Quick Start for Beginners to Drive a Stepper Motor
|
|
- Rosalind Gallagher
- 7 years ago
- Views:
Transcription
1 Freescle Semiconductor Appliction Note AN2974 Rev. 1, 06/2005 Quick Strt for Beginners to Drive Stepper Motor by: Mtthew Grnt 16-Bit Automotive Applictions Microcontroller Division Introduction This ppliction note is for novices who wnt generl quick-strt guide showing how to control stepper motor. Becuse stepper motors cn be used in vriety of wys nd re driven by vriety of devices, there is gret del of informtion vilble bout how these motors work nd how to use them. To reduce confusion, the focus of this ppliction note is on stepper motors tht cn be driven by microcontrollers. This document includes bsic informtion needed to get strted quickly, nd includes prcticl exmple tht is simple nd esy to implement. Wht is Stepper Motor? A stepper motor is n electriclly powered motor tht cretes rottion from electricl current driven into the motor. Physiclly, stepper motors cn be lrge but re often smll enough to be driven by current on the order of millimpere. Current pulses re pplied to the motor, nd this genertes discrete rottion of the motor shft. This is unlike DC motor tht exhibits continuous rottion. Although it is possible to drive stepper motor in mnner where it hs ner continuous rottion, doing so requires more finesse of the input wveform tht drives the stepper motor. Figure 1 illustrtes some bsic differences in stepper nd DC motor rottion. Freescle Semiconductor, Inc., All rights reserved.
2 Types of Stepper Motors DISCRETE ROTATION HCS12 MICROCONTROLLER STEPPER MOTOR x x CONTROL 1) HCS12 MICROCONTROLLER DC MOTOR CONTINUOUS ROTATION CONTROL 1b) Figure 1. Stepper vs. DC Motor Rottion Types of Stepper Motors There re vriety of stepper motors vilble, but most of them cn be seprted into two groups: Permnent-mgnet (PM) stepper motor This kind of motor cretes rottion by using the forces between permnent mgnet nd n electromgnet creted by electricl current. An interesting chrcteristic of this motor is tht even when it is not powered, the motor exhibits some mgnetic resistnce to turning. Vrible-reluctnce (VR) stepper motor Unlike the PM stepper motor, the VR stepper motor does not hve permnent-mgnet nd cretes rottion entirely with electromgnetic forces. This motor does not exhibit mgnetic resistnce to turning when the motor is not powered. 2 Freescle Semiconductor
3 Wht is Inside? Wht is Inside? Generlly, stepper motor consists of sttor, rotor with shft, nd coil windings. The sttor is surrounding csing tht remins sttionry nd is prt of the motor housing, while the rotor is centrl shft within the motor tht ctully spins during use. The chrcteristics of these components nd how they re rrnged determines whether the stepper motor is PM or VR stepper motor. Figure 2 nd Figure 3 show n exmple of these internl components. PERMANENT MAGNET STEPPER MOTOR SIGNAL B + CURRENT i + S SIGNAL A COIL WINDING N ROTOR SHAFT COMING OUT OF PAGE PERMANENT MAGNET DISK WITH TWO POLES DIRECTION OF MAGNETIC FIELD METAL CORE USED TO HELP CHANNEL THE MAGNETIC FIELD Figure 2. Permnent Mgnet (PM) Stepper Motor Tking closer look, the rotor in PM stepper motors is ctully permnent-mgnet. In some cses, the permnent mgnet is in the shpe of disk surrounding the rotor shft. One rrngement is mgnetic disk which consists of north nd south mgnetic poles interlced together. The number of poles on the mgnetic disk vries from motor to motor. Some simple PM stepper motors such s the one in Figure 2 only hve two poles on the disk, while others my hve mny poles. The sttor usully hs two or more coil windings, with ech winding round soft metllic core. When electricl current flows through the coil windings, mgnetic field is generted within the coil. The metllic core is plced within the coil windings to help chnnel the electromgnetic field perpendiculr to the outer perimeter of the mgnetic disk. Freescle Semiconductor 3
