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fsrguide

Course: MAS 836, Fall 2009
School: MIT
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product The information contained in this document is designed to provide general information and guidelines only and must not be used as an implied contract with Interlink Electronics, Inc. Acknowledging our policy of continual product development, we reserve the right to change, without notice, and detail in this publication. Since Interlink Electronics has no control over the conditions and method of use of our...

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product The information contained in this document is designed to provide general information and guidelines only and must not be used as an implied contract with Interlink Electronics, Inc. Acknowledging our policy of continual product development, we reserve the right to change, without notice, and detail in this publication. Since Interlink Electronics has no control over the conditions and method of use of our products, we suggest that any potential user confirm their suitability before adopting them for commercial use. Version 1.0 90-45632 Rev. D FSR Integration Guide & Evaluation Parts Catalog With Suggested Electrical Interfaces Force Sensing Resistors An Overview of the Technology ......................................................... Page 3 Force vs. Resistance.............................................................................................................. Page 3 Force vs. Conductance.......................................................................................................... Page 4 FSR Integration Notes A Step-by-Step Guide to Optimal Use .................................................... Page 6 FSR Usage Tips The Dos and Donts ......................................................................................... Page 8 Evaluation Parts Catalog Descriptions and Dimensions ............................................................... Page 9 General FSR Characteristics ........................................................................................................... Page 12 Simple FSR Devices and Arrays........................................................................................... Page 12 For Linear Pots .................................................................................................................... Page 13 Glossary of Terms ............................................................................................................................ Page 14 Suggested Electrical Interfaces - Basic FSRs ................................................................................ Page 16 FSR Voltage Divider .......................................................................................................... Page 16 Adjustable Buffers .............................................................................................................. Page 17 Multi-channel FSR to Digital Interface .............................................................................. Page 18 FSR Variable Force Threshold Switch ............................................................................... Page 19 FSR Variable Force Threshold Relay Switch ..................................................................... Page 20 FSR Current-to-Voltage Converter .................................................................................... Page 21 Additional FSR Current-to-Voltage Converters ................................................................. Page 22 FSR Schmitt Trigger Oscillator .......................................................................................... Page 23 Interlink Electronics manufactures custom FSR devices to meet the needs of specific customer applications. FSR devices can be produced in almost any shape, size, and geometry. To discuss custom design or to obtain a quote, contact Interlink Electronics at (805) 484-8855. Force Sensing Resistors An Overview of the Technology Force Sensing Resistors (FSR) are a polymer thick film (PTF) device which exhibits a decrease in resistance with an increase in the force applied to the active surface. Its force sensitivity is optimized for use in human touch control of electronic devices. FSRs are not a load cell or strain gauge, though they have similar properties. FSRs are not suitable for precision measurements. Force vs. Resistance The force vs. resistance characteristic shown in Figure 2 provides an overview of FSR typical response behavior. For interpretational convenience, the force Figure 1: FSR Construction vs. resistance data is plotted on a log/log format. These data are representative of our typical devices, with this particular force-resistance characteristic being the response of evaluation part # 402 (0.5 [12.7 mm] diameter circular active area). A stainless steel actuator with a 0.4 [10.0 mm] diameter hemispherical tip of 60 durometer polyurethane rubber was used to actuate the FSR device. In general, FSR response approximately follows an inverse power-law characteristic (roughly 1/R). Referring to Figure 2, at the low force end of the force-resistance characteristic, a switchlike response is evident. This turn-on threshold, or break force, that swings the resistance from greater than 100 k to about 10 k (the beginning of the dynamic range that follows a power-law) is determined by the substrate and overlay thickness and flexibility, size and shape of the actuator, and spacer-adhesive thickness (the gap between the facing conductive elements). Break force increases with increasing substrate and overlay rigidity, actuator size, and spaceradhesive thickness. Eliminating the adhesive, or keeping it well away from the area where the force is being applied, such as the center of a large FSR device, will give it a lower rest resistance (e.g. stand-off resistance). Figure 2: Resistance vs. Force FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 5 At the high force end of the dynamic range, the response deviates from