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Using Embedded Resistor Emulation and Trimming to Demonstrate Measurement Methods and Associated Engineering Model Development*

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Using Embedded Resistor Emulation and Trimming to Demonstrate Measurement Methods and Associated Engineering Model Development* IJEE 1830 Int. J. Engng Ed. Vol. 22, No. 1, pp. 000±000, 2006 0949-149X/91 $3.00+0.00 Printed in Great Britain. # 2006 TEMPUS Publications. Using Embedded Resistor Emulation and Trimming to Demonstrate Measurement Methods and Associated Engineering Model Development* PHILLIP A.M.SANDBORN AND PETER A.SANDBORN CALCE Electronic Products and Systems Center, Department of Mechanical Engineering, University of Maryland, College Park, MD, USA.E-mail: [email protected] Embedded resistors are planar resistors that are fabricated inside printed circuit boards and used as an alternative to discrete resistor components that are mounted on the surface of the boards.The successful use of embedded resistors in many applications requires that the resistors be trimmed to required design values prior to lamination into printed circuit boards.This paper describes a simple emulation approach utilizing conductive paper that can be used to characterize embedded resistor operation and experimentally optimize resistor trimming patterns.We also describe a hierarchy of simple modeling approaches appropriate to both college engineering students and pre-college students that can be verified with the experimental results, and used to extend the experimental trimming analysis.The methodology described in this paper is a simple and effective approach for demonstrating a combination of measurement methods, uncertainty analysis, and associated engineering model development. Keywords: embedded resistors; embedded passives; trimming INTRODUCTION process that starts with a layer pair that is pre- coated with resistive material that is selectively EMBEDDING PASSIVE components (capaci- removed to create the resistors.The layer contain- tors, resistors, and possibly inductors) within ing the resistor is laminated together with other printed circuit boards is one of a series of technol- layers to make the finished printed circuit board. ogy advances enabling performance increases, size One significant factor governing the applicabil- and weight reductions, and potentially cost advan- ity of embedded resistors is their tolerance level. tages in the manufacturing of electronic systems The tolerance to which a resistor can be fabricated [1].Figure 1 shows a comparison of surface mount determines the applications for which it can be and embedded resistors. used and potentially affects its impact on the yield Multilayer printed circuit boards are fabricated of the product.While discrete surface mount starting with dielectric layers that are plated on resistors can be pre-sorted by value, or even both sides with copper.Application-specific replaced during assembly when their value is not conductor patterns are created on each side of within the required range, embedded resistors the dielectric using a photosensitive resist and provide no such opportunity and must be within etching to remove the unnecessary copper.These design tolerance value before the board fabrication patterned `layer pairs' are stacked with a B-stage process is completed.Therefore, embedded resis- epoxy between them and laminated using high tors, depending on their method of fabrication and temperature and pressure.Holes can be drilled the application for which they are used, may be and plated in the laminated stack to create vertical `trimmed' to the desired value after they are connections.[Note, there are many printed circuit fabricated.To allow for trimming, embedded board fabrication process and material variations, resistors are designed to have a resistance value e.g., [2]. The process described here is one simpli- that is lower than that needed by the application. fied approach.] Embedded resistors (also called Trimming is then accomplished by cutting holes integral resistors) are fabricated by plating or into the resistor in order to increase its resistance printing a resistive material onto a layer that will value. be part of a printed circuit board (additive Embedded resistors are normally trimmed using process), or alternatively, using a subtractive a laser to micromachine a trough in the resistive element, [3].The length and path-shape of the trough determine the characteristics of the resis- tance change obtained.Several different path- * Accepted 18 May 2006. shapes can be used depending on the specific 1 2 P.A.M.Sandborn and P.A.Sandborn Fig.1. Surface mount and embedded resistors. trimming requirements.As the laser cuts the resistance' (in ohms per square), and L, W, and trough, the resistor value is measured and used T are the length, width, and thickness of the as feedback to control the trimming process. resistor.Therefore, for