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We now consider a more formal and generalized study of gravitational waves abstracted from sources and propagating at the speed of light. In particular, we study vacuum pp-waves where pp means plane fronted waves with parallel rays. Considered to travel in a at background spacetime described by the Minkowski metric, a pp-wave is one that admits a covariantly constant null vector eld. We now consider this de nition. Let k a be a null vector such that the covariant derivative vanishes; i.e., ka,b = 0 (13.28)

Because of variations in the PCB manufacturing process, additional CAM-tooling operations may be required. Variations in manufacturing that may call for additional tooling include the following:

Rivet lamination versus pin lamination Laser drilling Multiple panel sizes Very large lamination presses (48 in. 48 in.) A very high degree of automation

New processes or PCB product features that may require additional tooling processes include the following:

Embedded passives and embedded waveguides are complicated to implement in production. Alignment and overlap are critical. Proper scaling for the particular embedded materials is especially important, depending on whether the materials are additive or subtractive. Figure 20.18 shows some of the critical tooling dimensions.

An important step in all the processes already defined is the necessity for proper information management. Archival of PCB customer-supplied information and the files generated from the tooling process are critical for disaster recovery. Archiving systems available on the market also provide for centralized data management and distribution of the information to the various departments within an organization. 20.7.1 Macros Macros (or scripts, as they are sometimes called) are used to automate tooling operations. Most modern CAM systems come with the facility to create, edit, debug, and exercise macros. One example of a macro was shown in Fig. 20.9. This macro automatically scans all the CAM information (artwork and NC files) and reports minimum, maximum, and critical geometries. 20.7.2 Design-to-Fab and Assembly Automation Although a vast number of sophisticated CAD and CAM software packages are available today, experienced operators are still needed to exercise this software. During the era of captive printed circuit manufacturing by original equipment manufacturers (OEMs), internally developed software tools were created that actually automated the entire CAM tooling process. This level of automation was made possible through the development of software that automatically created drill, rout, fabrication, and panel drawings and manufacturing notes from the CAD database. In doing all this, the software captured in a digital header file all the pertinent information on the drawings. The header file could then automatically supply macros that would complete all the tooling. Although this software was never extended to the commercial market, today new automatic blueprint creation software is available that works off of the CAD database.

I would like to thank Jeff Miller, WISE Software Solutions (www.wssi.com), DownStream Technologies (www.downstreamtech.com), and Julian Coates of Valor, Inc. (www.valor.com) for their invaluable contributions to this chapter.

Historically, electrical components have been mounted on the outside of printed circuit boards, either with through hole leads or with terminations all on a single side (surface mount) with the interconnection traces embedded inside the board. Technology, however, has been developed to embed electrical components inside the board also. The earliest components to be embedded were resistors, which are made by etching a pattern on a sheet of resistive material and then connecting them with the rest of the circuit through the standard multilayer process. In addition, capacitors are formed from thin dielectric material between closely spaced copper-foil planes, and inductors are formed by etching coils of the copper conductive foil during innerlayer manufacture. These fabrication techniques have expanded to include the ability to place small, discrete passive components inside the board. This allows the normal multilayer board pressing operation to encapsulate these placed components.

Components These are the electrical units that make up all electrical devices. Passive components These components including resistors, capacitors, or inductors influence electrical flow in a circuit, but do not cause a gain in current or voltage. Active components In contrast, these components can provide gain in an electronic circuit. Integrated passive arrays Multiple passive devices may be packaged in either a leaded or surface-mount technology (SMT) package or sometimes in arrays of all the same value. Integrated passive component is a general term for multiple passive components that share a substrate and packaging. Most typically, integrated passives are on the surface of a separate substrate that is then placed in an enclosure and surface-mounted on the primary interconnect substrate, in which case they are called passive arrays or passive networks. This chapter discusses only embedded components.