Marco Leone

On the coupling of an external electromagnetic field to a printed circuit board trace

Compact analytical solutions are developed for the terminal responses of a printed circuit board (PCB) trace exposed to an external electromagnetic field in the frequency and time domain. The analysis based on transmission line theory in a scattered voltage formulation uses a quasi-TEM propagation model for the trace and the exact distribution of the external electric field within the air/dielectric medium for the excitation terms. From the general solutions obtained for arbitrary wave incidence and terminal impedances, several much simpler approximations are derived revealing the principal behavior and indicating the relevant parameters to minimize the coupling. Practical examples with a comparison of the different results are presented.

Efficient 2-D Integral Equation Approach for the Analysis of Power Bus Structures With Arbitrary Shape

A 2-D contour integral-equation method for the frequency-domain analysis of arbitrarily shaped power bus structures is presented. The numerically efficient approach allows the rapid and accurate computation of the frequency-dependent transfer parameters between an arbitrary number of ports, as required for embedding the power plane structure into network simulation. A formulation is developed for calculating the voltage distribution between the planes, as well as for determining the resulting radiated fields based on the field-equivalence principle. The method is applied for several test boards including a populated board with a surface-mount decoupling-capacitor network. The suggested approach is well confirmed by an analytical solution for the rectangular structure, by measurement and 3-D full-wave simulation results.

Closed-Form Expressions for the Electromagnetic Radiation of Microstrip Signal Traces

An analytical study of the unintentional electromagnetic radiation of a microstrip signal trace is presented. Based on transmission-line theory and appropriate far-field Greens functions, a closed-form solution for the electric field is developed, including the contribution from the vertical terminal connections. It allows calculating the frequency and directional response of the radiated emission, depending on the material and geometrical parameters and terminal load impedances. For the special case of matched termination, the general solution assumes a compact form, allowing to set up a formula for the peak-amplitude frequencies. It is shown that in the higher frequency region, where the wavelength is comparable or shorter than the line length, the frequency-response envelope continuously rises with 20 dB/dec. Based on appropriate simplifications, the asymptotic solution for the electrically short line is deduced, including a practical formula for the maximum electric field. It is found that the usual small-current-loop (magnetic-dipole) estimation is incomplete due to the omission of the electric-dipole contribution.

Inductive Network Model for the Radiation Analysis of Electrically Small Parallel-Plate Structures

Vertical interconnections between parallel-plate structures as often encountered in electronic designs are the source of various signal integrity and radiated-emission issues. The presented analysis is based on a coupled multiport equivalent-circuit model for frequencies below the first cavity resonance. A main subject is the determination of the self- and mutual port inductances, for which exact closed-form expressions are presented. For special port positions simple approximate formulas are derived. The results show that the considered structure is inherently resonant. The resonance frequency depends on the number and configuration of the ground interconnections and can be estimated from the equivalent circuit. The radiated emission of the whole structure is determined by the capacitive current in the network model, based on a simple Hertzian-dipole radiation characteristic. The model is validated by numerical 3-D field simulations and measurements.

Efficient Broadband Circuit-Modeling Approach for Parallel-Plane Structures of Arbitrary Shape

A methodology for creating highly efficient and inherently stable equivalent-circuit models for arbitrarily shaped parallel-plane pairs is presented. Based on Greens function with accelerated convergence, a general impedance expression is derived for circular ports, comprising the static capacitance and inductances and a small number of resonant terms. It can be directly cast into an equivalent multiport circuit for arbitrary number of ports, enabling the application in a SPICE circuit-simulation environment for broadband system analysis with active, passive, and nonlinear components. The equivalent-circuit elements are determined by a simple finite-difference scheme in combination with an analytical port model, which allows us to perform the required modal and the quasi-static analysis with a uniform mesh. Validation by numerical full-wave field simulations demonstrates the versatility of the suggested approach and the high computational savings of several orders of magnitude in frequency and time domain.

PEEC Formulation Based on Dyadic Green's Functions for Layered Media in the Time and Frequency Domains

This paper presents a novel time- and frequency-domain concept of modeling with the partial element equivalent circuit (PEEC) method, which applies the mixed potential integral equation (MPIE) with dyadic Greens functions for layered media (DGFLM-PEEC). On the one hand, it represents an exact full-wave semianalytical solution for an arbitrary configuration of traces and via holes in multilayered printed circuit boards. On the other hand, the DGFLM-PEEC model is represented in a circuit form, and thus, may be included in general-purpose circuit simulators. The paper derives a general DGFLM-PEEC formulation, which may be applied to all types of the MPIE with dyadic Greens functions. Using this concept, a particular type of layered media, namely a lossy dielectric between two grounds (stripline region), is thoroughly investigated and used to set up a particular DGFLM-PEEC model. The closed-form expressions for partial inductances and potential coefficients have been derived for this case. The time- and frequency-domain DGFLM-PEEC models for the stripline region have been validated using the measurements and the simulation by the method of moments.

Efficient computation of radiated fields from finite-size printed circuit boards including the effect of dielectric layer

The rigorous analysis of a finite-size printed circuit board by the method of moments based on a full discretization of the whole three-dimensional structure requires a high numerical and modeling effort. A suitable simplification which drastically reduces the computation time is to use an equivalent-wire model for the traces situated within an homogeneous medium with an effective dielectric constant to account for the dielectric layer. For the subsequent determination of the radiated fields the dielectric layer is commonly ignored. In this paper we show in which cases this can lead to considerable prediction errors, and present a method based on polarization currents to include the effect of the dielectric layer, retaining the numerical efficiency of this approach. Examples are given to demonstrate the importance of the proposed extension.

Simple, Taylor-Based Worst-Case Model for Field-to-Line Coupling

To obtain Electromagnetic Compatibility (EMC), we would like to study the worst-case electromagnetic field-induced voltages at the ends of Printed Circuit Board (PCB) traces. With increasing frequencies, modelling these traces as electrically short no longer suffices. Accurate long line models exist, but are too complicated to easily induce the worst case. Therefore, we need a simple analytical model. In this article, we predict the terminal voltages of an electrically long, two-wire transmission line with characteristic loads in vacuum, excited by a linearly polarised plane wave. The model consists of a short line model (one Taylor cell) with an intuitive correction factor for long line effects: the modified Taylor cell. We then adapt the model to the case of a PCB trace above a ground plane, illuminated by a grazing, vertically polarised wave. For this case, we prove that end-fire illumination constitutes the worst case. We derive the worst-case envelope and try to falsify it by measurement in a Gigahertz Transverse Electromagnetic (GTEM) cell.

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.

A Foster-Type Field-to-Transmission Line Coupling Model for Broadband Simulation

A passive and inherently stable multiport equivalent circuit for lossy transmission lines is presented. The convergence of the infinite modal representation is accelerated by appropriate inductances, for which an exact closed-form expression is developed. The order number of the truncated modal circuit is estimated by a simple relation, according to the required signal bandwidth. The coupling of arbitrary external electromagnetic fields is incorporated by a limited number of corresponding modal sources. The accuracy and versatility of the suggested SPICE-compatible equivalent circuit is demonstrated by examples in frequency and time-domain, including nonlinear terminations.