the power-law behavior, and eventually saturates to a point where increases in force yield little or no decrease in resist-ance. Under these conditions of Figure 2, this saturation force is beyond 10 kg. The saturation point is more a function of pressure than force. The saturation pressure of a typical FSR is on the order of 100 to 200 psi. For the data shown in Figures 2, 3 and 4, the actual measured pressure range is 0 to 175 psi (0 to 22 lbs applied over 0.125 in2). Forces higher than the saturation force can be measured by spreading the force over a greater Figure 3: area; the overall pressure is then kept Conductance vs. Force (0-10Kg) below the saturation point, and dynamic response is maintained. However, the converse of this effect is also true, smaller actuators will saturate FSRs earlier in the dynamic range, since the saturation point is reached at a lower force. Force vs. Conductance In Figure 3, the conductance is plotted vs. force (the inverse of resistance: 1/r). This format allows interpretation on a linear scale. For reference, the corresponding resistance values are also included on the right vertical axis. A simple circuit called a current-to-voltage converter (see page 21) gives a voltage output directly proportional to FSR conductance and can be useful where response linearity is desired. Figure 3 also includes a typical part-to-part repeatability envelope. This error band determines Figure 4: Conductance vs. Force (0-1Kg) Low Force Range the maximum accuracy of any general force measurement. The spread or width of the band is strongly dependent on the repeatability of any actuating and measuring system, as well as the repeatability tolerance held by Interlink Electronics during FSR production. Typically, the part-to-part repeatability tolerance held during manufacturing ranges from 15% to 25% of an established nominal resistance. Page 6 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Figure 4 highlights the 0-1 kg (0-2.2 lbs) range of the conductance-force characteristic. As in Figure 3, the corresponding resistance values are included for reference. This range is common to human interface applications. Since the conductance response in this range is fairly linear, the force resolution will be uniform and data interpretation simplified. The typical part-to-part error band is also shown for this touch range. In most human touch control applications this error is insignificant, since human touch is fairly inaccurate. Human factors studies have shown that in this force range repeatability errors of less than 50% are difficult to discern by touch alone. FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 7 FSR Integration Notes A Step-by-Step Guide to Optimal Use For best results, follow these seven steps when beginning any new product design, proof-of-concept, technology evaluation, or first prototype implementation: 1. Start with Reasonable Expectations (Know Your Sensor) The FSR sensor is not a strain gauge, load cell or pressure transducer. While it can be used for dynamic measurement, only qualitative results are generally obtainable. Force accuracy ranges from approximately 5% to 25% depending on the consistency of the measurement and actuation system, the repeatability tolerance held in manufacturing, and the use of part calibration. Accuracy should not be confused with resolution. The force resolution of FSR devices is better than 0.5% of full use force. 2. Choose the Sensor that Best Fits the Geometry of Your Application Usually sensor size and shape are the limiting parameters in FSR integration, so any evaluation part should be chosen to fit the desired mechanical actuation system. In general, standard FSR products have a common semiconductor make-up and only by varying actuation methods (e.g. overlays and actuator areas) or electrical interfaces can different response characteristics be achieved. 3. Set-up a Repeatable and Reproducible Mechanical Actuation System When designing the actuation mechanics, follow these guidelines to achieve the best force repeatability: Provide a consistent force distribution. FSR response is very sensitive to the distribution of the applied force. In general, this precludes the use of dead weights for characterization since exact duplication of the weight distribution is rarely repeatable cycle-to-cycle. A consistent weight (force) distribution is more difficult to achieve than merely obtaining a consistent total applied weight (force). As long as the distribution is the same cycle-to-cycle, then repeatability will be maintained. The use of a thin elastomer between the applied force and the FSR can help absorb error from inconsistent force distributions. Keep the actuator area, shape, and compliance constant. Charges in these parameters significantly alter the response characteristic of a given sensor. Any test, mock-up, or evaluation conditions should be closely matched to the final use conditions. The greater the cycle-to-cycle consistency of these parameters, the greater the device repeatability. In human interface applications where a finger is the mode of actuation, perfect control of these parameters is not generally possible. However, human force sensing is somewhat inaccurate; it is rarely sensitive enough to detect differences of less than 50%. Control actuator placement. In cases where the actuator is to be smaller than the FSR active area, cycle-to-cycle consistency of actuator placement is necessary. (Caution: FSR layers are held together by an adhesive that surrounds the electrically active areas. If force is applied over an area which includes the adhesive, the resulting response characteristic will be drastically altered.) In an extreme case (e.g., a large, flat, hard actuator that bridges the bordering adhesive), the adhesive can present FSR actuation Page 8 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Keep actuation cycle time consistent. Because of the time dependence of the FSR resistance to an applied force, it is important when characterizing the sensor system to assure that increasing loads (e.g. force ramps) are applied at consistent rates (cycle-to-cycle). Likewise, static force measurements must take into account FSR mechanical setting time. This time is dependent on the mechanics of actuation and the amount of force applied and is usually on the order of seconds. 