Frequency interpolation methods for accelerating parallel EMC analysis

Based on the method of moments (MoM), radio frequency (RF) ground voltage drop of any signal return path on printed circuit board (PCB) is modeled numerically. The full-wave treatment provides the flexibility in predicting RF ground voltage drop of non-ideal ground return, such as holes and slots in the ground plane. An example is given to illustrate the application aspect of RF ground voltage prediction for EMC design purposes. I. INTRODUCTION With ever-increasing operating speeds of electronic circuits, the effects of interconnects of printed circuit boards (PCBs) become significant and have to be accounted for in the design. Hence, accurate modeling of interconnects on PCB is gaining more attention in high- speed circuit design. Conventionally, a ground plane of a PCB as return path for signal trace is assumed to be ideal with zero potential difference. Usually, the voltage drop on a signal delivery path (signal and ground conductors) is usually lumped into the signal conductor for circuit analysis purposes. Hence, information on ground voltage drop of any signal delivery path is not readily available. As logic devices switch at very high speed and draw large amount of current during switching (very high di/dt), significant voltage drop in the ground conductor is expected even its inductance is very small (1)-(8). Therefore, additional information on ground voltage drop or ground bounce provides an assessment on the effectiveness of a specific ground design for high-speed circuit so that potential EMI problem can be identified and rectified. Most commercially available full-wave electromagnetic simulation tools are based on either finite element method (FEM) (9), method of moments (MoM) (10) or finite-difference time-domain (FDTD) method (11). These tools usually model interconnects as a two- port network, which is usually good enough for signal integrity analysis purposes but does not provide additional information on ground voltage drop. To predict the RF ground voltage drop of any arbitrary signal delivery path on PCB, full-wave treatment in the modeling is the only way to model it accurately. In this paper, a full-wave approach to model the RF ground voltage drop based on MoM is presented. With

The behavior of reradiated fields from PCBs, with the radar cross section being the main parameter of interest is investigated in this work. A rigorous approach to predict radiation from PCBs in a GTEM cell is presented. The analysis is based upon the use of the reciprocity theorem in combination with the method of moment applied to the scattered field. Thus, yielding a generalized impedance matrix, whose determinant represents the characteristic polynomial of the scattering system. The effectiveness of the method is demonstrated by investigating some canonical circuit configurations and structures illustrating sources of fundamental EMI mechanism. The validity and the accuracy of the analysis becomes obvious in view of the one-to- one correlation with measurements. I. INTRODUCTION Printed-Circuits Boards (PCB) are of overriding importance in modern microelectronics where they undergo a continu- ous package complexity. Multilayer structures, split reference planes, various interconnects like bends, vias, etc. and trace circuit configurations in form of rectangular/circular loop, bent wire, linear dipoles, etc., are commonly mounted and present on hihgly integrated PCBs. These structures have led to an upsurge of interest in the analysis of the possible elec- tromagnetic interference (EMI) since they are often sources of unintentional radiated emission which can alter the EMC performance of real PCBs. Especially, in presence of an RLC- circuit, high-speed signals routed on the board may carry over resonances. These resonances tend, on their own, to carry interferences over much longer distances, which can not be predicted by field or gavanic coupling. The behavior of the reradiated field, with the PCB radar cross section (RCS) being the main parameter of interest, is therefore a good figure of merit in diagnosing radiation problems on the board. This paper addresses these particular points. Especially, it provides a rigorous approach to predict radiation from PCBs in a Giagahertz transverse electromagnetic (GTEM) cell. The analysis is based upon the use of the reciprocity theorem in combination with the application of the method of moment (MoM) to the scattered field yielding a generalized impedance matrix, whose determinant represents the characteristic poly- nomial of the scattering systems. After deriving an expression for the RCS in the next section, the generalized impedance matrix is evaluated for arbitrar- ily shaped wire radiating elements with a conducting plane reflector (section III). The real-axis method characterized by Sommerfeld-type integrals and moment-method solutions (1)- (3) is used to calculate elements of the impedance matrices. The effectiveness of the method is demonstrated by inves- tigating some canonical circuit configurations and structures illustrating sources of fundamental EMI mechanism (section IV). The validity and the accuracy of the analysis become ob- vious in view of the one to one correlation with measurements (section V).

