PDR Paper FINAL DRAFT

Levitating Globe
Phillip Marr, David Wang, Seth Davidson and John Palermo
Division of Electrical and Computer Engineering
Preliminary Design Report for Senior Design
April 28, 2015
Faculty Advisor: Dr. Hsiao-Chun Wu

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Table of Contents
Table of Figures..................................................................................................................................4
Introduction.......................................................................................................................................7
Abstract.........................................................................................................................................7
Description of Preliminary Design Report.........................................................................................7
Problem Statement.............................................................................................................................8
Need and Objective Statement........................................................................................................8
Background....................................................................................................................................8
Levitron Ion by Fascinations.....................................................................................................9
Levitating Globe byNational Geographic.................................................................................10
Marketing Requirements...............................................................................................................11
Objective Tree..............................................................................................................................13
Tradeoff Matrices.........................................................................................................................14
Overall Design..................................................................................................................................15
Functional Decomposition.............................................................................................................15
Level 0......................................................................................................................................15
Level 1......................................................................................................................................16
Power Supply ...................................................................................................................................19
Circuits, Simulations and Formulas.................................................................................................20
Step-Down Transformer, Voltage-to-Current Converter...............................................................20
Step-Down Transformer.........................................................................................................20
Diodes ..................................................................................................................................21
Capacitors.............................................................................................................................21
Voltage Rectifier Circuit Simulation.........................................................................................22
Wireless Power ................................................................................................................................24
Transmission, Excitation, and Receiver Coils................................................................................25
Coupling Coefficient...............................................................................................................26
Inductor Quality Factor..........................................................................................................27
Finding Mutual Inductance.....................................................................................................29

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Oscillator..................................................................................................................................30
Hartley and Colpitts Oscillators...............................................................................................31
Colpitts Oscillator Circuit Simulation.......................................................................................32
DC Motor Controller.........................................................................................................................36
DC Motor Selection and Parameters...........................................................................................38
Counter-electromotive Force .................................................................................................38
Transmitter Xbee and Circuit..................................................................................................40
Converting the PWMsignal to Analog.....................................................................................43
Receiver Xbee........................................................................................................................47
DC Motor Circuit (H-bridge)....................................................................................................48
Rotational Position Tracking..............................................................................................................51
Infrared LED, Infrared Photo-Diode, Op-amp, Reflection material.................................................52
Infrared LED’s........................................................................................................................52
Infrared Photo-Diode’s...........................................................................................................54
Trilateration..........................................................................................................................56
Op-amps...............................................................................................................................57
Levitation Control.............................................................................................................................59
Hall Effect Sensors, Relays, Solenoids, and Permanent Magnets...................................................61
Hall Effect Sensors.................................................................................................................61
Relays...................................................................................................................................63
Permanent Magnets..............................................................................................................65
Solenoids ..............................................................................................................................67
Microcontroller Interface..................................................................................................................70
Circuits, Behavioral Models, and Formulas .....................................................................................73
Microcontroller - Raspberry Pi 2 Model B....................................................................................73

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Justification...........................................................................................................................73
Analog to Digital Converter – Microchip MCP3008 ......................................................................74
Serial Peripheral Interface (SPI) ..............................................................................................75
LCD Capacitive Touchscreen – Adafruit PiTFT 2.8” 320x280 pixels ................................................77
Graphical User Interface (GUI)................................................................................................77
Functional Decomposition......................................................................................................78
Internet Communication............................................................................................................80
Functional Decomposition......................................................................................................80
WiFi Module – Edimax EW-7811un.........................................................................................80
Software andAlgorithms...............................................................................................................81
SPI Pseudocode.........................................................................................................................81
Reading A/D converted voltages.............................................................................................81
Handling Rotational Position..................................................................................................82
Handling Rotational Position..................................................................................................83
Handling Hall Effect Voltages..................................................................................................83
GUI Pseudocode........................................................................................................................84
Tkinter..................................................................................................................................84
GUI Prototype .......................................................................................................................85
Motor Control Pseudocode........................................................................................................86
Generating the Pulse Width Modulation Signal .......................................................................87
Motor Direction and User Input..............................................................................................87
Project Management........................................................................................................................89
Work Breakdown Structure...........................................................................................................89
Gantt Chart ..................................................................................................................................95
Network Diagram........................................................................................................................ 100
Budget....................................................................................................................................... 101
Legal and Safety Concerns............................................................................................................... 104
Intellectual Property ................................................................................................................... 104
Safety......................................................................................................................................... 104
Works Cited...................................................................................................................................105