4. Use the Optimal Electronic Interface In most product designs, the critical characteristic is Force vs. Output Voltage, which is controlled by the choice of interface electronics. A variety of interface solutions are detailed in the TechNote section of this guide. Summarized here are some suggested circuits for common FSR applications. For FSR Pressure or Force Switches, use the simple interfaces detailed on pages 16 and 17. For dynamic FSR measurements or Variable Controls, a current-to-voltage converter (see pages 18 and 19) is recommended. This circuit produces an output voltage that is inversely proportional to FSR resistance. Since the FSR resistance is roughly inversely proportional to applied force, the end result is a direct proportionality between force and voltage; in other words, this circuit gives roughly linear increases in output voltage for increases in applied force. This linearization of the response optimizes the resolution and simplifies data interpretation. 5. Develop a Nominal Voltage Curve and Error Spread When a repeatable and reproducible system has been established, data from a group of FSR parts can be collected. Test several FSR parts in the system. Record the output voltage at various pre-selected force points throughout the range of interest. Once a family of curves is obtained, a nominal force vs. output voltage curve and the total force accuracy of the system can be determined. 6. Use Part Calibration if Greater Accuracy is Required For applications requiring the highest obtainable force accuracy, part calibration will be necessary. Two methods can be utilized: gain and offset trimming, and curve fitting. Gain and offset trimming can be used as a simple method of calibration. The reference voltage and feedback resistor of the current-to-voltage converter are adjusted for each FSR to pull their responses closer to the nominal curve. Curve fitting is the most complete calibration method. A parametric curve fit is done for the nominal curve of a set of FSR devices, and the resultant equation is stored for future use. Fit parameters are then established for each individual FSR (or sending element in an array) in the set. These parameters, along with the measured sensor resistance (or voltage), are inserted into the equation to obtain the force reading. If needed, temperature compensation can also be included in the equation. 7. Refine the System Spurious results can normally be traced to sensor error or system error. If you have any questions, contact Interlink Electronics Sales Engineers to discuss your system and final data. FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 9 FSR Usage Tips The Dos and Donts Do follow the seven steps of the FSR Integration Guide. Do, if possible, use a firm, flat and smooth mounting surface. Do be careful if applying FSR devices to curved surfaces. Pre-loading of the device can occur as the two opposed layers are forced into contact by the bending tension. The device will still function, but the dynamic range may be reduced and resistance drift could occur. The degree of curvature over which an FSR can be bent is a function of the size of the active area. The smaller the active area, the less effect a given curvature will have on the FSRs response. Do avoid air bubbles and contamination when laminating the FSR to any surface. Use only thin, uniform adhesives, such as Scotch brand double-sided laminating adhesives. Cover the entire surface of the sensor. Do be careful of kinks or dents in active areas. They can cause false triggering of the sensors. Do protect the device from sharp objects. Use an overlay, such as a polycarbonate film or an elastomer, to prevent gouging of the FSR device. Do use soft rubber or a spring as part of the actuator in designs requiring some travel. Do not kink or crease the tail of the FSR device if you are bending it; this can cause breaks in the printed silver traces. The smallest suggested bend radius for the tails of evaluation parts is about 0.1 [2.5 mm]. In custom sensor designs, tails have been made that bend over radii of 0.03 (0.8 mm]. Also, be careful if bending the tail near the active area. This can cause stress on the active area and may result in pre-loading and false readings. Do not block the vent. FSR devices typically have an air vent that runs from the open active area down the length of the tail and out to the atmosphere. This vent assures pressure equilibrium with the environment, as well as allowing even loading and unloading of the device. Blocking this vent could cause FSRs to respond to any actuation in a non-repeatable manner. Also note, that if the device is to be used in a pressure chamber, the vented end will need to be kept vented to the outside of the chamber. This allows for the measurement of the differential pressure. Do not solder directly to the exposed silver traces. With flexible substrates, the solder joint will not hold and the substrate can easily melt and distort during the soldering. Use Interlink Electronics standard connection techniques, such as solderable tabs, housed female contacts, Z-axis conductive tapes, or ZIF (zero insertion force) style connectors. Do not use cyanoacrylate adhesives (e.g. Krazy Glue) and solder flux removing agents. These degrade the substrate and can lead to cracking. Do not apply excessive shear force. This can cause delamination of the layers. Do not exceed 1mA of current per square centimeter of applied force (actuator area). This can irreversibly damage the device. Page 10 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Evaluation Parts Descriptions and Dimensions Figure 5: Part No. 400 (0.2 Circle) Figure 6: Part No. 402 (0.5 Circle) Active Area: 0.5 [12.7] diameter Active Area: 0.2 [5.0] diameter Nominal Thickness: 0.012 [0.30 mm] Material Build: Semiconductive