4 Wht is Inside? Depending upon the polrity of the electromgnetic field generted in the coil (north pole, out of the coil, or south pole, into the coil) nd the closest permnent mgnetic field on the disk, n ttrction or repulsion force will exist. This cuses the rotor to spin in direction tht llows n opposite pole on the perimeter of the mgnetic disk to lign itself with the electromgnetic field generted by the coil. When the nerest opposite pole on the disk ligns itself with the electromgnetic field generted by the coil, the rotor will come to stop nd remin fixed in this lignment s long s the electromgnetic field from the coil is not chnged. VR stepper motors work in very similr fshion. Figure 3 shows some of the physicl detils tht chrcterize its opertion. In VR stepper motor, the surrounding coils tht re physiclly locted opposite of ech other re energized to crete opposite mgnetic fields. For exmple, in Figure 3), coil C produces south-pole mgnetic field, nd coil C produces north-pole mgnetic field. The mgnetic fields produced by the coils pss through the ir gp nd through the metllic rotor. Becuse the mgnetic fields ttrct ech other, the metllic rotor spins in direction tht brings the nerest edges (2 nd 4) of the rotor s close s possible to the pir of energized coils (C nd C). Like the PM stepper rotor, the VR stepper rotor will remin ligned to the coils s long s coils C nd C re energized nd the mgnetic fields re not chnged. To move to the next stte nd continue this rottion, coils C nd C must be deenergized, while coils A nd A must be oppositely energized to ttrct rotor edges 1 nd 3 respectively. The sme process occurs with coils B nd B to ttrct rotor edges 2 nd 4 respectively, nd so on. Figure 3 shows how the rotor spins s the coils re energized nd de-energized. This is n exmple of 3-phse VR motor. VARIABLE RELUCTANCE STEPPER MOTOR A C C A C A B 4 B 4 4 B B B B A A 3) C 3b) C 3c) C A Figure 3. How the Vrible Reluctnce (VR) Rotor Spins From the exmples discussed erlier, we cn see tht if the electromgnetic fields in both the PM nd VR stepper motors re turned on, off, nd reversed in the proper sequence, the rotor cn be turned in specific direction. Ech time n electromgnetic field combintion is chnged, the rotor my turn fixed number of degrees. As these stte chnges in electromgnetic fields tke plce more rpidly, on the order of milliseconds, the rotor cn rotte fster, smoother, nd sometimes more quietly. Becuse of the mechnicl limittions of the system, the rotor cn only rotte effectively up to certin speeds. An externl device, such s n HCS12 microcontroller (or, MCU), is very good for controlling the electromgnetic sequences by directing the flow of current through the coil windings. To do this, softwre cn be written nd loded into n HCS12 MCU. 4 Freescle Semiconductor
5 Wveforms tht cn Drive Stepper Motor Wveforms tht cn Drive Stepper Motor Stepper motors hve input pins or contcts tht llow current from supply source (in this ppliction note, microcontroller) into the coil windings of the motor. Pulsed wveforms in the correct pttern cn be used to crete the electromgnetic fields needed to drive the motor. Depending on the design nd chrcteristics of the stepper motor nd the motor performnce desired, some wveforms work better thn others. Although there re few options to choose from when selecting wveform to drive twophse PM stepper motor, such s full-stepping or micro-stepping, this ppliction note focuses on one clled hlf-stepping. A grph of the wveform is given in Figure 4. In Figure 4), four signls re shown. These signls cn be produced by dedicted stepper driver or microcontroller. Ech signl (,, b, b) is pplied to coil terminl. Becuse ech coil hs two terminls, two signls must work together to drive single coil. If we consider terminl s positive reference, then the combintion of signls nd cuse the coil to see n effective signl A, shown in Figure 4b). Likewise, signl B in Figure 4b) is produced by combining signls b nd b from Figure 4). It is worth noting tht the individul wveforms (,, b, b) directly from the microcontroller pins to the coil terminls only vry from 0 V to +5 V. However, the effective signl (A, B) pplied to the coil vries from 5 V to +5 V, nd hs positive nd negtive duty cycles. Two of these effective wveforms shown in Figure 4b), 90 degrees out of phse cn be used to drive the PM stepper motor. Both wveforms re pplied to the motor simultneously. Ech trnsition in one of the wveforms corresponds to stte chnge (movement) in the motor. Altogether, Figure 4) nd b) show eight different sttes for hlfstepping. A step by step description of how these prticulr wveforms work together to move the motor shft follows. When coil signl A is positive nd coil signl B is zero, current flows into coil A through terminl nd out of terminl. This genertes north-pole electromgnetic field towrd the mgnetic disk, which repels the nerest north-pole section on the disk nd ttrcts