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Table of Figures
Figure 1: Mockup of final design..........................................................................................................8
Figure 2: Levitron Ion by Fascinations ..................................................................................................9
Figure 3: Levitating Globe by National Geographic..............................................................................10
Figure 4: Complete Requirements Specification..................................................................................11
Figure 5: Table of Marketing Requirements........................................................................................12
Figure 6: Objective Tree....................................................................................................................13
Figure 7: Engineering-Marketing Tradeoff Matrix ...............................................................................14
Figure 8: Engineering Tradeoff Matrix................................................................................................14
Figure 9: Level 0 Functional Decomposition of the Levitating Globe.....................................................15
Figure 10: Level 1 Functional Decomposition of the Levitating Globe...................................................16
Figure 11: Level 2 Functional Decomposition of the Power Supply.......................................................19
Figure 12: Transformer Winding Diagram...........................................................................................20
Figure 13: Full Wave Rectifier............................................................................................................21
Figure 14: Multisim of Step Down to 12 Volts.....................................................................................22
Figure 15: Transient Response for the 12 Volt Step Down ...................................................................22
Figure 16: 5V Rectifying Bridge..........................................................................................................23
Figure 17: Transient Response for Rectifying Bridge for 5 Volts............................................................23
Figure 18: Level 2 Functional Decomposition of the WirelessPower System ........................................24
Figure 19: Resonant Frequency Formula ............................................................................................25
Figure 20: Basic Coil Diagram.............................................................................................................26
Figure 21: Actual Inductor Model.......................................................................................................28
Figure 22: Increasing Q effect on Resonant Frequency Bandwidth.......................................................29
Figure 23: Faraday's Law of Induction ................................................................................................30
Figure 24: Hartley Oscillator Characteristic.........................................................................................31
Figure 25: Colpitts Oscillator Characteristic........................................................................................31
Figure 26: Resonant Frequency Formula for Colpitts Oscillator............................................................32
Figure 27: Colpitts Oscillator Circuit (~150 KHz) ..................................................................................32
Figure 28: Colpitts Oscillator Output Waveform..................................................................................33
Figure 29: 1 Wavelength of Output Waveform ...................................................................................34
Figure 30: Output Fourier Transform .................................................................................................34
Figure 31: Buffered Colpitts Oscillator Circuit .....................................................................................35
Figure 32: Buffered Colpitts Oscillator Output ....................................................................................35
Figure 33: Level 2 Functional Decomposition of the Motor..................................................................36
Figure 34: 6 RPM Gear Motor from ServoCity.....................................................................................38
Figure 35: Illustration of Brushed DC Motor Rotation Mechanics.........................................................39
Figure 36: Equivalent Model of Back-emf...........................................................................................39
Figure 37: Equivalent Model of a DC Motor........................................................................................40
Figure 38: Xbee Module by Digi.........................................................................................................40
Figure 39: Xbee Pinout Diagram.........................................................................................................41
Figure 40: Transmitter Xbee Wiring Diagram......................................................................................42

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Figure 41: Raspberry Pi 19.2 MHz PWM .............................................................................................44
Figure 42: Fourier Transform of PWM................................................................................................44
Figure 43: First Order Low-pass Filter.................................................................................................45
Figure 44: SlightlyAttenuated PWMSignal.........................................................................................46
Figure 45: Further AttenuatedPWMSignal ........................................................................................46
Figure 46: Second Order Low-pass Filter............................................................................................47
Figure 47: Comparison of First Order and Second Order Outputs.........................................................47
Figure 48: Ripple Voltage Transient....................................................................................................47
Figure 49: Xbee Receiver Module Wiring Diagram ..............................................................................48
Figure 50: H-bridge Circuit.................................................................................................................49
Figure 51: PWMCurrent in Direction A ..............................................................................................50
Figure 52: PWMCurrent in Direction B ..............................................................................................50
Figure 53: Level 2 Functional Decomposition of Rotational Positioning................................................51
Figure 54: Infrared LED......................................................................................................................52
Figure 55: Circuitry for Infrared LED operation ...................................................................................53
Figure 56: Output response of current flowing through LED ................................................................53
Figure 57: Infrared LED Array.............................................................................................................54
Figure 58: Infrared Photo-Diode ........................................................................................................54
Figure 59: Example of Infrared Photo-diode placement.......................................................................55
Figure 60: Example of Photo-diode....................................................................................................55
Figure 61: Circuitry for Infrared Photo-diode operation.......................................................................56
Figure 62: Trilaterationexample figure ..............................................................................................57
Figure 63: Non-inverting Op-amp......................................................................................................58
Figure 64: Final design for rotational positioning ................................................................................59
Figure 65: Level 2 Functional Decomposition of the Levitation Control System.....................................59
Figure 66: Hall Effect Sensor..............................................................................................................61
Figure 67: Hall Effect Sensor placement.............................................................................................62
Figure 68: Right Triangle for distance calculation................................................................................62
Figure 69: Hall Effect Sensor Block Diagram and output......................................................................63
Figure 70: NPN Transistor..................................................................................................................63
Figure 71: Relay design for solenoid operation...................................................................................64
Figure 72: Permanent Magnet...........................................................................................................65
Figure 73: Magnetic Field..................................................................................................................66
Figure 74: Distance with respect to force by magnetic field.................................................................66
Figure 75: Solenoid...........................................................................................................................67
Figure 76: Magnetic Field of Solenoid ................................................................................................68
Figure 77: Magnetic Field directly above Solenoid ..............................................................................69
Figure 78: Magnetic Field at an Angle to Solenoid...............................................................................70
Figure 79: Level 2 Functional Decomposition of the Microcontroller....................................................71
Figure 80: Raspberry Pi 2 Model B .....................................................................................................73
Figure 81: MCP3008 A/D converter connected to Raspberry Pi breakout.............................................74
Figure 82: Second Order Anti-Aliasing Filterfor Analog Inputs to MCP3008..........................................75