layer 0.004 [0.10] PES Spacer adhesive 0.002 [0.05] Acrylic Conductive layer 0.004 [0.10] PES Rear adhesive 0.002 [0.05] Acrylic Connector options a. No connector b. Solder Tabs (not shown) c. AMP Female connector Nominal thickness: 0.018 [0.46 mm] Material Build: Semiconductive Layer 0.005 [0.13] Ultem Spacer Adhesive 0.006 [0.15] Acrylic Conductive Layer 0.005 [0.13] Ultem Rear Adhesive 0.002 [0.05] Acrylic Connector a. No connector b. Solder Tabs (not shown) c. AMP Female connector Dimensions in brackets: millimeters Dimensional Tolerance: 0.015 [0.4] Thickness Tolerance: 10% FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 11 Active Area: 1.5 [38.1] x 1.5 [38.1] Nominal thickness: 0.018 [0.46 mm] Material Build: Semiconductive Layer 0.005 [0.13] Ultem Spacer Adhesive 0.006 [0.15] Acrylic Conductive Layer 0.005 [0.13] Ultem Rear Adhesive 0.002 [0.05] Acrylic Connectors a. No connector b. Solder Tabs (not shown) c. AMP Female connector Figure 7: Part No. 406 (1.5 Square) Dimensions in brackets: millimeters Dimensional Tolerance: 0.015 [0.4] Tolerance: Thickness 10% Page 12 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Active Area: 24 [609.6] x 0.25 [6.3] Nominal thickness: 0.135 [0.34 mm] Material Build: Semiconductive Layer 0.004 [0.10] PES Spacer Adhesive 0.0035 [0.089] Acrylic Conductive Layer 0.004 [0.10] PES Rear Adhesive 0.002 [0.05] Acrylic Connectors a. No connector b. Solder Tabs (not shown) c. AMP Female connector Figure 8 Part No. 408 (24 Trimmable Strip) Dimensions in brackets: millimeters Dimensional Tolerance: 0.015 [0.4] Thickness Tolerance: 10% FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 13 General FSR Characteristics These are typical parameters. The FSR is a custom device and can be made for use outside these characteristics. Consult Sales Engineering with your specific requirements. Simple FSR Devices and Arrays PARAMETER Size Range Device thickness Force Sensitivity Range Pressure Sensitivity Range Part-to-Part Force Repeatability Single Part Force Repeatability Force Resolution Break Force (Turn-on Force) Stand-Off Resistance Switch Characteristic Device Rise Time Lifetime Temperature Range Maximum Current Sensitivity to Noise/Vibration EMI / ESD Lead Attachment VALUE Max = 20 x 24 (51 x 61 cm) Min = 0.2 x 0.2 (0.5 x 0.5 cm) 0.008 to 0.050 (0.20 to 1.25 mm) < 100 g to > 10 kg < 1.5 psi to > 150 psi (< 0.1 kg/cm2 to > 10 kg/cm2) 15% to 25% of established nominal resistance 2% to 5% of established nominal resistance Better than 0.5% full scale 20 g to 100 g (0.7 oz to 3.5 oz) > 1M Essentially zero travel 1-2 msec (mechanical) > 10 million actuations -30C to +70C I mA/cm2 of applied force Not significantly affected Passive device Standard flex circuit techniques Dependent on materials Dependent on mechanics and FSR build Unloaded, unbent NOTES Any shape Dependent on materials Dependent on mechanics Dependent on mechanics With a repeatable actuation system With a repeatable actuation system Page 14 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces For Linear pots PARAMETER Positional Resolution Positional Accuracy VALUE 0.003 to 0.02 (0.075 to 0.5 mm) Better than 1% of full length NOTES Dependent on actuator size FSR terminology is defined on pages 14 and 15 of this guide. The product information contained in this document is designed to provide general information and guidelines only and must not be used as an implied contract with Interlink Electronics. Acknowledging our policy of continual product development, we reserve the right to change without notice any detail in this publication. Since Interlink Electronics has no control over the conditions and method of use of our products, we suggest that any potential user confirm their suitability before adopting them for commercial use. FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 15 Glossary of Terms Active Area Actuator Applied Force Array Break Force Cross-talk Driff Durometer EMI ESD The area of an FSR device that responds to normal force with a decrease in resistance. The object which contacts the sensor surface and applies force to FSRs. The force applied by the actuator on the active area of the sensor. Any grouping or matrix of FSR sensors which can be individually actuated and measured. The minimum force required, with a specific actuator size, to cause the onset of the FSR response. Measurement noise or inaccuracies of a sensor as a result of the actuation of another sensor on the same substrate. See also false triggering. The change in resistance with time under a constant (static) load. Also called resistance drift. The measure of the hardness of rubber. Electromagnetic interference. Electrostatic discharge. False triggering The unwanted actuation of a FSR device from unexpected stimuli; e.g., bending or cross-talk. Fixed Resistor Footprint The printed resistor on linear potentiometers that is used to measure position. Surface area and force distribution of the actuator in contact with the sensor surface. Force Resolution The smallest measurable difference in force. FSR Force Sensing Resistors. A polymer thick film device with exhibits a decrease in resistance with an increase in force applied normal to the device surface. Graphic Overlay A printed substrate that covers the FSR. Usually used for esthetics and protection. Housed Female A stitched on AMP connector with a receptacle (female) ending. A black plastic housing protects the contacts. Suitable for removable ribbon cable connector and header pin attachment. Hysteresis In a dynamic measurement, the difference between instantaneous force measurements at a given force for an increasing load versus a decreasing load. Interdigitating Electrodes The conductor grid. An interweaving pattern of linearly offset conductor traces used to achieve electrical contact. This grid is shunted by the semiconductor layer to give the FSR response. Lead Out or Busing System Lexan The method of electrically accessing each individual sensor. Polycarbonate. A substrate used for graphic overlays and labels. Available in a variety of surface