the nerest south-pole section. These forces cuse the motor to rotte in direction tht will lign opposite poles. Coil B is not energized. NOTE The orienttion of the rotor prior to energizing single coil my be unknown. It is possible tht, for exmple, the rotor could be positioned, s shown in Figure 7c), when ttempting to lign itself, s in Figure 7). Figure 7c) is the worst cse strting position for the desired lignment, shown in Figure 7). It is even possible tht initilly the rotor my not turn becuse the mgnetic forces of the coil could be eqully divided over pushing nd pulling the north nd south pole of the PM disk. If this hppens, then moving to the next sequentil step by energizing both coils should help jolt the rotor free. Freescle Semiconductor 5
6 Wveforms tht cn Drive Stepper Motor + 5 V COIL SIGNAL A + 0 V PORT PIN SIGNAL + 5 V time PORT PIN SIGNAL 0 V time + 5 V COIL SIGNAL B + 0 V PORT PIN SIGNAL b + 5 V time 4) 0 V PORT PIN SIGNAL b time DIFFERENT STATES WITH DISCRETE TRANSITIONS + 5 V V COIL SIGNAL A 5 V time + 5 V 0 V COIL SIGNAL B time 5 V 4b) Figure 4. Discrete Trnsitions While coil signl A is positively energized, the next trnsition occurs in coil signl B. Coil signl B rises nd positively energizes coil B, creting its own electromgnetic field. Electric current flows into terminl b nd out of terminl b. The north-pole of both coils now shre n ttrction for the south-pole of the disk, cusing the disk to relign (rotte) itself between shred ttrctions. The sme ction tkes plce with the south-pole of the coils nd north-pole of the PM disk. 6 Freescle Semiconductor
7 Wveforms tht cn Drive Stepper Motor For the next trnsition, coil signl A flls to zero, leving the signl in coil B to dominte the lignment of the PM disk. In summry, coils A nd B tke turns controlling the PM disk. Before one coil releses full control of the disk, it shres control of the disk with the other coil. This temporry shring cretes hlf-step in the trnsition of control from one coil to the next (hlf-stepping) nd llows smller, discrete turns to be tken by the motor. Although stepper motors re often used for their bility to mke discrete movements, they cn lso be used for smooth movements. In n idel cse, the wveforms tht would llow the smllest incrementl chnge would ctully be sinusoidl to ensure the smoothest trnsition between full steps. In such cse, the distinction between sttes nd specific steps become blurred. This implementtion my be well suited for pplictions tht seek to reduce or eliminte the discrete movement of the motor, which lso reduces noise nd vibrtion. This technique is often referred to s microstepping. Although the digitl wveforms in this exmple re not sinusoidl, their similrities to sinusoidl wveform cn still be noted by compring Figure 4 nd Figure 5. A series of electromgnet chnges over the period of both signls continue to work together in this fshion to rotte the PM disk. DIFFERENT STATES WITH SMOOTH TRANSITIONS + 5 V Smooth stte trnsitions produce smooth rotor movement for stepper motors. COIL SIGNAL A 0 5 V + 5 V COIL SIGNAL B 0 time time 5 V Figure 5. Smooth Trnsitions Freescle Semiconductor 7
8 How to Use n HCS12 Microcontroller to Drive the PM Stepper Motor How to Use n HCS12 Microcontroller to Drive the PM Stepper Motor HCS12 microcontrollers re good devices for driving stepper motors becuse they re fst, comptible with the discrete movements of steppers, nd cn be esily progrmmed to work with steppers of different types. Some exmples of use re precision movements, multi-xis control, sophisticted velocity profiling, nd incresed fult tolernce. In some instnces, microcontroller cn provide multiple solutions in single system becuse of their bility to be progrmmed to communicte with other systems while controlling stepper motor. This is especilly dvntgeous over dedicted stepper driver tht is more difficult to modify nd not likely to hve full communiction cpbilities. Microcontrollers cn lso generte the wveforms needed to produce movement in stepper motor. Becuse the desired performnce of stepper motor my vry, the lgorithm used by microcontroller to drive stepper motor is likely to vry s well. Some of these lgorithms cn become involved nd require intimte understnding of the motor, in ddition to very orgnized use of the microcontroller resources. To soften the pproch for beginners, this section gives generl description of how to use the port pins on n HCS12 microcontroller