Computer-Aided Resistive Taper Design

Matthew Thomas
Boeing Phantom Works

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    Resistive tapers, in which surface resistivity is graded or "tapered" in one or more directions, play an important role in the control of electromagnetic properties of materials and structures. This role is appreciated by those who fabricate conductive coatings and paper, dielectric coatings, and EMI/RFI shielded coatings. Unfortunately, the drawbacks to traditional resistive taper fabrication are significant. Resistive tapers are generally produced by blending materials of different resistivities in a binding medium and spraying the resulting blend. Such blending assumes that the individual component materials are homogeneous and that the product resistivity can be computed from a linear mixing rule. These assumptions are not always tenable. Also, spraying the resulting blend creates a resistive taper that is, at best, inexact. One usually must settle for a very coarse approximation to the desired grade. In addition, the traditional resistive taper quality depends upon the technician who sprays it. If the technician is highly skilled, the resistive taper quality is primarily limited by the blended material; if she or he is less skilled, the taper quality suffers accordingly. Technician fatigue also reduces taper quality, and robotic arms remain a prohibitively expensive alternative. Furthermore, spraying traditional resistive tapers works best for rectangular shapes. It is very difficult to spray a resistive taper in nonrectangular shapes. It is almost impossible to spray a taper whose resistivity is graded along a radial dimension. Conventional taper-spraying methods are simply incapable of creating such detailed, unconventional tapers.

    Motivated by a need for better and cost-effective tapers, computer-aided resistive tapers (CARTs) offer significant improvements over traditional resistive tapers. CARTs are created by photochemically etching a Mathematica-generated dot pattern into a kiloangstrom-thick metallic coating upon a 0.001"-thick polyimide or other substrate. This process is clean and inexpensive; it is similar to printed circuit board fabrication in the computer industry. The metallic coating is truly homogeneous, the dot pattern is well defined, and no mixing rule is needed to determine the resistivity variation in the taper direction. With Mathematica, one can create virtually any dot pattern, which leads to virtually any corresponding resistive taper. Compared to traditional resistive tapers, CARTs show well-controlled resistive grades. Only computer memory and one's understanding of mathematics limit the types of CART grades that can be created. In addition, CART production is robust in comparison to resistive tapers, and CARTs can be fabricated in a wide variety of shapes (e.g., ellipses, circles, trapezoids, shapes to fit into sharp corners) with no increase in fabrication costs. Established by U.S. Patent No. 5,712,613, CARTs offer an excellent example of the key role Mathematica has played and will continue to play in an important industrial fabrication process.