Umberto Paoletti

Analytical calculation of the point-to-point partial inductance of a perfect ground plane

The point-to-point partial self inductance of an infinite and perfectly conducting ground plane has been analytically calculated in closed form. The point-to-point mutual coupling between ground plane and a trace parallel to the ground plane has been expressed in terms of an integral, which should be solved numerically. The calculations are based on a new scalar potential directly related to the concept of partial inductances. Formulas for the conversion of partial inductances between the Lorenzs and Coulombs gauges are also obtained. The definition of partial inductance in terms of the vector potential (e.g. in [1]) implicitly introduces equivalent circuits, where the voltage represents a difference of a scalar potential defined by the electric field and by the magnetic vector potential at the same time. Therefore, it should not surprise the possibility of having a partial inductance also on perfect ground planes. A part from the definition of the magnetic vector potential, the definition of ground plane partial inductance depends on the application, in particular on the considered current distribution on the ground plane. For example, in [2] the ground plane inductance is defined in terms of the induced current on the ground plane by a micro-strip conductor. In the present work, we will consider the current injected in one point and extracted from a second point on the ground plane, similarly to [3]. This type of partial inductance appears when there are connections to a ground plane, such as cables or micro-strip terminations. In a less proper way, it can be used for approximately representing the inductance related to the displacement current, when a micro-strip is decomposed in short segments carrying constant current. The numerical calculation of the point-to-point ground partial inductance is already considered in software of widespread use, such as FASTHENRY [4]. However, the segmentation of the ground plane can become a problem for configurations with high density of conductors [5]. The calculation time increases for larger ground planes, also because the image theory cannot be directly applied to the calculation of partial inductances.

Quasi-static lumped element stand-alone package model for quad flat package

A new type of package model is introduced, which allows to take into account the effect of external structures, such as PCB traces and ground plane, by limiting at the same time the disclosure of internal details of the package. The model is verified with a scaled quad flat package (QFP) and two different printed circuit board (PCB) patterns, but the general procedure should be applicable to other types of package.

Indirect extension of the image theory to partial inductance calculations

Within the limitations implicit in the magneto-quasi-static approximation, partial inductances are a valuable tool for modeling IC package and interconnect inductances. In the calculation of partial inductances it is not possible to directly apply the image theory due to the absence of charges on the ground plane. In the present paper a correction term is obtained, which allows to calculate partial inductances with the image theory, avoiding in this way the problem of the ground plane segmentation. The formula is valid for conductors parallel to the ground plane. The accuracy of the formula is verified and discussed.

De-Embedding Technique for the Extraction of Parasitic and Stray Capacitances from 1-Port Measurements

A de-embedding technique for the measurement of very small parasitic capacitances of package or small module interconnects is presented. At high frequencies small parasitic capacitances become important, and measurement probes can strongly affect measurement results. The present technique is based on additional measurements with only one tip of the probe touching one conductor, while the second tip is kept floating on the substrate. A necessary condition for its application is that the measured capacitance does not depend on the position of the floating probe tip. Measurements with inverted probe tip polarities are also used. In this way, the capacitances between probe tips and DUT can be estimated together with the parasitic capacitances of interest. Depending on the required accuracy, de-embedding of different orders have been introduced, which consider capacitance configurations of increasing complexity. The technique requires the solution of one or more systems of non-linear equations. In the present example the minimization of the norm of the residual of the system has been treated as a least squares problem, and has been solved numerically with MATLAB. The accuracy of the measurement can be also approximately estimated with the residual. As application example, a small module with power and ground planes has been considered. Two different probes have been used. Even though the stray capacitances of the probes are very different, the values of the extracted parasitic capacitances are in agreement with each other. The accuracy has been verified also with simulation results. To this purpose, a combination of known formulas from the literature, a 2D Finite Element Method (FEM) tool and a 3D Boundary Element Method (BEM) tool have been used. A high accuracy can be obtained, even when a strong capacitive coupling between probe ground and DUT is present. The technique can be applied also when only a subset of measurement results are available.

Correction of the Method of Images for Partial Inductance Calculations of QFP

The inapplicability of the method of images to partial inductance calculation within the magneto-quasi-static approximation has been shown by the authors in previous works. This concept is restated in this paper, and some correction terms for the application of the method of images are proposed. A partial inductance calculation technique based on potential theory is also proposed, which does not require the calculation of the current distribution, and is limited at present to infinite perfectly conducting planes. The proposed correction terms are verified with simple structures at first, and later with the calculation of the partial inductance matrix of a quad flat package.

Effect of package parasitics on conducted and radiated emission with mixed-mode analysis

Based on a case study it is shown that the mixed-mode scattering parameters allow to consider some important effects related to package parasitics, which cannot be explained by considering completely differential type package models. In particular, a differential mode source at IC level can generate a common mode current at package level, which is in part transformed back into differential mode current and flows through the port connected to the PCB. Some design equations based on mixed-mode analysis are proposed, in order to reduce the common mode excitation, and make in this way the package more reliable.

On the extension of the image theory to partial inductance calculation

Within the limitations implicit in the magneto-quasistatic approximation, partial inductances are a valuable tool for modeling IC package and interconnect inductances. The inapplicability of the image theory to partial inductance calculation is discussed. The partial inductance matrix of a QFP is evaluated with the usage of some correction terms for the image theory.

The noise source modulation technique for the determination of electromagnetic noise path

The noise source modulation technique (NSMT) is proposed to determine the electromagnetic noise path when an EMC problem appears. The basic idea behind the NSMT is to apply a known time variation (modulation) to one of the possible noise paths and to observe its effect at the noise victim location. Different modulations can be applied to different noise paths simultaneously. Based on the type and amount of noise modulation at the victim location, the noise path can be determined.