to crete bsic, step-like movement in PM stepper motor. To proceed, some generl ssumptions bout the motor nd microcontroller hve to be mde. The stepper motor is ssumed to be 4-pin, two-phse PM stepper motor with two poles on the PM disk. An internl digrm of wht such motor might look like is shown in Figure 2. The input voltge of the motor is ssumed to be bout ±5 V, with typicl current somewhere between 1 20 millimpere. A motor of this size could weigh few ounces nd be 3 5 centimeters wide. This is one of the simpler types of motors nd will be the subject of exmple for the reminder of the ppliction note. To control the four pins of the motor, the microcontroller needs four output pins cpble of driving nd sinking somewhere between 1 20 millimpere out of ech pin. Port pins on n HCS12 microcontroller re suitble for this effort. Most microcontrollers hve registers tht cn be used to control logic levels of n I/O or port pin. We cn select four control bits from ny HCS12 I/O register tht is vilble. Let it be ssumed tht there is register clled register U, nd the port corresponding to this register is clled port U. For simplicity, we cn use the lower nibble of register U, U[3:0], to control port U pins U0, U1, U2, nd U3 of the microcontroller. Pins U3 nd U2 cn be used to control the current in coil B, nd pins U1 nd U0 cn be used to control the current in coil A. A connection should be mde from pins U3 nd U2 to the contcts of coil B. A connection should lso be mde from pins U1 nd U0 to the contcts of coil A. Current tht flows out of the U3 pin will flow into U2, nd vice vers. The sme condition pplies to pins U1 nd U0. 8 Freescle Semiconductor
9 How to Use n HCS12 Microcontroller to Drive the PM Stepper Motor HCS12 OUTPUT PORT REGISTER LOWER NIBBLE USED TO CONTROL STEPPER MOTOR STEPPER MOTOR Figure 6. Using n HCS12 MCU to Control the Stepper Motor With n pproprite lgorithm, we cn use pins U[3:0] of the HCS12 to produce the wveforms needed to drive stepper motor. The generl flow of the lgorithm cn be similr to the flow of stte mchine, which is to set the bits in register U to prticulr stte or configurtion, wit discrete mount of time, nd set the bits in register U to the next stte. For ech chnge in the microcontroller register stte, chnge is produced in the wveform tht cuses the motor to rotte fixed mount. The period of time required between register sttes will vry depending upon the motor nd the performnce desired, but is usully on the order of milliseconds. If the dely between chnges to the microcontroller register sttes is too short, the motor will not physiclly be ble to move fst enough to keep up with the register stte chnges. A dely tht is too long could crete motor response with noticebly rigid movements nd choppy noises with ech step. However, for the purpose of this ppliction note, it my be helpful to hve long dely between register sttes becuse it llows esy observtion of the motor response nd movement due to microcontroller register chnges. An esy wy to begin driving the motor is to focus on getting the motor to move single step t time, in the direction desired insted of mny steps t once. Trcing through n lgorithm with softwre debugger, if debugger is vilble, is wy of slowing the lgorithm down so the response of the motor cn be observed. After motor movement hs been chieved, direction reversl cn be ccomplished by switching the microcontroller connections to one of the motor coils. Figure 7 illustrtes exmple microcontroller register contents from stte 0 to stte 3, It lso shows the mtching PM stepper motor configurtion tht might occur in tht stte. Figure 7 lso corresponds with the grph in Figure 4 nd the drwing in Figure 6. Freescle Semiconductor 9
10 How to Use n HCS12 Microcontroller to Drive the PM Stepper Motor STATE 0 b b STATE 1 b b STATE 2 b b STATE 3 b b PORT REGISTER CONTENTS PORT REGISTER CONTENTS PORT REGISTER CONTENTS PORT REGISTER CONTENTS i + COIL SIGNAL A COIL SIGNAL B b b + S N i + COIL SIGNAL A COIL SIGNAL B b b + i S N + COIL SIGNAL A COIL SIGNAL B b b + i S N i + COIL SIGNAL A COIL SIGNAL B b b + i N S 7) 7b) 7c) 7d) Figure 7. HCS12 MCU Register Contents from Stte 0 to Stte 3 Below is n exmple of progrm tht performs hlf-stepping nd cn be used to drive stepper motor. The code turns the motor number of steps (100 hlf-steps) in one direction, nd then turns the motor bck the sme number of steps in the opposite direction. One of the dvntges of the code