This paper discusses the application of the so-called thin sheet approximation (TSA) for dielectric coatings to the calculation of the 3D coupling of printed circuit boards (PCBs) using the method of moments (MoM). By extending the TSA to open structures, the volume currents in the dielectric layer can be described by surface currents on the PEC conductor and the problem can be reduced to single current layers. As a consequence, the number of unknowns is reduced drastically. In order to verify the TSA approach and its accuracy and to investigate the influence of the layer and conductor thickness of coated PCBs, comparisons to results obtained by the classical MoM computation and a finite element (FEM) solver are given.

The research object in the work is the printed circuit boards (PCB) Production technological process using the additive technology of photopolymer 3D printing. The existing problem is that the manufacturing process of single-sided and double-sided PCBs, simple in technology, from the third to the fifth accuracy class, requires the use of a large amount of consumables and technological equipment. In turn, this affects the cost of the product. The research subject is models and methods for manufacturing PCB using photopolymer 3D printing. In order to reduce the cost of materials: film or aerosol photoresist, as well as reduce the number of technological operations, applying photoresist and for the manufacture of PCBs stencils, it is proposed to use photopolymer 3D printing technologies for the manufacture of PCBs. The paper analyzes the costs of Plexiwire Resin Basic Orange Transparen photopolymer resin for the manufacture of single-sided PCBs and calculates the cost of the consumable (resin) compared to the costs of dry film photoresist. 60 % cost of consumables (photopolymer resin) compared to dry film photoresist for making single-sided PCBs. The work is aimed at determining the dependence of the geometric dimensions of the PСВs topology and the consumption of photopolymer resin on the technological parameters of photopolymer exposure. A regression correlation model of the dependence of resin consumption on exposure parameters has been developed and correlation coefficients have been calculated. It has been established that with an increase in the exposure time of the photopolymer resin, the consumption of the photopolymer resin increases and the deviation of the geometric dimensions of the PCBs topology increases, which in turn negatively affects the quality of the product. Therefore, using the obtained regression model, it is possible to calculate the influence of parameters on the PCB topology and reduce the deviation of conductor sizes and resin consumption.

Analysis of field coupling and emissions from printed circuit boards (PCBs) is important for assessment of the immunity of the PCB to external radiation. Immunity of electronic systems is now tightly regulated in consumer markets. This paper presents a procedure for the analysis of susceptibility of PCBs. The procedure identifies a finite set of source and field points to increase the efficiency of the numerical testing. Reciprocity is used to decrease the number of external source locations that need to be used in the field coupling analysis through performing a radiation analysis. The numerical analysis of the PCB is performed using the Method of Moments (MoM). Numerical examples for the application of method are included. Further examples of the overall procedure will be presented.

The rapid development of information and communication technologies has driven the rapid growth of data traffic and the large requirement of high-speed optical transceiver modules. Usually, optical subassemblies through flexible printed circuit boards (PCBs) connect with the hard PCBs to compose as optical transceiver modules. Because of the impedance mismatch of connection between flexible PCB and hard PCB, the operation bandwidth of the module can be limited. In this paper, the design of connection between flexible PCB and hard PCB in optical subassembly modules will be investigated for increasing the operation speed of the module. First, the transmission bandwidth of flexible PCB is analyzed. High-frequency performances of three transmission line structures, micro-strip line, grounded coplanar waveguide, and top ground micro-strip line, are investigated in flexible PCB. High-frequency performances of flexible PCB with different bending types are also investigated. The flexible PCB has been verified to be suitable to use in 25 Gb/s applications. Next, the high-speed transmission performance is analyzed through the connection between flexible PCB and hard PCB, because the impedance mismatch usually occurs at the connection. The ground pads are added near the signal line of flexible PCB, and the ground pads are connected to the ground layer in PCB through ground vias. The anti-pad in hard PCB is added under the signal solder pad. The dip of S21 response can be eliminated by the optimized ground pad. The impedance mismatch can be reduced by the optimized anti-pad, the impedance increases from 40-Ω to 49-Ω at the connection between flexible PCB and hard PCB, and the transmission bandwidth can increase from 16.5 GHz to 23.5 GHz. TO-46 header is a common and low-cost packaging solution for DFB laser and photodiodes. The connection between flexible PCB and TO-46 header is also investigated. While the connection has a gap, the dip of frequency response will occur at lower frequency. While the connection is very close, the bandwidth can be larger than 25 GHz. The flexible PCB, hard PCB, and TO-46 header are combined together, and the 23 GHz transmission bandwidth can be obtained. The 25 Gb/s transmission eye diagram is also measured, and the eye height, rise time, fall time, and Q-factor are 268.14 mV, 13.78 ps, 13.56 ps, and 8.76, respectively. The combined flexible PCB, hard PCB, and TO-46 header are verified to be suitable to apply in 25 Gb/s optical subassembly modules, and will be able to be used in 100G Ethernet.