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Figure 83: Serial Peripheral Interface .................................................................................................76
Figure 84: PiTFT 2.8" 320x280 LCD Touchscreen.................................................................................77
Figure 85: GUI State Diagram ............................................................................................................78
Figure 86: Level 2 Functional Decomposition of the GUI Program........................................................78
Figure 87: Level 2 Functional Decomposition of Internet Communications...........................................80
Figure 88: SPI on the MCP3008 Timing Diagram .................................................................................81
Figure 89: Square Topology of Hall Effect Sensors...............................................................................83
Figure 90: GUI Demo Concept ...........................................................................................................84
Figure 91: GUI Mockup .....................................................................................................................85
Figure 92: Electromagnetic Spectrum............................................................................................... 105

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Introduction
Abstract
Science,technology,engineering,andmath(STEM) basedacademiccourseshave historically
had a difficulttime generatinginterestfromAmericanstudents.Whilenotanall-encompassingsolution
to the problem,ourgoal is tocreate an interactive levitatingEarthmodel displaywhichwill serveasan
effectivedemonstrationof conceptsandapplicationsof magnetismandsparkaninterestinthe fieldof
physics. Stable levitationviamagnetismwasonce thoughttobe infeasible twocenturiesago, butthis
documentwill showthatadvancesinmicroprocessortechnologyandcontrol systemshave made it
viable withpowerful real-worldapplications.AsalevitatingEarthmodel,itisimportanttodemonstrate
the conceptof rotation,whichcanbe accomplishedwiththe use of amotor.Motors relyon an
interactionbetween twomagneticfieldsandserve asan opportunitytodemonstrate how magnetic
fieldsare the linkbetween electrical andmechanical energyconversions.Finally,wirelesspowertransfer
isan emergingtechnologywhichcanbe usedto deliverelectrical energyacrossdistanceswithoutthe
use of physical connections. Throughfurtherexamination,itisdiscovered thatmagnetismisthe driving
force behindcurrent wirelesspowertransfermethods whichisbecomingprominentincommercial
products.Thisdocumentdescribes preliminarydesignimplementationsinorder toproduce the
complete workingdevice.
Description of Preliminary Design Report
The purpose of the preliminarydesignreport(PDR) documentistodescribe the design of
magneticallylevitatingaglobe,wirelesslypoweringitsmotor,andcontrolling itsvariousother
subsystems.This documentprovidesthe requirementsforachievingthislevitationeffectandthengives
a detailedexplanationof howourdesignteamintendstoimplementthe solution.The functional
decomposition,behavioral models,powersupplycircuits,andalgorithms thatwill be usedforall
subsystemsare below.Alsoincludedare safetyandlegal concernsforoursystemandteam
managementdetailsrelatingtoourwork breakdownandbudget.