textures. Page 16 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Melinex Part or Device PES Pin Out Repeatability A brand of polyester(PET). A substrate with lower temperature resistance than Ulterm or PES, but with excellent flexibility and low cost. Similar to Mylar. The FSR. Consists of the FSR semiconductive material, conductor, adhesives, graphics or overlays, and connectors. Polyethersulfone. A transparent substrate with excellent temperature resistance, moderate chemical resistance, and good flexibility. The descriptions of a FSRs electrical access at the connector pad (tail). The ability to repeat, within a tolerance, a previous response characteristic. Response Characteristic The relationship of force or pressure vs. resistance. Saturation Pressure The pressure level beyond with the FSR response characteristic deviates from its inverse power law characteristic. Past the saturation pressure, increases in force yield little or no decrease in resistance. Sensor Solder-tabs Each area of the FSR device that is independently force sensitive (as in an array). Stitched on AMP connectors with tab endings. Suitable for direct PC board connection or for soldering to wires. Space and Trace The widths of the gaps and fingers of the conductive grid; also called pitch. Spacer Adhesive The adhesive used to laminate FSR devices tighter. Dictates stand-off. Stand-off The gap or distance between the opposed polymer film layers when the sensor in unloaded and unbent. Stand-off Resistance The FSR resistance when the device is unloaded and unbent. Substrate Tail Ulterm Any base material on which the FSR semi-conductive or metallic polymers are printed. (For example, polyetherimide, polyethersulforne and polyester films). The region where the lead out or busing system terminates. Generally, the tail ends in a connector. Polyetherimide (PEI). A yellow, semi-transparent substrate with excellent temperature and chemical resistance and limited flexibility. Interlink Electronics, Inc. holds international patents for its Force Sensign Resistor technology. FSR is a trademark and Force Sensing Resistors is a registered trademark of Interlink Electronics. Interlink and the six dot logotype are registered marks or Interlink Electronics. Ultem and Lexan are registered trademarks of G.E., Melinex is a registered trademark of ICI, and Mylar is a trademark of E.I. Dupont & Co. FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 17 Suggested Electrical Interfaces Basic FSRs Figure 9 FSR Voltage Divider FSR Voltage Divider For a simple force-to-voltage conversion, the FSR device is tied to a measuring resistor in a voltage divider configuration. The output is described by the equation: VOUT = (V+) / [1 + RFSR/RM]. In the shown configuration, the output voltage increases with increasing force. If RFSR and RM are swapped, the output swing will decrease with increasing force. These two output forms are mirror images about the line VOUT = (V+) / 2. The measuring resistor, RM, is chosen to maximize the desired force sensitivity range and to limit current. The current through the FSR should be limited to less than 1 mA/square cm of applied force. Suggested opamps for single sided supply designs are LM358 and LM324. FET input devices such as LF355 and TL082 are also good. The low bias currents of these op-amps reduce the error due to the source impedance of the voltage divider. A family of FORCE vs. VOUT curves is shown on the graph above for a standard FSR in a voltage divider configuration with various RM resistors. A (V+) of +5V was used for these examples. Page 18 FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Adjustable Buffers Similar to the FSR Voltage Divider, these interfaces isolate the output from the high source impedance of the Force Sensing Resistor. However, these alternatives allow adjustment of the output offset and gain. In Figure 10, the ratio of resistors R2 and R1 sets the gain of the output. Offsets resulting from the non-infinite FSR resistance at zero force (or bias currents) can be trimmed out with the potentiometer, R3. For best results, R3 should be about one-twentieth of R1 or R2. Adding an additional pot at R2 makes the gain easily adjustable. Broad range gain adjustment can be made by replacing R2 and R1 with a single pot. Figure 10 Adjustable Buffer The circuit in Figure 11 yields similar results to the previous one, but the offset trim is isolated from the adjustable gain. With this separation, there is no constraint on values for the pot. Typical cal for R5 and the pot are around 10k. Figure 11 Adjustable Buffer FSR Integration Guide and Evaluation Parts Catalog with Suggested Electrical Interfaces Page 19 Figure 12 Multi-Channel FSR-to-Digital Interface Multi-Channel to FSR-to-Digital Interface Sampling Cycle (any FSR channel): The microcontroller switches to a specific FSR channel, toggling it high, while all other FSR channels are toggled low. The RESET channel is toggled high, a counter starts and the capacitor C1 charges, with its charging rate controlled by the resistance of the FSR (t ~ RC). When the capacitor reaches the high digital threshold of the INPUT channel, the counter shuts off, the RESET is toggled low, and the capacitor discharges. The number of counts it takes from the toggling of the RESET high to the toggling of the INPUT high is proportional to the resistance of the FSR. The resistors RMIN and RMAX are used to set a minimum and maximum counts and therefore the range of the counts. They are also used periodically to re-calibrate the reference. A sampling cycle for RMIN is run, the number of counts is stored and used as a new zero. Similarly, a sampling cycle for RMAX is run and the value is stored as the maximum range (after subtracting the RMIN value). Successive FSR samplings are normalized to the new zero. The full range is zoned by dividing the normalized maximum counts by the number of desired zones. This will delineate the window size or width of each zone. Continual sampling is done to record changes in FSR resistance due to change sin force. Each FSR is sel...