below is tht it cn be esily modified to keep trck of motor s position. It lso hs the dvntge of hving the port sttes stored in sequentil order in n rry. Simply cycling through the sttes sequentilly nd plcing the stte vlues on port pins will cuse stepper motor to move. This is written in C. #define NUM_OF_STATES 8 //There re 8 different sttes in this prticulr exmple. #define DELAY_MAX 2000 //The mximum # of counts used to crete time dely. void min(void) { /*******************CREATE VARIABLES*******************/ int i; //Used in for loop //This rry ctully contins the stte vlues tht will be plced on Port U. //Stte #0 corresponds to vlue of 0x06, stte #1 corresponds to vlue of 0x02, etc. chr stte_rry[num_of_states] = {0x06, 0x02, 0x0A, 0x08, 0x09, 0x01, 0x05, 0x04}; int steps_to_move; //The # of rottionl steps the motor will mke. chr next_stte; //Used to select the next stte to put in register U. /********************SET UP PORT U********************/ DDRU = 0xFF; //Writing 0xFF to DDRU sets ll bits of Port U to ct s output. PTU = 0; //Init Port U by writing vlue of zero to Port U. /******************************************************/ steps_to_move = 100; //Set the # of steps to move. An rbitrry positive # cn be used. next_stte = 0; //Init next_stte to stte 0. next_stte cn strt from ny stte //within the rnge of possible sttes in this exmple, 0-7. PTU = stte_rry[next_stte]; //Init Port U to the strting stte. In this exmple, //since only 4 pins re needed to control the motor, only //the lower nibble of Port U is being used. This line //selects stte 0 nd plces the corresponding vlue //(0x06) in the lower nibble of Port U. 10 Freescle Semiconductor
11 How to Use n HCS12 Microcontroller to Drive the PM Stepper Motor for(i = 0; i < DELAY_MAX; i++) { //Wit here for while. } while (steps_to_move > 0) { if (next_stte > (NUM_OF_STATES - 1)) //If next_stte is greter thn the highest //vilble stte, 7, then cycle bck to 0 { next_stte = 0; } PTU = stte_rry[next_stte]; //Plce new vlue in Port U. Rottion my be observed for(i = 0; i < DELAY_MAX; i++) { //Wit here for while. } next_stte++; //Increment next_stte. Cycling though the sttes cuses rottion //in one direction. Decrementing sttes cuses opposite rottion. } steps_to_move--; //Subtrct 1 from the totl # of steps remining to be moved. //The following code rottes the motor bck in the opposite direction. steps_to_move = 100; while (steps_to_move > 0) { if (next_stte < 0) { next_stte = (NUM_OF_STATES - 1); } PTU = stte_rry[next_stte]; for(i = 0; i < DELAY_MAX; i++) { //Wit here for while. next_stte--; } steps_to_move--; } } //End of Min Freescle Semiconductor 11
12 How re Stepper Motors Used? How re Stepper Motors Used? Stepper motors hve found their wy into mny different res of control systems. The wide populrity of these motors cn be ttributed in prt to the vrious wys the motor cn be driven nd becuse of its comptibility with digitl systems. In prticulr, stepper motors re idel for control systems tht require discrete, esily repetble movements t moderte to low frequencies. Steppers re most commonly used in open-loop position control pplictions. Figure 8 below shows n exmple block digrm of system with microcontroller, stepper motor, nd feedbck. In the cse of stepper motors, the feedbck is not lwys needed but cn still be provided for precision ssistnce. In contrst, DC motors need feedbck becuse they hve hrder time mking precision movements nd require circuit tht cn compenste for the risk of drifting or overshooting trget position. The feedbck circuitry for the position of motor is likely to be more complicted for dc motors thn for stepper motors. Stepper motors hve worked well in fctories nd ssembly environments, in pplictions such s robotic rms nd precision ssembly controls. They cn be found in printers, disk drives, toys, crs, nd host of other pplictions nd products. MOTOR CONTROL BLOCK DIAGRAM WITH FEEDBACK POSITION DETECTION (FEEDBACK) MICROCONTROLLER OR MOTOR DRIVER MOTOR ROTOR OR GEAR OTHER SYSTEM Figure 8. Exmple System with n MCU, Stepper Motor, nd Feedbck Efficient Motor Control with n HCS12 Microcontroller Actul control of stepper motor in rel pplictions is not trivil. Often, the motor is single component within system of other devices tht must ll work in unison for successful opertion. A microcontroller responsible for driving the motor cn lso hndle other tsks or service other devices within the system, but writing liner