Electric Field Calculation via Surface-Volume-Surface Integral Equation

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Solution Overview

Problem

Classical surface integral equations in electromagnetics require determining electric and magnetic dipole strengths by tangential field components, limiting flexibility in field representation, whereas fictitious currents can be arbitrary as long as they produce the correct field, suggesting a more flexible representation is possible.

Innovation Solution

The method involves constraining fictitious currents through the volume equivalence principle instead of the surface equivalence principle, leading to a new Surface-Volume-Surface (SVS) EFIE, where the electric field inside a scatterer is represented as a superposition of electric and magnetic waves emanating from the boundary, weighted by arbitrary surface vector functions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If classical surface integral equations are used to determine electric and magnetic dipole strengths by tangential field components, then the field representation is mathematically rigorous, but the flexibility in field representation is limited

Engineering Contradiction:

Improveflexibility in field representationVSAvoidconstraint on fictitious currents

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent inverts the traditional approach by not determining fictitious currents from tangential field components, but rather allowing arbitrary fictitious currents and determining the tangential field components from them. This inversion resolves the contradiction by freeing the fictitious currents from constraints while maintaining mathematical rigor through the revised integral equation formulation.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The patent changes the fundamental parameters of the integral equation formulation by replacing the traditional relationship where tangential fields determine fictitious currents with a new relationship where arbitrary fictitious currents determine tangential fields. This parameter change enables greater flexibility in field representation while maintaining mathematical consistency through the modified equivalence principle.

Inventive Principle:

Principle #35Parameter changes

2Adaptability or versatility

If arbitrary fictitious currents are used to represent the electric field, then flexibility in integral representation is increased, but the requirement to determine true field component determination is relaxed

Engineering Contradiction:

Improveintegral representation flexibilityVSAvoidfield component determination accuracy

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent introduces an intermediary relationship where arbitrary fictitious currents serve as intermediate representations that are mathematically transformed into accurate field component determinations through the revised integral equation. This intermediary approach allows flexibility in current selection while ensuring precision in field representation through the rigorous mathematical framework.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Ease of manufacture

If surface equivalence principle is used to constrain fictitious currents, then the mathematical formulation is traditional and well-established, but the representation flexibility is reduced

Engineering Contradiction:

Improveformulation simplicityVSAvoidfield representation flexibility

Core Design Contradiction:

Ease of manufactureVSAdaptability or versatility

Solution Approach 1:

The patent applies the inversion principle by reversing the traditional surface equivalence principle application. Instead of using tangential fields to determine fictitious currents (traditional approach), the patent uses arbitrary fictitious currents to determine tangential fields (inverted approach), thereby achieving both formulation simplicity and enhanced flexibility simultaneously.

Inventive Principle:

Principle #13The other way round (Inversion)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach allows for greater flexibility in integral representations of the electric field, enabling accurate field reproduction within the scatterer without necessitating true field component determination, and is demonstrated to be effective in 3D scattering problems through numerical validation.

Implementation Method 1

the electric field inside a scatterer is represented as a superposition of electric and magnetic waves emanating from the boundary, weighted by arbitrary surface vector functions

Methodology Applied

Scientific EffectSuperposition principle:

Implementation Method 2

constraining fictitious currents through the volume equivalence principle instead of the surface equivalence principle, leading to a new Surface-Volume-Surface (SVS) EFIE

Methodology Applied

Scientific EffectVolume equivalence principle:

Data Source

PatentUS10302684B2Method for determining electric field and related applications

Publication Date: 2019.05.28 OKHMATOVSKI VLADIMIR

AI summary

A method for calculating electric field having contributions of an incident electric field from a source and an electric field emitted from another object distinct from the source but in a path of the incident electric field, which is often termed a “scatterer”. This method is formed by a new single-source integral equation which represents the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Calculation of electric field using this method is particularly but not exclusively suited for applications such as fault detection in simulations of power systems, remote sensing of stratified structures such as ice, and circuit design concerning chips in electronic packages on circuit boards.