Wigner-Function-Based Propagation of Stochastic Field Emissions From Planar Electromagnetic Sources

Abstract

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract-Modelling the electromagnetic radiation from modern digital systems -acting effectively as extended, stochastic sources as part of a complex architecture -is a challenging task. We follow an approach here based on measuring and propagating field-field autocorrelation functions (ACFs) after suitable averaging. From the modelling side, we use the Wigner transform of the ACFs to describe random wave fields in terms of position and direction of propagation variables. An approximate propagator for the components of the radiated magnetic field is constructed for these ACFs based on a linear flow map. Field-field ACFs at aperture level are obtained from scanning measurements of complex sources. Distance and spatial resolution of the scanning plane is less than a wavelength from the source plane to capture the imprint of evanescent waves in the nearfield ACFs. Near-field scanning and efficient near-to-far field propagation is carried out and compared with measurements. Results of this study will be useful to assist far-field predictions, source reconstruction, and emission source microscopy.

Near-Field Scanning and Propagation of Correlated Low-Frequency Radiated Emissions

“…The fields obtained through linear NFS of a single in-plane magnetic component at different heights z are then used to calculate the CF using (1) and (2). The two-probe procedure described in [7] was adopted to calculate the CF from space-time fields obtained through linear NFS of a single in-plane magnetic component at different heights z using (1) and (2). The discretisation of (1) and (2), along with an algorithm to compute the discrete WF, is explained in detail in [7].…”

“…A statistical approach is then appropriate. As discussed in [7], radiation from such complex sources may be exemplified by aperture scanning of the transverse magnetic fields over planes parallel to the source and calculation of a spectral field-field correlation function.…”

“…In a full 3D simulation, x = (x, y) and d = 2, but we also discuss a simplified analysis in which x is represented by a single component x and d = 1. Both the CF and WF of propagating [7] and weakly evanescent [15] wave densities have been studied extensively for a planar source. …”

“…These methods have been inherited and adapted to predict the radiation of circuits and devices. More recently, statistical methods have been introduced to characterise fluctuating fields arising from multifunctional digital electronics in the absence of phase references [6], [7].…”

“…Near-to-Far Field (NFF) propagation methods have been used to characterise antennas [8] and circuitry [9], and have recently been extended to broadband complex statistical sources, including mobile phones [10], [11], PCBs [12], [6] and open reverberation chambers [7]. The focus in this work is, however, on studying Near-to-Near field (NNF) to understand the role evanescent waves in the propagation of complex, partially coherent, stochastic fields.…”