An innovative approach is described for diagnosing faults in printed circuit boards (PCB) and PCB components through the detection, analysis, and localization of electrical field changes that occur within and around the PCB. This method utilizes electromagnetic emissions (EME) originating from the PCB to determine circuit health. EME from rapidly changing voltages and currents within high-speed logic and other circuits have traditionally been seen as a problematic source of interference that must be eliminated to as great an extent as possible. However, changes within these emissions can be a highly significant indicator that a failure has occurred within a PCB component as well as within adjacent circuit card paths of the board itself. Further, the hardware and software requirements needed to capture and analyze these emissions are relatively simple in comparison to todaypsilas highly complex automatic test equipment. This unique approach involves analyzing electromagnetic emission signatures through automated means, and ascribing failures to the circuit board as a whole, as well as to the individual circuit board components.

"Electronic manufacturing is currently one of the fastest growing industrial areas. This is due to the rapid advances in the computer and telecommunications sectors. Due to these advances, new surface mount devices have been developed to achieve greater miniaturisation at lower costs. As a result, a new surface mount technology has been developed to mount these devices onto printed circuit boards. However, problems exist with aspects of this process, principally open solder joints which result from circuit board warpage. The aim of this thesis is to undertake a) both an experimental and theoretical investigation of the reflow solder process and b) to develop thermal and structural models to analyse circuit board warpage. This research should aid manufacturing engineers in understanding the influence of the solder reflow process parameters on board warpage. Extensive experimental testing of the circuit board materials during the process is also presented. The thermal model detailed in this thesis simulates a) forced convective heat transfer through air impingement to the boards and b) the three dimensional temperature distribution within a composite laminate. The thermal model predicts the temperature distribution within a populated laminated composite circuit board to within 3% when compared to experimental data. The experimental results show that the convective heat transfer coefficient is primarily dependant on Reynolds number, and also the orifice to plate distance and orifice diameter. It was found that at high Reynolds number, the heat transfer coefficient increases significantly at low orifice to board distance. This heat transfer rate has to be balanced against the maximum speed of the air to prevent the components been blown off the boards. The 5mm diameter orifice provides the optimum balance between air speed and heat transfer rate. The structural model simulates the influence of a) board support, b) reflow temperature profile, c) components on the board and d) board layup on circuit board deformation. The experimental appraisal and model predictions show that the warpage of the printed circuit boards is dependant on a) support of the board during the process, b) symmetry of the board layup, c) coefficients of thermal expansion of the board materials, d) temperature distribution in the boards i.e. symmetric or nonsymmetric about board centre and e) temperature applied to the board. This research proves that if adequate support is applied to the boards during the reflow soldering process then, the warpage of the printed circuit boards may be kept within acceptable margins. Board warpage exists in current printed circuit boards because a) the boards cannot be manufactured truly symmetric in layup and b) Non-uniform temperature distributions are present in the board during the solder reflow process which leads to non-uniform expansion of the constituent laminate layers due to their varying coefficients of thermal expansion."

Electromagnetic disturbances for vehicle-mounted radios can be caused mainly by conducted noise currents flowing out from vehicle-mounted multi-layer printed circuit boards (PCBs) to wire-harnesses. Using actual electronic equipment for vehicles, we previously showed that combining, not separating, the ground layer patterns of a digital circuit and an analog circuit is more advantageous to reduce the noise current outflow, while the mechanism remains unknown. In the present study, based on an idea that this mechanism should generate from a change in the amount of common return currents flowing to the ground, we measured noise current outflows from five types of simple PCBs having different ground patterns, which were validated from simulation with the method of moment. As a result, we could confirm that slits on a ground pattern allow conducted noise currents to flow out from PCBs, while the levels for the symmetric two slits ground types are smaller compared to the case for the asymmetric two slits ground types. The mechanism could be explained qualitatively from balanced conditions of an equivalent bridge circuit.