softwre to hndle complex motor control cn leve little bndwidth for the microcontroller to tend to other mtters. In the simple exmple code given, the microcontroller wstes much of its computing power stuck in dely loop before performing ny other meningful tsk. More efficient use of the microcontroller cn be obtined by using n HCS12 with motor control module. The interrupt cpbility of the motor control module llows the microcontroller to run sequentilly through softwre until the motor needs to be serviced. After motor interrupt occurs, softwre cn mke quick register djustments to chrcteristics like polrity, period length, nd duty cycle, before returning to norml flow. For more detils bout pplictions like motor control nd HCS12 microcontrollers, refer to 12 Freescle Semiconductor
13 Efficient Motor Control with n HCS12 Microcontroller This pge intentionlly left blnk. Freescle Semiconductor 13
14 Efficient Motor Control with n HCS12 Microcontroller This pge intentionlly left blnk. 14 Freescle Semiconductor
15 Efficient Motor Control with n HCS12 Microcontroller This pge intentionlly left blnk. Freescle Semiconductor 15
16 How to Rech Us: Home Pge: E-mil: USA/Europe or Loctions Not Listed: Freescle Semiconductor Technicl Informtion Center, CH N. Alm School Rod Chndler, Arizon or Europe, Middle Est, nd Afric: Freescle Hlbleiter Deutschlnd GmbH Technicl Informtion Center Schtzbogen Muenchen, Germny (English) (English) (Germn) (French) support@freescle.com Jpn: Freescle Semiconductor Jpn Ltd. Hedqurters ARCO Tower 15F 1-8-1, Shimo-Meguro, Meguro-ku, Tokyo Jpn or support.jpn@freescle.com Asi/Pcific: Freescle Semiconductor Hong Kong Ltd. Technicl Informtion Center 2 Di King Street Ti Po Industril Estte Ti Po, N.T., Hong Kong support.si@freescle.com For Literture Requests Only: Freescle Semiconductor Literture Distribution Center P.O. Box 5405 Denver, Colordo or Fx: LDCForFreescleSemiconductor@hibbertgroup.com Informtion in this document is provided solely to enble system nd softwre implementers to use Freescle Semiconductor products. There re no express or implied copyright licenses grnted hereunder to design or fbricte ny integrted circuits or integrted circuits bsed on the informtion in this document. Freescle Semiconductor reserves the right to mke chnges without further notice to ny products herein. Freescle Semiconductor mkes no wrrnty, representtion or gurntee regrding the suitbility of its products for ny prticulr purpose, nor does Freescle Semiconductor ssume ny libility rising out of the ppliction or use of ny product or circuit, nd specificlly disclims ny nd ll libility, including without limittion consequentil or incidentl dmges. Typicl prmeters tht my be provided in Freescle Semiconductor dt sheets nd/or specifictions cn nd do vry in different pplictions nd ctul performnce my vry over time. All operting prmeters, including Typicls, must be vlidted for ech customer ppliction by customer s technicl experts. Freescle Semiconductor does not convey ny license under its ptent rights nor the rights of others. Freescle Semiconductor products re not designed, intended, or uthorized for use s components in systems intended for surgicl implnt into the body, or other pplictions intended to support or sustin life, or for ny other ppliction in which the filure of the Freescle Semiconductor product could crete sitution where personl injury or deth my occur. Should Buyer purchse or use Freescle Semiconductor products for ny such unintended or unuthorized ppliction, Buyer shll indemnify nd hold Freescle Semiconductor nd its officers, employees, subsidiries, ffilites, nd distributors hrmless ginst ll clims, costs, dmges, nd expenses, nd resonble ttorney fees rising out of, directly or indirectly, ny clim of personl injury or deth ssocited with such unintended or unuthorized use, even if such clim lleges tht Freescle Semiconductor ws negligent regrding the design or mnufcture of the prt. Freescle nd the Freescle logo re trdemrks of Freescle Semiconductor, Inc. All other product or service nmes re the property of their respective owners. Freescle Semiconductor, Inc All rights reserved. AN2974 Rev. 1, 06/2005
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationHow To Network A Smll Business
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More information4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors.
4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy.
