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14 The PCB Magazine • June 2017 • Thin-film resistors are formed using lam- inates coated with resistive material deposited using vapor deposition onto copper foil. After chemically defining the resistor element geom- etry, the sheet layer is laminated (with the resis- tor element side down) to the designated circuit board layer. Ideal for multilayer organic circuit board fabrication, thin-film technology ensures the excellent uniformity of resistor material across the sheet, furnishing higher yields and improved resistor tolerances. Integrated thin- film resistor foil is supplied in a variety of foil widths and thicknesses using Grade 3 copper foil. Copper thicknesses of 18 µm (0.5 oz) and 35 µm (1 oz) are commonly available. Due to the printing and curing complexi- ty and process time for thick-film resistors, the printed board fabricator will prefer applying only one resistor value material onto the sub- strate base layer. Likewise, the thin-film sheet material is furnished in a single base value. The resistor base values are based on a square geom- etry. For example, the resistor value specified is 2KΩ. The fabricator prepares a base value of 1 KΩ material. The geometry furnished on the de- sign file to furnish the 2KΩ resistor element will be two squares in length. Likewise, a 2.5KΩ re- sistor element would require two and one-half squares. To maximize the number of resistor el- ements on the circuit layer, several techniques can be considered to achieve greater utilization of the process. For the more complex values the designer can string a number of squares togeth- er in either a single-line or serpentine configu- ration. Calculating Resistor Geometry Both thick-film and thin-film resistor mate- rials are formulated to furnish a wide range of primary values. The resistance of a linear resis- tor is written as: R = π × L/A = (π/t) × (L/w) = R s (L/W) Where, π = resistivity L = resistor length W = resistor width R s = sheet resistance in %/sq A = cross-section area T = Film thickness The thick-film materials are available in re- sistance values that range between 1Ω and 1 MΩ per square, while the thin-film sheet ma- terials can be furnished with resist values that range from 25Ω per square to 1 KΩ per square. The resistance value can be designed based on the equation of R = R s x N, where N is the number of squares, or aspect ratio. Using these standard resistor equations, along with actual resistor linearity and blend curves, the design- er will be able to calculate and design a variety of options for a given desired value. When de- veloping the resistor element in an 'L' shape or a serpentine configuration, the square geome- try at the corner transition will furnish a value that is only one-half the base value of the resist material. It is recommended by the suppliers to furnish resistor widths and lengths greater than 0.25 mm (0.010 in). Larger resistor dimensions will reduce the reliance on the print variations or accuracy of the copper etch processes to help in achieving the final resistor target tolerance. In regard to ter - minating the resistor elements, the land pattern geometry provided for the resistor termination should allow for a nominal 0.25 mm to 0.50 mm overlap of the resist material and consider allow - ances for fabrication process variables. When higher power loading is required the resistor must be sized accordingly. Refer to the supplier's resistor calculator for resistor sizes based on power dissipation requirements. For greater detail regarding formed resistor design, material and process parameters refer to IPC- 7092, IPC-2316 and IPC-4811 for additional in- formation. Part 2 of embedded component technology will focus on formed capacitor and inductor el- ement design, and will appear in the June issue of The PCB Design Magazine. PCB Vern Solberg is an independent technical consultant specializing in surface mount technology and microelectronics design and manufacturing technology. To read past columns or to contact the author, click here. EMBEDDING COMPONENTS, PART 1