 2.1 Definitions
  • 2.2 Remarks and examples
  • 2.3 Compound asymptotic approximations
  • 2.3.1 Elementary example
  • 2.3.2 Bessel function of order zero
  • 2.4 Asymptotic expansions
  • 2.5 Historical and supplementary remarks
  • 2.6 Problems
  • References
  • 3. Concepts from complex variables
  • 3.1 Gamma function and related functions
  • 3.2 Power series
  • 3.3 Analytic continuation
  • 3.3.1 Removable singularities
  • 3.3.2 Geometric series
  • 3.3.3 Analytic continuation defined: uniqueness
  • 3.3.4 Further examples
  • 3.3.5 Integrals that are analytic functions of a parameter
  • 3.4 Multivalued functions and branch points
  • 3.4.1 Square root
  • 3.4.2 Further examples
  • 3.4.3 The point at infinity
  • 3.5 Branches and principal values of multivalued functions
  • 3.5.1 Square root
  • 3.5.2 Logarithm and powers other than the square root
  • 3.5.3 The function [square root of] z2-1
  • 3.5.4 Values on branch cuts
  • 3.6 Applications to antennas and electromagnetics: nonsolvability
  • 3.6.1 Hallén's and Pocklington's equations with the approximate kernel
  • 3.6.2 Integral equation related to the method of auxiliary sources (MAS)
  • 3.7 Supplementary remarks and further reading
  • 3.8 Problems
  • References
  • 4. Laplace's method and Watson's lemma
  • 4.1 Laplace's method
  • 4.1.1 Simple example
  • 4.1.2 Related examples
  • 4.1.3 Stirling's formula: leading term
  • 4.1.4 An application to the thin-wire circular-loop antenna
  • 4.2 Watson's lemma
  • 4.2.1 Statement of lemma and motivation
  • 4.2.2 Remarks and extensions
  • 4.2.3 Examples
  • 4.2.4 Stirling's formula revisited and Lagrange inversion theorem
  • 4.2.5 An application to the method of auxiliary sources
  • 4.3 Additional remarks
  • 4.4 Problems
  • References
  • 5. Integration by parts and asymptotics of some Fourier transforms
  • 5.1 Integration by parts and Laplace transforms
  • 5.1.1 Complementary error function
  • 5.1.2 Remarks
  • 5.2 Integration by parts and Fourier transforms
  • 5.2.1 Simple example: Riemann-Lebesgue lemma
  • 5.2.2 Remarks on the lemma
  • 5.2.3 Simple example continued
  • 5.2.4 Example with zero boundary terms
  • 5.3 More on Fourier transforms
  • 5.4 Applications to wire antennas
  • 5.4.1 On the kernels of Hallén's and Pocklington's equations
  • 5.4.2 Behavior of current near delta-function generator
  • 5.5 Problems
  • References
  • 6. Poisson summation formula and applications
  • 6.1 Doubly infinite sums
  • 6.1.1 Formula and its derivation
  • 6.1.2 Remarks
  • 6.1.3 A first example
  • 6.1.4 Application: infinite linear array of traveling-wave currents
  • 6.1.5 Application: coupled pseudopotential arrays
  • 6.2 Finite sums
  • 6.2.1 Formula and proof
  • 6.2.2 Remarks
  • 6.2.3 Elementary example
  • 6.2.4 Continuous functions with equal endpoint values
  • 6.2.5 Application: cylindrical array of traveling-wave currents
  • 6.3 Problems
  • References
  • 7. Mellin-transform method for asymptotic evaluation of integrals
  • 7.1 Summary of Mellin-transform method
  • 7.2 Lemmas for residue calculations
  • 7.3 Simple example
  • 7.4 On the convergence of Mellin-Barnes integrals
  • 7.5 Application to highly directive current distributions
  • 7.6 Further reading
  • 7.7 Problems
  • References
  • 8. More applications to wire antennas
  • 8.1 Problem pertaining to magnetic frill generator
  • 8.1.1 Statement of problem
  • 8.1.2 Preliminaries
  • 8.1.3 Derivation of Eq. 8.6
  • 8.2 Oscillations with the approximate kernel: case of delta-function generator
  • 8.2.1 Integral equation: nonsolvability
  • 8.2.2 Numerical method: solution for nonzero discretization length
  • 8.2.3 Asymptotic approximation for small discretization length
  • 8.3 On the near field due to oscillating current
  • 8.3.1 Statement of problem
  • 8.3.2 Derivation of Eq. 8.46
  • 8.4 Supplementary remarks
  • 8.5 Problems
  • References
  • A. Special functions
  • Preliminaries
  • Exponential, sine, and cosine integrals
  • Definitions and small-argument expansions
  • Large-argument expansions
  • Complete elliptic integral of the first kind
  • Bessel and Hankel functions
  • Definitions and small-argument asymptotic approximations
  • Large-argument asymptotic expansions
  • Large-order asymptotic approximations
  • Addition theorem for Hankel function of order zero
  • Modified Bessel functions
  • Generalized hypergeometric functions
  • Problems
  • References
  • B. On the convergence/divergence of definite integrals
  • Some remarks on our rules
  • Rules for determining convergence/divergence
  • Examples
  • References
  • Authors' biographies
  • Index.