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Problem Statement
Figure 1: Mockup of final design
Need and Objective Statement
Accordingto Teachfor America,Americanstudentslagfarbehindtheirinternationalpeersin
understandingof the subjectsof science,technology,engineering,andmath(STEM).The UnitedStates
was ranked25th
inmath and 17th
inscience among27 industrializednations [1].Itisexpectedthat60%
of jobscreatedinthe 21st
centurywill require STEMbasedskills, butonlyanestimated20% of the
currentworkforce possessesthese skills [2].While STEMbasedjobsare generallyamongthe most
lucrative inAmerica,amongstudentswhoare proficientinmath,upto 27% are disinterestedinSTEM
subjects[3].There isa needto solve the disconnectionbetweenSTEMsubjectsandstudentinterest.
The objective of thisprojectistocreate an Earth model globe levitatingabove aplatform
throughthe use of magnetism.The device will serve asademonstrationof magneticconceptsandspark
an interestinthe fieldof physicsforstudentsof anyage.The rotationof the Earth model will be
performedona realistictiltedaxis. The featuresof the globe will be poweredwirelesslyandremove the
needforbatteries.A userinterface will introduce interactivityandgive the useranumberof controls
overthe globe’sactivity.
Background
The basic theorybehindthe conceptof thisprojectisbasedonthe interactionbetweentwoor
more magneticfields.When opposite-polesof magnetsare placedin proximitytoeachother,the
magnetsattract each other.Incontrast, a repulsiveeffectoccurswhen like-polesare placedin

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proximity.The repulsive effect canproduce anunstable levitationwhichrequiresotherforcesinorder
to balance the systemandcreate stabilization.
There are several productscommerciallyavailable whichare similartoourfinal design vision:
LevitronIonby Fascinations
The LevitronIonis the productwhichmost closelyresemblesthe aestheticsof the designwe
hope to achieve.Whilemostdevicesonthe marketrelyonoverheadmagnetismtostabilizethe globe,
the LevitronIon containsonlya base overwhichthe globe levitates.A permanentmagnetinthe bottom
of the globe andanotherpermanentmagnet inthe base provide the liftof the globe.A setof
electromagnetsinthe base are fedfroma control circuitwhichreceivesinputfromapositioningsensor
and adjuststhe electromagnetsaccordinglytoprovidestable levitation.The magnetinside of the globe
isremovable andacts as a platformforwhichany object12 ouncesor lesscan be levitated.
Figure 2: Levitron Ion by Fascinations
Users of the LevitronIonhave beencritical of a numberof frustrationswiththe product.If the
“sweetspot”isnot foundwhentryingtoinitiallylevitate the globe,the control circuitcanmalfunction
and cause overheating.While some usershave reportedstablelevitationforanumberof monthsor
yearsconsecutively,manycustomersseemtobe unwillingtoovercome the learningcurve of placingthe
globe properlyoverthe base.The LevitronIoncanrotate continuouslyonanuprightaxis,butrequires
the userto manuallybeginthe rotationof the globe withtheirhandsandthe rotationisnotedtobe

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interferedwitheasilybycommonoffice objectssuchasmetal filingcabinets.The globe alsooffersno
interactivityaspectsandismostlyconsideredanovelty.
LevitatingGlobe by NationalGeographic
The LevitatingGlobe byNational Geographicfeaturesanoverheadlevitationsystem.A
permanentmagnetinthe topof the globe isattractedto an electromagnetinthe topof the stand.The
force of gravitypullsdown onthe globe while the electromagnetpulsesbasedonfeedbackfroma
control circuitwhichdetectsthe globesdistance fromitsarmwithpositional sensors. Thisconstant
pulsingallowsthe forcestobalance themselveswhilethe globe levitatesinplace. Thisoverhead
magnetismconceptisthe mostcommonon the marketfor productsof thistype.
Figure 3: Levitating Globe by National Geographic
Thismodel featuresproblemssimilartothe LevitronAG.The topof the stand overheatsif the
properlocationisnotfoundwheninitiallyplacingthe globe.Whilethe LevitronAGcanprovide stable
and continuousrotation,the NationalGeographicversiononlyrotatesforalimitedamountof time after
the userappliesaforce.Again,due to lackof interactivity,the productisgenerallyconsideredanovelty
item.
In orderto differentiateourmodel fromthe currentmarketimplementations,the goal isto
provide the userwithalessfrustratingexperience of findingthe properinitial balancingpoint.
Automatedrotationcontrol throughthe use of a motor whicheliminatesthe needforaphysical
interactionbetweenthe userandthe globe isalsodesired.Interactivityconceptssuchasgivingthe user
control overthe speedof rotationand the abilitytoinputa longitude coordinate throughauser
interface isa conceptwhichwill bringthe device tolifeandmake the productmore than a novelty.