a constant aspect ratio Unfortunately, laser trimming equipment is expen- (L/W), a small planar resistor (dimensions in the sive and the process of trimming potentially repre- thousands of the inch) has the same resistance sents a throughput bottleneck in the board characteristics as a large area planar resistor fabrication process.Trimming has been identified (dimensions of inches), and trimming of small as one possible impediment to the widespread use resistors can be emulated using large area resistors. of embedded resistors [4, 5]. To emulate planar embedded resistors, we used This paper describes a simple methodology for conductive paper purchased from PASCO Scien- experimentally assessing embedded resistor trim tific (Model PK-9025).This type of paper is patterns that can be supplemented with the devel- usually used for tracing lines of equipotential and opment and verification of simple models that can electric fields, and comes in 8.5 Â 11 inch pages be used to extend the experimental results.The with a centimeter grid printed on it.Prior to work described herein has been successfully used exploring trimming of the resistors, each page of by both pre-college high school students and paper is cut to the desired resistor shapeÐin our within an undergraduate electronic packaging case approximately 1 cm was removed from all the curriculum for college-level mechanical and elec- edges of the pages and the remaining page is cut in trical engineering students.Students are motivated half to create two 28 Â 10 cm resistors.In order to by being able to work on a topic that is at the measure the resistance, metal clamps are placed on forefront of electronic systems design and fabrica- the ends of the resistor and an ohmmeter is tion, yet conceptually simple enough so as not to attached to the clamps via alligator clips, Fig.2. defeat their limited knowledge of physics and Students make an initial set of measurements on a engineering.The experiment and modeling single piece of paper by assembling the test setup, described in the paper provides students with an measuring, and disassembling the test setup, then understanding of resistance, resistance measure- repeating the process 10±15 times.The first thing ments, experimental uncertainty analysis, the en- noticed is that the resistance of the conductive gineering model development and verification paper varies from page-to-page.In order to make process, and the use of models to extend experi- the measurements from different pages compar- mental results. able, a page-specific `normalization' must be deter- mined.In order to normalize a page's mean resistance to 65 k ,65k was divided by the EMULATING EMBEDDED RESISTORS mean resistance from the initial measurements for the page to obtain a scaling factor, then each For a constant sheet resistance (ohms per measurement from that page of paper (as it is square), the resistance of a planar resistor does trimmed) is first multiplied by the scaling factor not change with size (i.e., length or width) as long before comparison with other pages.[For the 28 Â as the ratio of length to width (`aspect ratio') is 10 cm resistors suggested, 65 k was found to be constant, the approximate average resistance value over many pages of conductive paper and was therefore L L L L used as the normalization target.] R R ; 1 A TW T W W The way that the page measurements are normalized adjusts for page-to-page variation in where is the bulk resistivity, A is the cross- resistance due to variations in the sheet resistance sectional area of the resistor, R is the `sheet (R) but does not affect variations in the contact to Using Embedded Resistor Emulation and Trimming to Demonstrate Measurement Methods 3 semiconductor).Students can also check to see if thermocouple effects are significant by switching the ohmmeter connection and determining if there is any significant change in the resistance measured.In our experience, thermocouple effects, if present, are smaller than the measurement uncertainty.[The thermocouple effect is due to the thermal emf generated by the change in the temperature at the junction of the conductive paper and the silver contacts on each end, which form thermocouples.If the temperature at both ends of the resistor is the same, the thermal emfs will cancel and the resistance measured is the same, regardless of the way the meter is connected.If the temperature at one end is different from the other than the measured resistance will differ when the meter connections are switched.] Fig.2. Experimental setup. the conductive paper or other series resistance effect within the measurement path.Variations in RESISTOR TRIMMING: the sheet resistance could be due to thickness EXPERIMENTAL RESULTS variations in the conductive coating or moisture absorption by the paper.Variations in the Once the baseline measurements are made on a measurement path are quantified as measurement
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