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(b) For - (Part of Crack in Compression Zone)Fz= 0 2 R ( - )( t - d ) f - 2 R t f = Ri 2 p ( - )(1 - d t ) - =Ri 2 p 2 R f t R2p ( 2 - d t ) = 1 - d t - i 2 R f t = Ri 2 p 1 - d t - 2-d t 2 R f t Mx= 0 M nsc = 2 f R 2 ( t - d ) -0cos d + 2 f R
UCSD - MU - 206
IMPROVISATION:METHODS AND MODELSin: Generative processes in music (ed. J. Sloboda) Oxford University Press 1987 Jeff Pressing (text only)I.IntroductionII.A survey of pertinent research (a) (b) Some physiology and neuropsychology Motor control and sk
Washington - PSYCH - 333
CHAPTER 16 OBJECT PERCEPTION AND SCENE ANALYSIS16.1 SCENE ANALYSIS Scene analysis is the process through which all of the information taken in through one or more sensory modalities produces a representation and awareness of the environment. It depends o
Colorado - AMATH - 1350
APPM 1350 Spring 2005 Exam1 Solution p p x+3 2 0 x+3 2 x+3+2 (x + 3) 4 p p = &quot; &quot; = lim 1. (a) lim = lim = lim x!1 x!1 x!1 (x x!1 (x x 1 0 x 1 x+3+2 1)( x + 3 + 2) 1 1 1 lim p =p = x!1 ( x + 3 + 2) 4 4+2 p (b) limx!2x 1 p = 1)( x + 3 + 2)jx x2j 0 = &quot; &quot;
Wheaton College - MATH - 102
1 Let f (x) = x-2 1. 2. 3. 4.andg(x) = 14 sin(3x) + 2x2 - 4x3 + 1Does f (x) satisfy the hypotheses of the IVT on the interval [0, 3]? Does g(x) satisfy the hypotheses of the IVT on the interval [0, 3]? Use the IVT to show that g(x) has a root between x
University of Montana - PH - 141
Homework - Do the following chapter 5 problems. THE THREE KINDS OF TIME. The designers of particle accelerators use electromagnetic elds to boost particles to relativistic speeds while at the same time constraining them to move in a circular path inside a
MIT - MATH - 118
Math 118 : Winter 2009 : Midterm solutions 1. Split eikx = cos(kx) i sin(kx). Since the function is odd, the cosine terms give a zero contribution. We havesin(kx)xdx =1 kcos(kx)dx xcos(kx) k.The integral vanishes. Notice that cos(kx) = (1)k . What i
Washington University in St. Louis - ESE - 447
l3 z q3 P x O2 q2 O x q1 l2 l1 yFigure 1: Double Link pendulum modeled as uniformly distributed rods representing links 1 ,2 and 3 in cartesian coordinatesFrom the figure, it can be seen that, OP = OO2 + O2 P From class notes K1 = 1 J1 q1 , V1 = m1 gzc1
Maryland - C - 661
2005 Spring CMSC 661 March 29 Scribed notes by Hyunyoung SongThese notes were taken from Prof. Dianne Olearys March 29 class. Scribes that are not in your class notes are surrounded with boxes. Each Section tried to rephrase the class notes in easier not
SUNY Stony Brook - AMS - 361
AMS 361: Applied Calculus IV (DE &amp; BVP)Outline for Lecture 102. 3 Classical Mechanics modelsResistance Proportional to Velocity (dropping to earth)Note: My description (particularly the notation) of this problem is different from the textbook, but bas
University of Illinois, Urbana Champaign - FIN - 513
Barrier Options Question Solution 1 Question: Your favorite securities dealer, Taiwan Securities, offers you a new type of zero-coupon reset convertible bond that potentially converts into common stock of the China Semiconductor Company (CSC). The convert
Portland - CLASS - 479
Security &amp; SurveillanceAbout SMaL Camera Technologies, Inc.SMaL Camera Technologies is an award-winning developer of highly innovative electronic imaging solutions for the digital camera, security &amp; surveillance, consumer electronics and automotive mark
Columbia - WW - 2040
Submitted to Management Science manuscript MS-0001-2008.xxxReal-Time Delay Estimation in Overloaded Multiserver Queues with AbandonmentsRouba Ibrahim, Ward WhittDepartment of Industrial Engineering and Operations Research, Columbia University, New York
N. Illinois - M - 232
MATH 232 Fall 2000 Show all your work. No calculators are allowed.FINAL EXAMName (print) SSN1. (12 points) Consider the curve defined by the parametric equations x = 1 - cos t, y = t - sin t, 0 t 2. (a) Find an equation of the tangent line to the curve