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Marketing Requirements
Marketing Requirements Engineering Requirements Justification
1
1. The product shouldcost
lessthan$100 for an
enduser.
Cost shouldnotbe a barrierto
useful educationtools.This
pricingisbasedon similar
designs.
3, 6, 7
2. It will be possibletorun
the device with100%
uptime.
Thiswill provide aninteresting
and continuousdisplayina
classroomsetting.
1, 4
3. The device will
demonstrate atleast3
magneticapplications.
It isimportantto show that
magnetismhasseveral practical
applications.
1, 6
4. The device will use 10%
lessenergythancurrent
market
implementations.
Withthe abilitytorun
continuouslyif desired,itis
importantforthe device tobe
energyefficient.Thisalso
teachesaboutreducingwaste.
1, 2, 3, 4
5. The globe will calibrate
itself andfinditsproper
equilibriumwithout
physical userinput.
The device needstobe easyfor
teachersandyoungstudentsto
initialize withoutfrustration.
5
6. The UI will give the user
a minimumof 5 different
typesof interactionwith
the globe.
The controlsthroughthe UI are
whatwill allow studentsto get
involvedandgive themfirst-
handexperiencewiththe
manipulationof magneticfields.
1, 6, 7
7. The globe will be durable
enoughtowithstanda
drop of at least6 inches
incase of sudden
removal frompower.
The globe isexpectedtolevitate
no more than a few inchesabove
the platform.A 6 inchrating
ensuresthatitcan fall without
damage fromits stable levitation
height
Marketing Requirements
1. The device shouldserve asaneffectivedemonstrationof magneticprinciplesforuse ina
classroomenvironment.
2. The device shouldbe easytosetup.
3. The device shouldbe stable andresistive toexternalforces.
4. The device shouldlevitate androtate ona tiltedaxis.
5. A userinterface shouldbe availabletointroduce interactivityaspectsandallow usercontrol.
6. The device performance shouldremainconsistentafterperiodsof extendeduse.
7. The globe shouldbe durable.
Figure 4: Complete Requirements Specification

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Magnetic
Principles
Levitation
&Rotation
Stable
EasySet-Up
User
Interface
Uptime
Durable
Geometric
Mean
Weight
Magnetic
Principles
1 1 3 5 7 3 9 3.11 0.30
Levitation&
Rotation
1 1 3 5 7 3 9 3.11 0.30
Stable 1/3 1/3 1 3 5 1 7 1.42 0.14
Easy Set-Up 1/5 1/5 1/3 1 5 1/5 5 0.68 0.07
User
Interface
1/7 1/7 1/5 1/5 1 1/5 5 0.36 0.03
Uptime 1/3 1/3 1 5 5 1 7 1.53 0.15
Durable 1/9 1/9 1/7 1/5 1/5 1/7 1 0.19 0.02
Figure 5: Table of Marketing Requirements
Sevenmarketingrequirementswere developedinordertodescribe whatourvisionof a
successful projectis.Mostrelevanttoourneedstatement,the device shouldserve asaneffective
demonstrationof magneticprinciples.The device isdesignedtoinspire curiosityinyoungstudents in
hopesthattheywill desire tolearnaboutitsprinciplesof operation.A devicewhichistobe usedas an
educational tool inthe classroomshouldbe easyto setup.A teacherbecomingfrustratedoverthe
initializationof thisdevice wouldmeanitsuse infewer classrooms. Currentmarketimplementations
require time andpractice tostabilize levitation whichare importanttoavoid.The device shouldbe
stable initslevitationandresistivetoexternal forcesdue tothe amountof studentswhocouldinteract
withiton a dailybasis.Asthe device levitates,itshouldrotate onatilted axisinthe same orientation
that the Earth doesto provide amore accurate experience. A userinterface shouldbe providedinorder
to getstudentsinvolved.Givingstudentsareasonto explore,ratherthan simplyanobjecttolook at,
increasesthe chance thatthisprojectis successful. Inordertomaximize convenience forstudentsand
teachers,the device shouldbe able torunconsistentlyandindefinitelywithoutbecomingunstableor
overheating.The Earthneverstopsitsrotationandneithershouldthe globe.Finally,the device should
be durable inorderto ensure thatit can be usedformanyclassesof studentsandminimize costsfor
educational institutions.
In conjunctionwiththe marketingrequirements,asetof engineeringrequirementswascreated
to complete the requirementsspecification. Inordertobringthe device intomore classrooms,the final
productshouldcost lessthan$100 (pricingbasedonthe Levitronion,MSRPfromFascinations).Costs
shouldnotbe a barrierto useful educational tools. One-hundredpercentuptimeshouldbe possible in
orderto allowthe productto be an educational tool aswell asaninterestingandfunctional display.This
requirementensuresthatthe globe will operateundersafe conditionsforaslongasthe userwishes.As
a device designedtobe a demonstrationof magneticprinciplesandapplications,the globe should
demonstrate nolessthan3 applications toprovide arobustexperience forthe users. The endgoal of
thisdevice isforitsuse in educational institutions. Anefficientpowerrequirementallowsthe device to
be operatedat lowcost.In orderto provide aneasyto setup experience,the equilibriumpositionof the

