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by: Shyanne Lubowitz
Shyanne Lubowitz
The U
GPA 3.85


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About this Document

Class Notes
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This 4 page Class Notes was uploaded by Shyanne Lubowitz on Monday October 26, 2015. The Class Notes belongs to ECE 2210 at University of Utah taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/230012/ece-2210-university-of-utah in ELECTRICAL AND COMPUTER ENGINEERING at University of Utah.

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Date Created: 10/26/15
AC Notes ECE 221000 357 on AC Alternatlng Current rev who05 ThIs term Is used for any tImervaryIng voltage or current waveform Perlodlc waveforms Waveshape repeats T Perlod repeat tIme 1 A GmP TtUde f frequency cycles second f 7 7 Vave VDC i i i i i T 21 t39lme a radIan frequency radIanssec n 2 1L f I I A amplitude perlod T DC average I I Slnus0ldal AC yt Alcosngt t Phasor Phase voltage m V p cosngtlt vm Vp em current it Ip cosngt t 1a Ip em At At Phase I 360ng or 1 l2 n rad Adding and subtracting Slnusoldal AC voltages or currents Voltages and currents are represented by phasors draw on a real 7 ImagInary quotphasorquotdlagram These phasors add and subtractlust llke vectors v10 Vpllcosngtlt v20 Vp2 c05ngt t9 The problem V3l v10 v20 7 Draw phasors as shown VldmVp1amp and Vzdm VPZ Add the phasors lust as you would vectors to get V3010 Vp3 m Vp3 Vp1c05VVp2 0592V arctan V pllsinW V pzlslme V pl wSW V ame Convert phasor back to tImerdomaIn voltage V3t V 1t V20 V p3 cosngtlt v Done Phasor analysis For steadystate s39lrluso39ldal response ONLY T L lol 1 addIng d on a complex plane for a very good reason The math Is all based on the Euler39s eguatlon m m In rm Euler39s eguation e mm usan OR cos0l sin9 1 NW cosm t9jlsinmlt9 1148qu cosngt t e lfwe freeze thIs at tIme t0 then we can represent cosngtlt 9 by 6 8 That39s the phasor Capacltors and lnductors In AC cIrcuIts cause 90 phase shlfls between voltages and currents because they Integrate and dlfferentlate But IntegratIon and dlfferentlatlon Is a pIecerofrcake In phasors Drop the wt 10 to gel Calculus ghel mm MW awe n w mt890dc Aye 30ch dt 1 v 9904 l J M We at 7 L A eywltel 7 1 M WHOM A ell g V n ya u AC Notes Phasor analysis with impedances For steadystate sinusoidal response ONLY 39 p c Capacitor d 1 j 1 i Civ v 7 i tct Z if V jm Ijogt C dt C C c C C jmC oC C jwC Inductor d 1 IWL vL LaiL 1L i VLtdt zL jwL VLjo jwLIjogt Resistor VR Z R V gt RIM J VRiRR 1117 R39 R1 0 39 1 39 R You can use impedances just like resistances as long as you deal with the complex arithmetic ALL the DC circuit analysis techniques will work with AC serieS Z Z Z r 1 Voltage divider II I n 11 V V n Zeqzlz2z339 Z tomlz1Z2Z3 Example RA C Wquot If R1ZOO l 0211 L116mH and 040003d SEC zeq R 1 jtoL then zeq R 1 jtoL ZOO 17125jQ64jQ20061j n j39w39c jwC parallel Current divider i 11 I I Zn total 1 1 iii Z1 Z2 Z3 Example R C L If R200n 0211 L16mH and 040003d SEC Ze then Ze 1 1 q 1 1 1 q 1 j 1 31 1 7 7 7wC77 810 17700156317 R 1 jmL R mL 2009 9 n jwC 601Q917Q 109795670 179 A601Q2917Q2109639Q 21an 567639deg 6019 Example Find V0 in the circuit shown Express it as a magnitude and phase angle the way V5 is expressed V Z 1 25 235jQ VS6VeJlsdeg 460d Z2 227mm 5g 1 V S Simple voltage divrder 1 2 V0 lz 2i compodeg 40n lzzl ammodeg 69282Q 2240769282j m Z1Z2 255235j 240ne 69282jQ6534282j 11 734236Qe39127 8 eg z rjisodeg 2 8093 y13deg 17 6Ve 80399 3917607727181 13119 51421119 0 s 6VJlt lt r gt E 653V J g 12731deg e e Z 1 Z 2 73486ne 734869 AC Notes Allowable Course Navigation 0 Line Following 0 Phototranistor IR Emitter Pair 0 Wall Finding o Ultrasonic Range nder 0 IR Range nder 0 Touch sensors 0 Mechanical Arms 0 Decoders on wheels treads etc Allowable Mobility 0 Wheels Maximum Diameter of 80mm 0 Treads Maximum Cog Diameter of 80mm 0 Mechanical Legs Discontinuous contact with the ground Allowable Robot Size 0 Max footprint of 250mm unlimited height 0 Max weight of2 kg Robot Rules L Locomotion The robot may move through the course using any method as long as it does not damage the course It also must not leave any parts behind Protection The robot must keep the HandyBoard motors HBridge Ultrasonic Range nder voltage divider battery pack and any integrated circuits shielded from water Other 39 r are A J to be shielded as well Each robot will be required to demonstrate that all of the components are protected 4 weeks before the competition Appearance The robot must contain a removable exterior skin that will provide a nished appearance Additionally the inside of the robot should be neatly organized and each component should demonstrate quality craftsmanship Power Source The robot must be powered by only the 72 volt battery and 5 Volt HandyBoard battery provided Autonomy The robot will be turned on at the beginning of the course and will begin movement when LED beacons are simultaneously lit up on all four courses Additionally the robot must navigate through the course autonomously with no help from the team members Design and Manufacturing Each group must design and manufacture all aspects of their robot Prebuilt components such as wheels treads motors etc are allowed Budget Each team will be given 50 for parts on their robots and will be able to use 20 out of pocket Six 15 motor credits as well as all necessary electronic equipment will be supplied to each team Robot Contact The robots may engage each other at the end of the course but no intentional damage may be dealt Any intentional damage in icted will result in elimination from the competition IN I If lie IFquot IO Il 90 2 Kill Switch Each robot will be required to have a kill switch on the top of the robot in the event that it gets stuck in the course Competition Rules 1 N 5 P O l Contest Table All four courses will be identical and will be 1 wide and a maximum of 1 tall Each robot must begin behind a designated starting line Objective The objective for each robot is to navigate through the obstacle course and to stay inside the nishing square Time Limit The course shall be completed in XX seconds Winning The competition ends when the time has expired Whichever robot is closest to the nishing square will be declared the winner Interference The team members must stay out of the competition area at all times Number of People on Course There will only be one person from each team allowed on the starting line of each course Staging Area While four teams are competing on the obstacle course four more teams will be in the staging area and must be ready to compete 30 seconds after the current competition ends


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