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76 DESIGN007 MAGAZINE I JUNE 2021 geometry can be extended further in length to provide a broad range of resistor values. When the resistor element length becomes too long, however, it can restrict or block efficient cir- cuit routing paths. To compress the surface area required for the more complex resistor elements, it is common practice to compress the physical area using a "serpentine" configu- ration typical of that exhibited in Figure 4. e design rules for the serpentine-config- ured resistor pattern are significantly different than the straight bar configuration detailed above. When developing the resistor element in a serpentine configuration the designer must adjust the basic value at each corner of the serpentine pattern. e square geometry located at each corner transition will furnish a value that is only one-half the resist material's base value. e 19-square resistor pattern illus- trated in Figure 5 represents a 15K-ohm resis- tor utilizing 1K-ohm base value material. Regarding individual resistor tolerance con- trol, thin-film material suppliers note that most circuit board fabricators will anticipate a resistor tolerance at or less than 20%. e resulting tolerance will be dependent on the precision of the image and etch process. Pre- cise etch control will repeatedly produce resis- tors with a tolerance range encompassed by what the fabricator can maintain on controlled impedance lines and the published sheet toler- ance. Variation of the tolerance can be mini- mized by maintaining a uniform element width (> 200-micron) for the resistor patterns and fine-tuning the resistor element length to achieve the required target resistor value. But the designer must keep in mind that over spec- ifying resistor tolerance will likely impact pro- cessing costs. Sourcing Thin-Film Resistive Materials Resist coating can be furnished on any cop- per foil thickness, but thicknesses of 12 µm, 18 µm (0.5 oz) and 35 µm (1 oz) are likely to be more available because they are com- monly selected for a wide range of multilayer organic circuit board applications. e two leading suppliers of the copper foils furnished with the resistive coatings in North America Figure 3: Subsurface conductor layer with formed thin-film resistors. (Image source: Ohmega Technologies, Inc.) Figure 4: Serpentine-configured thin-film resistor examples. (Image source: Ohmega Technologies, Inc.) Figure 5: Serpentine resistor element design rules.