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## Source reconstruction using equivalent currents

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In this chapter the source reconstruction using equivalent currents is a mature technique with a number of interesting applications such as field transformation (NF-FF/NF-NF), electromagnetic diagnostics, design optimization, general source modeling, and antenna synthesis. Its formulation and numerical solution are based on the widely popular MoM and therefore inherits its well-known properties such as accuracy and flexibility and profits directly from advanced techniques developed around MoM such as low-frequency, large-scale, and multi-resolution solvers to mention some. It has been found that the DEqF provides robust results and the best accuracy in real-world situations both for diagnostics and for field transformations, while the simpler SEqFs could be of interest in order to reduce memory and time requirements when the loss in accuracy is acceptable, or when dealing with data from simulation.

Chapter Contents:

• 2.1 Introduction
• 2.2 Formulation of the source reconstruction problem
• 2.2.1 Application of the equivalence theorem
• 2.2.1.1 Zero interior fields—Love's equivalence
• 2.2.1.2 Jeq-only/Meq-only formulation
• 2.2.2 Uniqueness of the solution to the reconstruction problem
• 2.3 Numerical solution of the source reconstruction problem
• 2.3.1 Discretization
• 2.3.2 Setup of the linear system
• 2.3.3 Application of existing Method of Moments codes in source reconstruction
• 2.4 Probe correction
• 2.4.1 Reciprocity and the reception formula
• 2.4.2 Formulation of the source reconstruction problem with probe correction
• 2.5 Application examples
• 2.5.1 Application as an investigation and diagnostic tool
• 2.5.2 Application in field transformations
• 2.5.2.1 Near-field to near-field
• 2.5.2.2 Near-field to far-field
• 2.5.3 Array antenna synthesis
• 2.6 Numerical tests on the accuracy of source reconstruction
• 2.7 Conclusions and outlook
• References

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