George Mason - C - 702
CSI 702 2006 FINAL Exam - Take-Home CSI 702 2006 Midterm Exam - Take-Home1The test is closed book, closed notes, no web access. You are encouraged to type the answers, but hand written notes are acceptable as well. The test should take no more than four
Penn State - KEF - 113
3601 S. Atherton St State College, Pa 8144666841 AngelFoodBethelChurch@gmail.com http:/home.comcast.net/~scbethel/ www.angelfoodministries.com Order In PersonThis is a must for Food Stamps (EBT) At the church office: Saturday, Nov 22thFOR $30 YOU TAKE
Illinois Tech - MATH - 589
Math 589 Midterm Spring 08, Take-home Part1. (10 points) Consider the convection-diusion equation ut + aux = buxx , 0 &lt; t &lt; tF , 0 x 1, (1)where a and b &gt; 0 are constants. Using Fourier Analysis, show that the (FTCS) scheme for Eq. (1) satises | 1 (call
E. Kentucky - FILES - 753
Take Home Exam EECS 753 Due: March 26, 2003The purpose of this take home exam is for you to read the papers on Streams C and Handel C so we can discuss them in class after the break. In answering the questions, you may use any additional papers or inform
Lake County - CONF - 134
Assessing the Value of Coordinated Sire Genetics in a Synchronized AI Program by Joe Parcell, Daniel Schaefer, David Patterson, Mike John, Monty Kerley and Kent HadenSuggested citation format: Parcell, J., D. Schaefer, D. Patterson, M. John, M. Kerley, a
Chester - ECO - 343
www.rian.ru Natural Resources Ministry annuls Sakhalin II probe approval18/09/2006 17:32 MOSCOW, September 18 (RIA Novosti) - Russia's Natural Resources Ministry said Monday it had decided to annul its approval of the results of a 2003 state probe i
Columbia - MATH - 212
Math 212 Spring 2008: Solutions: HW #5Instructor: S. Cautis 1. section 3.1, #4 We have f /x = y 2 exy + 4x3 y 3 and f /y = 2xyexy + 3x4 y 2 . Hence 2 2 f /x2 = y 4 exy + 12x2 y 3 2 f /xy = 2yexy + 2xy 3 exy + 12x3 y 2 2 f /yx = 2yexy + 2xy 3 exy + 12x3 y
Kentucky - TRANSMITTA - 120503
SenateTransmissionOn December 2, 2003, the Undergraduate Council reviewed and approved the following:New CourseCHE 295 -Organic Chemistry Workshop (1) Peer-led team problem solving. Two-hour workshop offered on a pass-fail basis only. [Enrollment in CH
UNL - JDEP - 284
JDEP 284H Foundations of Computer SystemsGiving credit where credit is dueMost of slides for this lecture are based on slides created by Dr. Bryant, Carnegie Mellon University. I have modified them and added new slides.Processor Architecture II: Logic
Milwaukee School of Engineering - CS - 421
CS421-Lecture 66 January 2005OpenGL ShadingBehavior is based on vertices glShadeModel(GLenum mode); GL_FLATSingle vertex Depends on primitive type (see p. 176)GL_SMOOTHInterpolation of all vertices Uses Gouraud shading1Gouraud Shading (1)Computat
Duke - STA - 216
Outline Motivation Mixtures of Normals Mixtures for Residual DistributionsLecture 16: Mixtures of Generalized Linear ModelsOctober 26, 2006Lecture 16: Mixtures of Generalized Linear ModelsOutline Motivation Mixtures of Normals Mixtures for Residual Di
Gordon MA - CS - 211
CS211 Lecture: Modeling Dynamic Behaviors of Systems; Interaction Diagrams in UML last revised September 18, 2007 Objectives: 1. To introduce the notion of dynamic analysis 2. To show how to create and read Sequence Diagrams 3. To show how to create and r
Columbia - CB - 337
Religious Worlds of New YorkReligion W4620 Spring 2007 Professors Monday 2:10-4 Jack Hawley jsh3@columbia.edu 219a Milbank (BC) 80 Claremont Room 101 Courtney Bender cb337@columbia.edu 80 Claremont Room 202 (CU) Mondays 4-5:30 and by appointmentOffice H
Arizona - A - 204
Title: From pebbles to planets. (cover story) Subject(s): PLANETS - Origin; COSMOLOGYSource: Astronomy, Feb98, Vol. 26 Issue 2, p56, 6p, 8cAuthor(s): Yulsman, TomAbstract: Discusses the formation of planets. Overview on theKant-Laplace hypothesis on
UCF - COP - 3503
