Abstract: In a method producing an electronic circuit includes analyzing pre-register-transfer level phase of a power distribution network in an electronic circuit design. The power distribution network is defined to include a matrix of a number repeated leaf cells, wherein each of the matrix of repeated leaf cells corresponds to a model leaf cell wherein the model leaf cell includes an alternating Vdd and Gnd grid on top of an interposer. A plurality of local ports of the model leaf cell is defined. The plurality of local ports is defined where each of the matrix of repeated leaf cells is coupled to adjacent ones of the matrix of repeated leaf cells. The model leaf cell is simulated using an implementation of an integral equation based solver to compute electromagnetic scattering parameters (S-parameters) that correspond to the model leaf cell. The electromagnetic S-parameters are cascaded across the matrix using a binary merge algorithm.

Abstract: In a method for modeling electromagnetic effects in a planar circuit that employs a plurality of through-silicon vias in a domain, a region around each through-silicon via is described in terms of a cylindrical accumulation mode basis function. The cylindrical accumulation mode basis function is incorporated into an equivalent circuit that describes selected electrical characteristics of each through-silicon via. A plurality of localized intervals around each through-silicon via is selected. A multilayer Green's function is approximated for IMNzz? (wherein M and N identify selected layers and wherein zz? designates layer boundaries in a layer through which the through-silicon via passes) in each localized interval without approximating the Green's function over the entire domain. Coefficients IMNzz? are approximated over a predetermined range of frequencies (?). Admittance parameters based on of IMNzz? are calculated over a frequency sweep.

Abstract: In a method for analyzing pre-register-transfer level phase of a power distribution network in an electronic circuit design, in which the power distribution network is defined to include a matrix of a number repeated leaf cells, wherein each of the matrix of repeated leaf cells corresponds to a model leaf cell wherein the model leaf cell includes an alternating Vdd and Gnd grid on top of an interposer. A plurality of local ports of the model leaf cell is defined. The plurality of local ports is defined where each of the matrix of repeated leaf cells is coupled to adjacent ones of the matrix of repeated leaf cells. The model leaf cell is simulated using an implementation of an integral equation based solver to compute electromagnetic scattering parameters (S-parameters) that correspond to the model leaf cell. The electromagnetic S-parameters are cascaded across the matrix using a binary merge algorithm.

Abstract: In a method for modeling electromagnetic effects in a planar circuit that employs a plurality of through-silicon vias in a domain, a region around each through-silicon via is described in terms of a cylindrical accumulation mode basis function. The cylindrical accumulation mode basis function is incorporated into an equivalent circuit that describes selected electrical characteristics of each through-silicon via. A plurality of localized intervals around each through-silicon via is selected. A multilayer Green's function is approximated for IMNzz? (wherein M and N identify selected layers and wherein zz? designates layer boundaries in a layer through which the through-silicon via passes) in each localized interval without approximating the Green's function over the entire domain. Coefficients IMNzz? are approximated over a predetermined range of frequencies (?). Admittance parameters based on of IMNzz? are calculated over a frequency sweep.