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Again, the value of embedded capacitors must be designed to the correct size. The value of a formed embedded capacitor is given by the Eq. 21.2. C = A Dk K/t where C is the value of the capacitor A is the area of the formed planar capacitor L W Dk is the dielectric constant of the capacitor material t is the thickness between the capacitor plates K is a conversion constant = 8.854 10 14 Farads/cm 21.4.2.2 Capacitor Design Parameters. Similar design tolerancing for capacitor design parameters (compared to resistors in Sec. 24.4.1) is available for capacitors, as shown in Fig. 21.3. (21.2)

Even conventional epoxy glass laminate has some capacitance value, and the oldest formed embedded capacitors were carefully controlled thin conventional glass/epoxy laminate layers. Both epoxy resin and E-glass have dielectric constants of about 4, not a particularly large value. However, by eliminating the glass and adding compounds such as barium-titanate to the epoxy or polyimide resin, dielectric constants can be improved to the 10 to 20 range. If really high capacitance values are needed, ceramic or inorganic compositions must be used. Newer technologies demonstrate dielectric constants in the 100 to 2,000 range, capable of forming large value capacitors inside the circuit board. These larger capacitors are useful for decoupling, one of the largest uses of capacitors. Thickness is the divisor in the capacitance formula. The smaller the dielectric thickness, the higher the device capacitance. Early formed embedded distributed capacitors simply used the readily available 100 micron (4 mil) epoxy/glass innerlayer construction, common in multilayer circuit boards. Then, thinner woven glass allowed 50 micron glass/epoxy layers, doubling the device capacitance. Finally, polymer only or barium-titanate-filled polymer demonstrated thicknesses down to 8 microns, improving capacitance 6 to 20 times the value of the original 100 micron epoxy glass. With the thinner materials comes a higher price tag for precision laminate manufacture and special fabrication/handling techniques. The cost/benefit analysis is a trade-off between these premium materials and the smaller-size/higher-capacitance values of the filled polymers.

This tells us that if l a is covariantly constant, then the gravitational wave of a pp-wave spacetime

Inductors Inductors use the magnetic effects of electrons traveling in wires to influence the travel speed of other electrical signals. Typically inductors are a coil configuration. No special material technology has been demonstrated for inductors. These spirals of copper circuitry are typically formed similarly to the copper-conductive traces of innerlayers. Again, design software must determine the line width, length of the coil, and the number of turns of copper to size the proper inductor.

Resistor Materials Resistors, discrete or formed, are actually very poor electrical conductors when compared to copper. Their function is to restrict the flow of electricity in a circuit. Common compositions of resistors include metal oxides, carbon particles, or small conductive particles separated widely by an organic polymer. Conventionally, the value of a resistor is rated in ohms ( ), with higher values restricting more current. Also, resistors are sized by tolerance in percentage, allowable maximum current, and parameters that deal with the electrical frequency of operation. Material suppliers have designated the range of resistance values that are optimum for their material. The designer determines the length and width that is allowable in the design, and then determines which material to specify for manufacture so that the final resistor value is achieved in the allocated circuit board space. Formed embedded resistors of similar values are designed on one specific layer so that the maximum economic value is achieved for that layer. Materials are also available that can combine mixed values of resistance on one layer. Polymer thick films (PTF) are applied by successive screen print/cure cycles so that all the desired resistance values can be made on one layer. Also, some sheet capacitance manufacturers laminate a layer of resistor foil as one electrode in their construction. Therefore, a fabricator can mix resistance and capacitance on one sheet type raw material.

Public Speaking and Presentations Demysti ed is divided into three sections: Getting Started, Putting the Pieces Together, and Stand and Deliver. If one of these phases is most interesting or challenging for you, start your reading there. At the end of each chapter you ll nd ve multiple choice questions to test your learning. The chapters within each section stand alone, so feel free to open to any topic for a quick tip or suggestion.