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globe above the base shouldbe self-calibratingand require noextraneousphysical inputfromthe user.
Thisreducesthe needforlengthyorconfusinginstructions whichcanleadto frustration.Byprovidinga
UI whichgivesthe usera minimumof 5 differentinteractions,ithelpsensure thatthe device will be
interestingfora longerperiodof time.Finally,if the globe isable towithstandasuddenfall froma
heightof 6 inchesitwill be durable enoughtowithstandourdesiredheightof approximately2inches
fromthe base.Thiswill alsomake the globe more resistanttowearfromthe expected multipleusers.
Objective Tree
Figure 6: Objective Tree
The marketingrequirementsforthe projectwere organizedintoanobjectivetree whichgroups
objectiveswithfunctional similarities.The mostimportantobjective isthatthe globe levitates.A
successful levitationwill be definedbyitsstability,resistivitytoexternal forces,anditsabilitytolevitate
ina continuousfashion.The secondmostimportantobjective isthatthe globe rotates.Thiswillbe
Levitating Globe
Levitates
(0.55)
Stable
(0.65)
Resistive to
external forces
(0.28)
Continuous
(0.07)
Rotates
(0.24)
Realistic tilted axis
(0.75)
Variable Speeds
(0.25)
User Interface
(0.12)
Rotation direction
and speed
(0.57)
Regional data
(0.04)
Coordinate
selection
(0.25)
World clock
(0.12)
Easy to use
(0.07)
Self-calibrates
(0.5)
No batteries
(0.5)

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accomplishedonatiltedaxisandwithvariable rotationspeeds.The userinterface isthe nextobjective.
Throughthe interface,auserwill be able tochange rotational speedanddirectionof the globe.
Longitudinal coordinateselectionwill allowthe usertorotate to the desiredpointwhileworldclock
mode will rotate the globe basedonthe current time of day.Regional datacan also be acquiredwhich
will give informationonnews,weatherandfacts.Finally,the globe will be easytouse bycalibrating
withoutuserinputandwithnobatteryrequirementsdue tothe wirelesspower.
Tradeoff Matrices
Cost
Uptime
Demonstration
Count
Self-Calibration
Interactions
Durability
- + + + + +
1) Effective Demo + ↓↓ ↑↑ ↑ ↑↑
2) Easy Set-up + ↓ ↑↑ ↑
3) Stability + ↓↓ ↑↑ ↑↑
4) Levitation/Rotation + ↑↑ ↑
5) User Interface + ↓↓ ↑↑
6) Consistent
Performance
+
↓ ↑↑ ↑
7) Durability + ↓ ↑↑
Figure 7: Engineering-Marketing Tradeoff Matrix
Cost
Uptime
Demonstration
Count
Self-Calibration
Interactions
Durability- + + + + +
Cost - //////////// ↑ ↑ ↑ ↑ ↑
Uptime + //////////// //////////// ↑
Demonstration
Count
+
//////////// //////////// ///////////// ↑
Self-Calibration + //////////// //////////// ///////////// ////////////
Interactions + //////////// //////////// ///////////// //////////// //////////
Durability + //////////// //////////// ///////////// //////////// ////////// ////////////
Figure 8: Engineering Tradeoff Matrix

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Overall Design
Functional Decomposition
Level 0
Figure 9: Level 0 Functional Decomposition of the Levitating Globe
Levitating Globe forLevel 0 Functionality
Module LevitatingGlobe Project
Inputs Power:V AC
User input:UserInput
Outputs Levitation:1.5inch stable levitation
Rotation:continuousleft/right,longitudeinput, real timeclock,speedcontrol 5-10
rpm, specificdegreerotations
User inputinformation:LCDdisplay,weatherinformation,coordinate information
Functionality Stablylevitate aglobe thatrotatesona tiltedaxis.Userinputshouldcontrol aspects
of thatrotation.Aninterface will displaycontrolsandinformationforthe userto
interactwithglobe.

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Level 1
Figure 10: Level 1 Functional Decomposition of the Levitating Globe
PowerSupply for Level 1 Functionality
Module PowerSupply
Inputs Power:V AC
Outputs Power:multipleV DC
Functionality Convertwall ACvoltage toDC voltage.Provide differentDCvoltagestothe many
systems.

