A technique for the determination of the equivalent currents distribution from a known radiated field is described. This Inverse Radiation Problem is solved through an Integral Equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field (NF-FF) transformation purposes as well as for diagnostic tasks. The algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three-dimensional (3D) surface that can be fitted to the arbitrary geometry of the antenna. The innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3D surface. For that purpose, both the magnetic and electric equivalent currents are considered in the integral equations. Regularization techniques are also introduced to improve the convergence of the proposed iterative solution. The paper concludes with several results related to the practical verification of the Equivalence Principle and the characterization of a horn antenna.

Reconstruction of Equivalent Currents Distribution Over Arbitrary Three-Dimensional Surfaces Based on Integral Equation Algorithms

In this paper, a simple method to obtain the equivalent radiation emitting sources of an electronic circuit using the near-field scanning method is presented. The model is based on a set of elemental dipoles that substitutes the electronic circuit and radiates the same magnetic field. Two different approaches are presented: a set of electric dipoles and a set of magnetic dipoles. In order to build the model, both the magnitude and phase of the magnetic field are required. These measurements are carried out using the "near-field scanning method," and two procedures are presented: using the vector network analyzer and the spectrum analyzer. Finally, the model is applied to two different cases: to obtain the radiated near-field of a component (microcontroller) and to obtain the field of a complete electronic board.

Modeling Magnetic Radiations of Electronic Circuits Using Near-Field Scanning Method

This paper describes in detail difierent formulations of the inverse-source problem, whereby equivalent sources and/or flelds are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric fleld data at a specifled (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal flelds, and of their practical impact. Love's (zero interior fleld) equivalence is the only equivalence form that yields currents directly related to the flelds on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The flrst is the single-equation, two-current formulation which is most common in current literature, in which no interior fleld condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one fleld is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the beneflts of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured fleld for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples conflrm that single- equation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

/pdf/field-and-source-equivalence-in-source-reconstruction-on-3d-2d9rzuf3k5.pdf

Field And Source Equivalence In Source Reconstruction On 3D Surfaces

This paper presents a novel formulation of the source reconstruction problem on arbitrary three-dimensional (3-D) surfaces based on integral equations. Rigorous boundary integral field identities are employed to enforce that the two unknown currents are Maxwellian on the reconstruction surface; this leads to a dual integral-equation formulation, in contrast to the single-equation formulation found in literature. Numerical tests against reference currents allow a quantitative assessment of the improvements in accuracy afforded by the novel formulation, with important benefits in diagnostic applications.

Improved-Accuracy Source Reconstruction on Arbitrary 3-D Surfaces

A new method for predicting the far-field radiated emissions and for finding the radiation sources of a device from near-field measurements is presented. It is based on the substitution of the original device by an equivalent set of elemental dipoles, placed over the main radiating sources, which radiate the same near-field (and therefore, far-field). This equivalent set of elemental dipoles is generated using a genetic algorithm. From the position and type of the equivalent elemental dipoles, the position of the actual radiating sources is determined. Since the field produced by an elemental dipole is known, the far-field radiation of the actual radiating source can be calculated. The new method has been tested using synthetic data and real measurements from the radiation generated by a modem PCB demonstrating its viability and usefulness.

A genetic algorithm based method for source identification and far-field radiated emissions prediction from near-field measurements for PCB characterization

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method.

A. Taaghol

Papers

Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM