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Principles of Cost Trade-Off The circuit design tools identify the resistors and capacitors that must be added to make an electronic circuit functional. The tools simulate circuit operation and size the resistors and capacitors as appropriate. Whether a resistor is purchased and mounted on the board surface or formed inside the board from a layer of resistive material has little effect on the electrical operation of a circuit. Therefore, if many resistors can be formed inside the board from the same series of chemical steps, the inclusion of perhaps thousands of internal resistors costs no more than adding one internal formed resistor. The critical economic analysis is to find the cost of adding internal formed resistors and then dividing by the number that can be used internally to see whether embedded resistors inside the board make sense.

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Resistors Resistors were the first component to be embedded in a multilayer board, making it a truly three-dimensional interconnection and circuit system. While early designs were custom for

each applicaton, over time design standards and best practices have been developed, which allow for successful inclusion of resistors, and other components, without the need to start from the beginning The following discussion provides these for resistors, with subsequent sections providing similar information for other components 21411 Resistor Terminology The designer must size embedded formed passive resistors This is in contrast to the library selection of conventionally manufactured resistors that are selected from a table of available components The principle of embedded resistors is given by the following formula for a term ohms per square; this means that any square area defined in the material will have the same resistance and that by grouping squares appropriately, the designer can define the resulting resistance Resistance in any resistor is determined by Eq 21.

1 R = r L/A where R = resistance in ohms r = resistivity in ohm meters (inches) L = length of the resistor A = cross-sectional area (resistor thickness times resistor width) Note: Resistivity (r) is a material property It is a constant at a given temperature and expressed in resistance units (ohms) for area and length For instance, the resistivity of copper is r = 709 e 7 ohm in2/in Sheet resistance is a commonly used term to describe raw materials used in embedded formed resistors These materials are manufactured in sheet form with a constant thickness, giving a uniform R value for any square resistor Therefore, the material is specified by its sheet resistance value, given in ohms/square ( / ) The resistance of a specific resistor is simply designed by changing the ratio of length to width.

For instance, 100 / material forms a 100 ohm resistor in any square configuration A resistor three squares long by one square wide would be 300 , and a resistor two squares wide by one square long would be 50 21412 Resistor Design Parameters The circuit board designer is responsible for sizing the resistor to give the appropriate value Material suppliers have given their sizing parameters to computer-aided design (CAD) software companies for entry in their component libraries Also, manufacturing tolerances for each supplier product have been communicated to computer-aided manufacturing (CAM) suppliers Figure 212 gives typical design parameters for sizing both the active embedded formed resistor area and the termination pads for the traditional copper innerlayer upon which the resistor is built (Eq 211).

Capacitor Design All production formed capacitors use laminate-like materials. Most typically, the capacitor manufacturer starts with an especially flat copper foil on at least one side. This copper foil is precisely coated with the dielectric material: filled polymer. Either the top foil electrode is then laminated or two layers of coated foil are bonded polymer to polymer. 21.4.2.1 Capacitor Terminology. Capacitors are electrical elements that store charge on parallel electrode plates. They are not batteries that operate chemically. Capacitors store more charge with closer parallel plates, and the higher the dielectric constant, the more charge is stored.

LW Pw Print width PL Print length RW Resistor width RL Resistor length TW Termination width LW Line width EZ Encapsulant zone (CTF only)