More informationEngineer-to-Engineer Note
Engineer-to-Engineer Note EE-265 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our
More informationEngineer-to-Engineer Note
Engineer-to-Engineer Note EE-280 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil
More informationHow To Power A Power Supply On A Powerline (Power Supply) (Power Source) (Wired) (Wire) (Powered) (Unmanned) (Electric) (Plastipower) (Motor) (Power)
Preferred Device Silicon Bidirectionl Thyristors Designed primrily for full-wve c control pplictions, such s light dimmers, motor controls, heting controls nd power supplies; or wherever full-wve silicon
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A - April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationHow To Set Up A Network For Your Business
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationRotating DC Motors Part I
Rotting DC Motors Prt I he previous lesson introduced the simple liner motor. Liner motors hve some prcticl pplictions, ut rotting DC motors re much more prolific. he principles which eplin the opertion
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More information1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam
1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211 - Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges
More informationSection 5-4 Trigonometric Functions
5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationWelch Allyn CardioPerfect Workstation Installation Guide
Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.5 or lter For network instlltion, plese refer to
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationSpace Vector Pulse Width Modulation Based Induction Motor with V/F Control
Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationAccording to Webster s, the
dt modeling Universl Dt Models nd P tterns By Len Silversn According Webster s, term universl cn be defined s generlly pplicble s well s pplying whole. There re some very common ptterns tht cn be generlly
More informationAPPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS
APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS TABLE OF FIGURES Figure 1: Spectrl Response of CMOS Imge Sensor...3 Figure 2: Byer CFA Ptterns...4
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
More informationIntroducing Kashef for Application Monitoring
WextWise 2010 Introducing Kshef for Appliction The Cse for Rel-time monitoring of dtcenter helth is criticl IT process serving vriety of needs. Avilbility requirements of 6 nd 7 nines of tody SOA oriented
More information2. Transaction Cost Economics
3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service
More informationUnleashing the Power of Cloud
Unleshing the Power of Cloud A Joint White Pper by FusionLyer nd NetIQ Copyright 2015 FusionLyer, Inc. All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system, or trnsmitted,
More informationClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment
ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationNetwork Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
More informationFacilitating Rapid Analysis and Decision Making in the Analytical Lab.
Fcilitting Rpid Anlysis nd Decision Mking in the Anlyticl Lb. WHITE PAPER Sponsored by: Accelrys, Inc. Frnk Brown, Ph.D., Chief Science Officer, Accelrys Mrch 2009 Abstrct Competitive success requires
More informationEE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form- example shown
EE247 Lecture 4 Ldder type filters For simplicity, will strt with ll pole ldder type filters Convert to integrtor bsed form exmple shown Then will ttend to high order ldder type filters incorporting zeros
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationEnterprise Risk Management Software Buyer s Guide
Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationEasyMP Network Projection Operation Guide
EsyMP Network Projection Opertion Guide Contents 2 About EsyMP Network Projection Functions of EsyMP Network Projection... 5 Vrious Screen Trnsfer Functions... 5 Instlling the Softwre... 6 Softwre Requirements...6
More informationWeek 11 - Inductance
Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationVendor Rating for Service Desk Selection
Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl
More information5 a LAN 6 a gateway 7 a modem
STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationCS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001
CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationTechniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist
Techniques for Requirements Gthering nd Definition Kristin Persson Principl Product Specilist Requirements Lifecycle Mngement Elicit nd define business/user requirements Vlidte requirements Anlyze requirements
More informationUplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu
Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationBabylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity
Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University
More informationData replication in mobile computing
Technicl Report, My 2010 Dt repliction in mobile computing Bchelor s Thesis in Electricl Engineering Rodrigo Christovm Pmplon HALMSTAD UNIVERSITY, IDE SCHOOL OF INFORMATION SCIENCE, COMPUTER AND ELECTRICAL
More informationActive & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/2015-05/31/2016 Summary of Benefits and Coverage:
Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge for: Single & Fmily Pln Type: NPOS This is only summry. If you wnt more detil bout your coverge nd costs, you cn get the complete
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2010
2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD
More informationBlackbaud The Raiser s Edge
Riser s Edge Slesce.com Comprison Summry Introduction (continued) Chrt -(continued) Non-Prit Strter Pck Compny Bckground Optionl Technology Both Slesce modules supports hs become include over Slesce.com
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationGFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI MilArchiver 6 C2C Archive One Policy Mnger Who we re Generl fetures Supports
More informationClipping & Scan Conversion. CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2005
Clipping & Scn Conersion CSE167: Computer Grphics Instructor: Stee Rotenberg UCSD, Fll 2005 Project 2 Render 3D hnd (mde up of indiidul boxes) using hierrchicl trnsformtions (push/pop) The hnd should perform
More informationFAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University
SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility
More informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
More informationJaERM Software-as-a-Solution Package
JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More informationAntiSpyware Enterprise Module 8.5
AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility
More informationtrademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007
trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
More informationProtocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff
Protocol Anlysis 17-654/17-764 Anlysis of Softwre Artifcts Kevin Bierhoff Tke-Awys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention
More informationAnthem Blue Cross Life and Health Insurance Company University of Southern California Custom Premier PPO 800/20%/20%
Anthem Blue Cross Life nd Helth Insurnce Compny University of Southern Cliforni Custom Premier 800/20%/20% Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge Period: 01/01/2015-12/31/2015
More informationffiiii::#;#ltlti.*?*:j,'i#,rffi
5..1 EXPEDTNG A PROJECT. 187 700 6 o 'o-' 600 E 500 17 18 19 20 Project durtion (dys) Figure 6-6 Project cost vs. project durtion for smple crsh problem. Using Excel@ to Crsh Project T" llt ffiiii::#;#ltlti.*?*:j,'i#,rffi
More informationSolenoid Operated Proportional Directional Control Valve (with Pressure Compensation, Multiple Valve Series)
Solenoid Operted Proportionl Directionl Control Vlve (with Pressure Compenstion, Multiple Vlve Series) Hydrulic circuit (Exmple) v Fetures hese stcking type control vlves show pressure compensted type
More informationPrescriptive Program Rebate Application
Prescriptive Progrm Rebte Appliction Check the pproprite progrm box for your rebte. OID Internl Use Only Cooling FSO (Fluid System Optimiztion) Foodservice Equipment Heting Lighting Motors & Drives Customer
More informationLectures 8 and 9 1 Rectangular waveguides
1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationHow To Control A Motor Control On An Hvac Platform
Freescale Semiconductor Document Number:AN4616 Application Note Rev. 0, 10/2012 Flap Motor Control Based On HVAC Platform by: Shawn Shi, Albert Chen, Alex Liu 1 Introduction According to the world market
More informationCHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
More informationChromebook Parent/Student Information
Chromebook Prent/Student Informtion 1 Receiving Your Chromebook Student Distribution Students will receive their Chromebooks nd cses during school. Students nd prents must sign the School City of Hmmond
More information15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
More informationMODULE 3. 0, y = 0 for all y
Topics: Inner products MOULE 3 The inner product of two vectors: The inner product of two vectors x, y V, denoted by x, y is (in generl) complex vlued function which hs the following four properties: i)
More informationDecision Rule Extraction from Trained Neural Networks Using Rough Sets
Decision Rule Extrction from Trined Neurl Networks Using Rough Sets Alin Lzr nd Ishwr K. Sethi Vision nd Neurl Networks Lbortory Deprtment of Computer Science Wyne Stte University Detroit, MI 48 ABSTRACT
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationUNITED STATES DEPARTMENT OF AGRICULTURE Washington, D.C. 20250. ACTION BY: All Divisions and Offices. FGIS Directive 2510.
UNITED STATES DEPARTMENT OF AGRICULTURE Wshington, D.C. 20250 ACTION BY: All Divisions nd Offices FGIS Directive 2510.1 12-11-73 FEDERAL TORT CLAIMS I PURPOSE This Instruction: A Sets forth the bsic provisions
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More informationFile Storage Guidelines Intended Usage
Storge 1 Google Cloud 2 Other cloud storge Exmple or Box, Dropbox, Crbonite, idrive File Storge Guidelines Usge Fculty nd student collbortion Specil use cses. When non-lcc employee nd students need ccess
More informationHow To Know What A Pressure Ulcer Is
Pressure Ulcers ecourse: Module 2 Quiz I 1. Blck, brown or tn tissue tht dheres firmly to the wound bed or ulcer edges nd my be either firmer or softer thn surrounding tissue is:. Eschr b. Slough c. Grnultion
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationProject 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
More information