Array Implementation of a Queue ClassBefore I get to the code, let's consider some design issues. First off, what instance variables are needed to maintain a Queue object? As the title indicates, the main instance variable we are going to use is an array
Iowa State - FDFE - 10965
Heidi Hirschy: AmeriCorps Fall 2000-2001 School Year Placement at Table Mound Elementary School and Summer PlacementWhile serving as an AmeriCorps member for a year, I was placed in many settings in the Dubuque area. During the school year, I was placed
Ferris State - GS - 762
GS 762Instructor: Dr. Burkhard Schaffrin2. Rank-deficient Gauss-Markov Model and Generalized Inverse Matrix (10/5/2000) 2.1 The Least Square Adjustment with Multiple Solutions Gauss-Markov Modely = A + e, nx1 nxm mx1 2 e ~ (0, o P -1 ) , q = rk A &lt; min
USF - NR - 26120
DepressionEmpower yourself with knowledge Depression can affect every area of a person's life, including work and family. There are a number of symptoms which signal depression. If someone you know has been trying to cope with several of these problems,
Kettering - IME - 100
Solutions to Homework Number Four Due Monday August 4, 20081) Describe the green sand casting process. Include in your description a drawing showing all parts of a green sand mold. Explain the role of each part based on casting in general. All casting pr
Texas San Antonio - CRIM - 3113
SYKES AND MATZANEUTRALIZATIONSocial Process - Control Techniques of Neutralization Denial of Responsibility Denial of Injury Denial of the Victim Condemnation of the Condemners Appeal to Higher Loyalties Drift
BU - CS - 538
BU CAS CS 538.1CAS CS 538. Problem Set 5Problem 1. Let w(Gen, Enc, Dec) be a polynomially secure public-key cryptosystem. It is intuitively obvious that it should be hard to compute SK from the PK. Yet if you think about it, you can see that security o
North Texas - VK - 0040
Group Assignment 3 SetsIntroduction. Every area of mathematics uses sets in some way. For example, number theory is concerned with a particular set of numbers (whole numbers). This assignment introduces the basic ideas of sets. Learning Goals. In this gr
Evansville - EE - 210
EE210 Lab Experiment II Kirchhoff's LawsObjective: Verify Kirchhoff's Laws Procedure: 1. Construct the circuit shown in the Figure 1. Measure and record the four voltages (VS, VR1, VR2, VR3) and the four currents (IA, IB, IC, ID). Be sure to record not o
Wisc Parkside - ACCT - 302
ACCT302 Ch.15 Quiz Name:_ Score:_1.Treasury Stock Transactions. On 1/2/05, Case Inc. purchased 10,000 shares of its own $1 par value C.S. for $30/share. (2 pts)Dr. T.S. 300,000 Cr. Cash 300,000 On 1/10/05, Case re-issued 2,000 shares of the treasury st
Cal Poly Pomona - CHM - 315
Predict the major product. I CH3NaOCH2CH3 CH3CH2OHA)B)C)CH3 OCH2CH3D)CH3 OCH2CH3E) No Reaction(racemic)
University of Toronto - CSC - 263
=CSC 263H Notes about the final examination Winter 2004=-Preparing for final exam- - Remember that for the final exam, you will be allowed to bring ONE 8.5&quot; x 11&quot; sheet of paper, _hand_written on both sides, and nothing else, except what you need
Yale - CS - 156
CPSC156a: The Internet Co-Evolution of Technology and SocietyDecember 2, 2003 Review for Second Exam(Subtopics are examples!) Security Internet Security Authorization, identification, etc. Spam Business models Technical protection systems P2P systems M
USC - SCF - 480
480 MORNING CLASS SCHEDULE Spring 2009 SCA112 Tuesday, January 13th: 9-1030AM: Introduction to core 480 faculty and SAs, discussion of syllabus/class structure/calendar review, hand out safety/conduct guidelines, discussion of collaborative craft approach
Loyola Maryland - CS - 462
xo x # ! w ! # x @i0Bv0iXuiDi&quot;00&quot;6)X&amp;6sX&amp;iVriX)ffXigXs)$)fr0iX&amp;i)0' q ! ! ! y d ! ! x d j ! x ! # t o y' x # y' !' # ! # ' ! x ! # ! o h ! # x ! x !' x # ! x y k # ! x m x x # ! x k j x h ! x ! x d x ! h ! #' ! x pfi(if)Xn0iRXXf$ii# $lXiXBi68ifiie0i0iRgf