This study analyzes laser processing of glass-based printed circuit boards which have the capability to replace conventional substrate materials when electronics are required to operate at elevated temperatures. There is significant potential for glass-based circuit boards within the field of aerospace and electric mobility. The new circuit board concept consists of thin copper-coated borosilicate glass with thicknesses ranging from 150 µm to 500 µm. Conventional mechanical processing of this new circuit boards induces stress on the thin glass which can lead to damage of the substrate. Therefore, laser processing with a picosecond laser source is suggested as a tool within the production process of the new circuit boards. Two necessary processes are investigated using a pulsed picosecond laser with a pulse duration of 7 ps at a wavelength of 515 nm. Precise drill-holes for vertical connections of multilayer boards were produced where chipping at the cutting edge must be avoided. Selective ablation of the copper coating was performed to generate the electrical circuits. The results show that a well-defined ablation process is crucial to achieve adequate electrical isolation without damaging the glass substrate. The study also underlines the huge potential of laser processing with picosecond laser sources, which have proven to be a versatile instrument to drill thin glass and generate electrical circuits by selective ablation.This study analyzes laser processing of glass-based printed circuit boards which have the capability to replace conventional substrate materials when electronics are required to operate at elevated temperatures. There is significant potential for glass-based circuit boards within the field of aerospace and electric mobility. The new circuit board concept consists of thin copper-coated borosilicate glass with thicknesses ranging from 150 µm to 500 µm. Conventional mechanical processing of this new circuit boards induces stress on the thin glass which can lead to damage of the substrate. Therefore, laser processing with a picosecond laser source is suggested as a tool within the production process of the new circuit boards. Two necessary processes are investigated using a pulsed picosecond laser with a pulse duration of 7 ps at a wavelength of 515 nm. Precise drill-holes for vertical connections of multilayer boards were produced where chipping at the cutting edge must be avoided. Selective ablation of the ...

Ball grid array (BGA) component packages challenge the circuit board design with signal routing and layout, creating in some cases extra board layers and added vias all resulting in increased costs for the printed circuit board (PCB). As component densities increase and microBGA (μBGA) and other fine pitch components become more common, microvia‐in‐pad technology will ease the transition to these fine pitch components. This paper presents and profiles a cost‐effective solution to interconnecting BGAs on PCBs using laser drilled blind vias connecting the outer three or more layers of a multilayer circuit board. Following a discussion on the design advantages, a comprehensive outline of the PCB fabrication process explores a new procedure for the rapid production of via‐in‐pad multi‐depth blind via laser drilling.

We evaluate the discrimination power of different graph invariants in order to identify an appropriate measurement of similarity among printed circuit boards. We show that computationally expensive algorithmic evaluation of circuit boards equivalence based on the topology of the circuit boards is unnecessary in practice. Instead, the information about the circuit boards can be stored in terms of graph invariants, namely, number sequences characterizing the boards, which requires much less memory and enables quicker recognition of board equivalence. This straightforwardly leads to fast practical implementations of the search engines for the printed circuit boards. Our approach is multidisciplinary, as the tools were drawn from two fields; the industrial electronic engineering field, and the theoretic fields of graph theory and algorithms. A real case study on a search engine for printed circuit boards is conducted to illustrate the proposed approach. Finding an easily computable and complete set of graph invariants remains a challenging mathematical question.

A hybrid FEM/MOM method was used to solve a canonical printed circuit board (PCB) problem. The PCB is populated with three traces. One is a signal line and the other two are I/O lines that extend beyond the boundary of the board. The finite element method (FEM) was used to model the fields in the volume around the on-board trace. The method of moments (MOM) was employed to model the equivalent surface currents on the board and the current on the off-board traces. The FEM and MOM equations were coupled by forcing the continuity of tangential fields on the dielectric boundary. An efficient meshing strategy was employed to reduce the memory requirements. The major contributors to far fields in different frequency bands and for different polarizations are discussed.

Numerical analysis of crosstalk between two traces in a printed circuit board is presented using the method of moments (MoM). In the high-frequency range, the attenuation constant is neglected in the theory for its very small values. The width of the trace is accurately determined for the trace impedance of 50 ohm from the charge distribution on the traces without using an approximated empirical formula. Line capacitances are determined from the total charge on the conductors and the line potentials. The coupling capacitance and inductance are determined from in-phase and out-of-phase excitations between the traces. Crosstalk interference is calculated from these coupling parameters. Results of crosstalk obtained from the above technique are verified by comparing with those obtained from four other methods: (1) Ansoft HFSS software tool, (2) even mode and odd mode analysis, (3) empirical formulae of parasitic elements, and (4) measurements using a vector network analyser. All the results agreed well. The results obtained by using the method of moment technique are more stable, reliable, and accurate among all the described different methods. This paper shows that the analytical method using MoM is a useful tool for predicting crosstalk interference in PCB without using expensive simulation software.

The Modified Hermitian and skew-Hermitian splitting (MHSS) iteration method was presented and studied by Bai, Benzi and Chen (Computing, 87(2010), 93-111) for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical experiments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear system.