Christian Bednarz

Exact Analytical Solution for the Via-Plate Capacitance in Multiple-Layer Structures

An exact analytical solution for the via-plate capacitance in multilayer printed-circuit board (PCB) structures is presented. The formulation is based on Laplaces equation for the static electric potential within the via-plate region, which is electrically small for a large frequency range. The potential distribution is determined by the separation of Laplaces equation in cylindrical coordinates for the three subdomains: via barrel and pad, antipad, and the plate region. It is shown that the unknown via-plate capacitance is determined by only one single coefficient of the resulting linear equation system. The influence of additional via pads is readily included. The results are compared with previously published approaches and validated by 2-D static, as well as by 3-D full-wave numerical simulations.

Improved Expression for the Via-Plate Capacitance Based on the Magnetic-Frill Model

In the recent years, several methods for the calculation of the via-plate capacitance in multilayer printed circuit boards have been developed. A widely used analytical approach is the application of a magnetic-frill current as an equivalent TEM excitation within the antipad. Recently, the comparison of the corresponding capacitance expression with an exact static analytical solution and with numerical simulations has shown some discrepancies, especially for large pads. In this letter, the cause for the error is found to be an inconsistent admittance definition. Based on an alternative complex-power approach, a novel capacitance expression is developed which agrees quite well with reference data.

Broadband Circuit Model for Wire-Interconnection Structures Based on a MoM-Eigenvalue Approach

A novel highly versatile broadband Foster-type circuit model for arbitrary wire networks with moderate radiation losses is presented in this paper. Based on a quasi-static method-of-moments-eigenvalue problem, a modal multiport circuit is derived with minimal computational effort, offering fast convergence and inherent stability for time-domain simulations with arbitrary active/passive nonlinear loads. The model order can be estimated rigorously from the given frequency range. Incident electromagnetic field excitation is considered by additional modal sources, which are calculated with minimal effort. The proposed model is validated in the frequency and time domain.

Efficient FEM-Based Modal Circuit Representation of Arbitrarily Shaped Plate Pairs

A novel finite element method-based technique for the calculation of all circuit parameters of an efficient broadband equivalent network representation of parallel-plane pairs with arbitrary geometry is presented. It is based on an eigenvalue analysis in combination with the solution of the quasi-static Poisson equation for the magnetic vector potential. Compared with a recently presented simple finite difference scheme, the suggested FEM approach considerably reduces the modeling and computational effort, enabling an adaptive meshing in the presence of small circular ports. The proposed approach is validated by a practical example, demonstrating the considerable computational savings and the versatility for practical applications.

Exact solution for via-plate capacitances including the finite plate thickness

In this paper a straightforward analytical solution is presented for the exact calculation of the via plate capacitance in multilayer structures, considering the finite thickness of the plates. The capacitance is obtained from the static potential distribution and results in the determination of a single coefficient of an infinite equation system, which can be truncated after a few unknowns. The convergence of the solution is independent of the plates thickness. Thus the novel approach does not require additional effort in comparison with previous approaches where the plate thickness is omitted. The results are validated by numerical 3D full-wave simulations.

Equivalent circuit model for radiating lossy wire-interconnection structures including external field coupling

A broadband equivalent circuit model for arbitrary lossy wire networks including moderate radiation losses is extended in order to account for frequency-dependent ohmic losses. Based on a quasistatic Method-of-Moments-eigenvalue problem a modal multiport circuit is derived with minimal computational effort, offering fast convergence and inherent stability for time-domain simulations with arbitrary active/passive non-linear loads. Incident electromagnetic field excitation is considered by additional modal sources. The proposed model is validated in the time domain.

Broadband Switching Noise Estimation of Resonant Low-Loss Structures for Unipolar Pulse Excitation

A simple and straightforward method to estimate the maximal instantaneous voltage peak during switching operations in resonant structures is presented. It is based on the time-domain analysis of an elementary RLC circuit as a model for such systems. For short pulses, a very simple relation is obtained, independent of the pulse shape. For slow excitations, the noise amplitude is safely estimated solely by the slew rate. Pulses with arbitrary length and shape are approximately treated by a trapezoid with effective width and rise time, for which an accurate solution is derived. The approach is extended to current pulse trains. Several validation examples demonstrate the applicability and versatility of the developed estimation formulas.