A decoupled source current reconstruction method for noisy and reactive near-field to far-field transformation

Abstract

In this article, a decoupled source current reconstruction method (SRM) for noisy and reactive near-field (NF) to far-field (FF) transformation is introduced. It is shown that the traditional SRM for NF/FF transformation shows instability in the regions that the amounts of noise or reactive radiations are noticeable. Therefore, in these regions, equivalent currents should be determined from a Tikhonov SRM equation. However, this equation increases the computational cost of the SRM. To simplify the Tikhonov SRM equation, a Tikhonov radial field retrieval algorithm is also proposed. In this algorithm, the Tikhonov integral equation is decoupled by considering and retrieving the radial components of the electric field. Results of far-field calculation with both the proposed Tikhonov SRM equation and Tikhonov radial field retrieval algorithm with three different antennas are presented and compared with those of the full-wave simulation and measurements. The results show more accurate field transformation with the proposed algorithms. K E Y W O R D Sfield transformation, reactive near-field, source current reconstruction, Tikhonov inverse problem | I NT ROD UCTI ONAdvanced and accurate measurement of the antenna radiating characteristics in a controlled environment has attracted considerable attentions in the recent years. Measuring the nearfields of the antenna under test (AUT) and reconstructing the far-field (FF) radiation is one of the most widely used advanced measurement techniques. 1-14 Near-field (NF) measurements have dramatically reduced the dimensions of test facilities and test costs and increased measurement speeds.Recently, measuring the field data in the close proximity of the radiator is also possible with the electro-optic field technology. [12][13][14][15] Although measuring the reactive near-field radiation of an AUT is a big step forward for further reducing the cost and speed of the antenna measurements, these measurement systems are applicable when a method for accurately transforming the reactive near-field to far-field radiations is also being developed. However, up to the authors' knowledge, most of the available NF to FF transformation method are placed in the region that the reactive radiations are negligible and the effects of evanescent modes on the field transformation procedure have not already studied. [1][2][3][4][5][6][7][8] For NF to FF transformation, two main methods have already been reported over the past years. The oldest method which has been used widely is the modal techniques. 1,2 Brief reports about the reactive near-field transformation with modal techniques can be found in Refs. 13 and 14. In these papers, a stable field transformation is obtained by optimizing the field sampling positions of the AUT in a way that creates a transformation matrix with the most convenient singular values. This reduces the effects of reactive radiation as will be discussed in this article.The newest method for NF to FF transformation which is more flexible but has a higher computatio...

Study on the Propagation Characteristics of Partial Discharge in Switchgear Based on Near-Field to Far-Field Transformation

“…When PD occurs in HV equipment, the near-field to far-field transformation used for the study the signal propagation is based on Huygens' Principle (the equivalence theorem) [26][27][28]. The radiating sources of PD are enclosed inside surface S, as shown in Figure 1.…”

Hybrid Tikhonov source current reconstruction method for large‐scale problems

“…Source current reconstruction method (SRM) is an efficient technique for reconstructing equivalent currents of the antenna under test (AUT) from the near (NF) or far-field (FF) measurements [1][2][3][4][5][6][7][8][9][10][11]. This method is based on the equivalence principle in which the AUT radiation is modelled by the equivalent currents at a fictitious surface enclosing the original AUT sources.…”

“…In all of these papers, it has been shown that the Tikhonov SRM is more stable in the presence of Gaussian noise or systematic measurement errors. In a recently published paper by the authors, it is demonstrated that the Tikhonov SRM is also necessary for the noiseless region with a large amount of reactive radiation [11].…”

“…A key issue in the implementation of the Tikhonov equation is to choose an optimum regularisation parameter that balances the error due to regularisation with the error due to the noise. In the above-mentioned papers, the small SRM matrix equation is solved by the singular value decomposition method (SVD) [1][2][3], and therefore the methods such as generalised cross-validation (GCV), or L-curve method, can be used for estimating the regularisation parameters from the SVD of the impedance matrix [3,10,11].…”