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Wireless PowerSystem for Level 1 Functionality
Module WirelessPowerSystem
Inputs Power:V DC
Outputs Power:V DC
Functionality Transmita voltage wirelesslyviaresonantinductive couplingtothe DC motor.
Convertthe DC inputvoltage toACfor transmissionandrectifybacktoDC to control
the motor.
DC Motor for Level1 Functionality
Module DC Motor
Inputs Power:V DC
Motor control signals
Outputs Rotation:continuousleft/right,longitudeinput,real timeclock,speedcontrol 5-10
rpm, specificdegreerotations
Angle:positionindegreesbasedonlocationof globe shell
Functionality Rotate the levitatingglobe basedonuserinput.Mustspinconsistently,without
jerkinessataspeedof 5-10 rpm.
Position Tracking forLevel 1 Functionality
Module PositionTracking
Inputs Power:V DC
Angle:detectedfacingof globe toallow usercontrol of rotation
Outputs SensorOutput:IR beamreportedangle
Functionality Shootan IR beamat a polarizedportionof globe todetectpositionangle.Reportthis
to microcontrollersothatfacingof globe can be controlled.
Levitation Control System forLevel 1 Functionality
Module LevitationControl System
Inputs Power:V DC
Response:relaysturnelectromagnetson/offbasedonphysical positionof alevitating
permanentmagnetinglobe.
Outputs Feedback:amplifiedHall effect sensorvoltageoutputdetectinglevitatingpermanent
magnet’sposition
Levitation:stable
Functionality Controlslevitatingglobe’sstabilityviaelectromagnets.Detectslocationof a
permanentmagnetinthe globe andoutputsthe locationfromthree Hall effect
sensorscorrespondingtoa(x,y,z) position.Turnsrelayson/off basedoninputfrom
microcontrollerinorderto“push”globe intoplace.

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Microcontrollerand LCD Interfacefor Level 1 Functionality
Module MicrocontrollerandLCD Interface
Inputs Power:5V DC
Feedback:levitationcontrol systemamplifiedHall effectvoltages
User input:LCD touchscreen
Sensoroutput:IR beamangle
Outputs Motor Control Signals:encodedserialdatacorrespondingtocontrol bits
Response:control relaystoturn electromagnetson/off
Display:userinterface controlsandinformation
Functionality Acts as brainsof the sensors. Hasan LCD touchscreenforuserinteractionsuchas
motor controls.Sendsmotorcontrol bitsviaserial RFtransmission.Usesglobe
positiontokeeprotationaccurate.Calculateson/off of relaysforstability.

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Power Supply
The functional 2 decompositionbelow takesthe powersupplyfromthe wall outletandstepsit
downto usable alternatingcurrentforthe differentsubsystemsimplementedinthisproject(12V and5V
AC).Thenthe alternatingcurrentsare passedthoughrectifierstobecome directcurrentsandfinally
filteredbefore goingtotheirrespectivesubsystems.
Figure 11: Level 2 Functional Decomposition of the Power Supply
Transformer for Level 2 Functionality
Module Transformer
Inputs Power:120V AC
Outputs Power:5 V AC
Functionality Reduce the ACvoltage froma wall outletdowntoa more useable range forour
powersupply.

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Rectifier forLevel 2 Functionality
Module Rectifier
Inputs Power:5 V AC
Outputs Power:V DC (rectified)
Functionality Produce a directcurrentfrom the alternatingcurrentprovidedbythe transformerto
powerthe microcontroller.
Smoothing Filter for Level 2 Functionality
Module SmoothingFilter
Inputs Power:5 V DC
Outputs Power:V DC
Functionality Ensuresthat the voltage doesnotgo above orbelow five percentof 5voltsfor the
Microcontroller.
Circuits, Simulations and Formulas
Step-DownTransformer,Voltage-to-CurrentConverter
Step-DownTransformer
Withthe wall outletsupplying120 volts,the voltage needstobe “stepdown”inorderfor our
systemstooperate.
Figure 12: Transformer Winding Diagram
The varyingcurrent inthe transformer'sprimarywindingcreatesavaryingmagneticflux inthe core and
a varyingmagneticfieldimpingingonthe secondarywinding.The varyingmagneticfieldatthe
secondaryinducesavaryingelectromotive force inthe secondarywinding.The primaryandsecondary
windingsare wrappedaroundacore of infinitelyhighmagneticpermeability sothatall of the magnetic
flux passesthroughboththe primaryandsecondarywindings. [4]
𝐿 =
µ𝐴𝑁2
𝑙
A 10:1 transformercan be simulatedinMultisimasthe defaultone primaryandone secondarycoils.
Withthe voltage loweredwithinoperatingrange,itneedstobe rectifiedintoadirectcurrent.

