Localizing Equivalent Dipole Sources for Radiated Stochastic Interference

Interference between different analog and digital circuits within an electronic device has become a key issue regarding wireless communication and signal integrity. Since the actual sources of radiated electromagnetic interference are often very complex and in general unknown, the radiated noise needs to be treated as a stochastic electromagnetic field. As long as Gaussian statistics can be assumed, the stochastic electromagnetic field can be completely described by its second order moments, given by auto- and cross-correlation spectra. Especially in electromagnetic compatibility considerations, the locations of the origins of the noisy radiated interference are of particular interest. If those locations are known, one can identify hot-spots of radiated energy and hence the sources of interference. In this paper, we present a method for localizing equivalent dipoles directly on the device, when the tangential field components on all pairs of points on an observation plane at a known distance h from the source plane are known. The tangential field components on all pairs of points can be obtained by two-probe scanning in the near-field. From the tangential field components, we calculate the auto- and cross-correlation spectra on the observation plane. In the next step we place a fine virtual grid on the source plane, i.e. at a distance -h from the observation plane, and calculate the numerical propagator for each grid point to each observation point using a method of moments discretization of the dyadic Green's function in the near field. From this finely discretized numerical propagator, we form the inverse propagator by means of the Moore-Penrose pseudo inverse. This inverse propagator is optimal in a least-squares sense. With the inverse propagator known, we can give an estimate of the spectral energy density in the virtual source plane. The actual locations of the equivalent dipoles can be identified as the maxima of the spectral energy density. The number of equivalent dipoles still remains to be estimated. It turns out that the number of independent sources corresponds to the number of dominant principal components, which are obtained by performing a principal component analysis on the given data set. Altogether, we have formulated an algorithm for identifying the locations of radiating noise sources by using an inverse numerical propagator in the near-field and principal component analysis, in order to perform a model order estimation. Finally the locations of equivalent dipoles are calculated by identifying N maxima of the estimated spectral energy density in the source plane, where N is the number of dominant principal components of the correlation matrix.     «

Interference between different analog and digital circuits within an electronic device has become a key issue regarding wireless communication and signal integrity. Since the actual sources of radiated electromagnetic interference are often very complex and in general unknown, the radiated noise needs to be treated as a stochastic electromagnetic field. As long as Gaussian statistics can be assumed, the stochastic electromagnetic field can be completely described by its second order moments, giv...     »