21
Diodes
A diode has a lowresistance tocurrentinone direction,andhighresistanceinthe other.
However,diodeshave more complicatedbehaviorthanthis,due totheirnonlinearcurrent-voltage
characteristics.Semiconductordiodesbeginconductingelectricityonlyif acertainthresholdvoltageor
cut-involtage ispresentinthe forwarddirection.
Usingthe ideal diode equationabovedoesnotsimulateareal diode.Thatequationcanbe modeled
below.
Where n isthe idealityfactor,anumberbetween1and2 whichtypicallyincreasesasthe current
decreases.Diodesinacertainarrangementcanconvertalternatingcurrentsintoadirectcurrent. [5]
Figure 13: Full Wave Rectifier
Capacitors
A capacitoris an electrical componentusedtostore energyelectrostaticallyinanelectricfield.
These typically containatleasttwoelectrical conductors separatedbyadielectric.Anideal capacitor
doesnotdissipate energy withaconstantcapacitance. The SIunitof capacitance isthe farad,whichis
equal toone coulombpervolt.
𝐶 =
𝑑𝑄
𝑑𝑉
Theyis alsobe usedto filteroutanyripplespresentedfromanalternatingcurrentrectifiertodirect
current.
𝑉( 𝑡) =
1
𝐶
∫ 𝐼( 𝜏) 𝑑𝜏+ 𝑉(𝑡𝑜)
𝑡
𝑡𝑜

22
Voltage Rectifier CircuitSimulation
For the preliminarycircuitdesign,a stepdowntransformerof the 120V of the wall outletto5V is
used. ForsimplicityinMultisim,the transformerwill be representedwitha5V ACsource operatingat60
Hertz. Take inmindthat these simulationshave nottakeninforthe account of the load resistance each
terminal ismeanttopowerthe othercomponentsof thisproject.
Figure 14: Multisim of Step Down to 12 Volts
Figure 15: Transient Response for the 12 Volt Step Down

23
Figure 16: 5V Rectifying Bridge
Figure 17: Transient Response for Rectifying Bridge for 5 Volts
As seenfromthe simulation above,the voltagedropacrossthe diodesneedtobe accountedfor
if the subsystemsare touse a specificvoltage level.A voltage regulatorwill be neededforthe 5volt
powersupplytothe RaspberryPi,as itneedstobe specificallyat5 volts.

24
Wireless Power
Figure 18: Level 2 Functional Decomposition of the Wireless Power System
Oscillator forLevel 2 Functionality
Module Oscillator
Inputs Power:V DC
Outputs Power:V AC
Functionality Produce an ACvoltage inthe KHz to MHz range for use inresonantfrequencypower
transfer.
Transmitter Coil for Level 2 Functionality
Module Transmission Coil
Inputs Power:V AC
Outputs Oscillatingmagneticfield
Functionality Produce an oscillating magneticfieldinthe KHztoMHz range,equal to frequencyof
the Colpittsoscillator.
ExcitationCoil forLevel 2 Functionality
Module ExcitationCoil
Inputs Oscillatingmagneticfield
Outputs Oscillatingmagneticfield
Functionality Resonantly tunedtothe frequencyof the transmissioncoil.Generatesamagnetic
fieldwithgreatervoltage inductionpotential due tothe lackof resistance.

25
Receiver Coil for Level2 Functionality
Module ReceiverCoil
Inputs Oscillatingmagneticfield
Outputs Power:V AC
Functionality BecomesinducedwithanACvoltage due tothe receivedoscillatingmagneticfield.
Tunedto resonantfrequencywiththe oscillatingmagneticfield.
Rectifier forLevel 2 Functionality
Module Rectifier
Inputs Power:V AC
Outputs Power:V DC
Functionality RectifiesanACvoltage intoaDC voltage which will produce useable powerforaDC
motor.
Transmission,Excitation,andReceiverCoils
In orientingthe inductorcoilsforwireless powertransfer,atransmission,excitationand
receivercoil will be used.The transmissioncoil receivesanoscillatingcurrentwaveformdue toan
oscillatingvoltageacrossitscoils.The selectedfrequencyof thisoscillationisimportantinchoosing
parametersforthe excitationandreceivercoil astheymustbe tunedtobe resonantwiththe
transmissionfrequencybythe followingformula:
Figure 19: Resonant Frequency Formula
Where f0 is the resonantfrequencyandLand C are the self-inductance andcapacitance valuesof the
receivercoil andloadedcapacitorsrespectively.The excitationcoil istightlycoupledand resonantly
tunedwiththe transmissionfrequency whichallowsthe excitationcoil togenerate itsownoscillating
magneticfield.Resistance isminimizedinthe excitationcoil inordertoproduce a more efficientoutput
at the receiver.The receivercoil operatessimilarlytothe excitationcoil,butisgenerallyfurtheraway
fromthe transmitter.The voltage waveformacrossthe receivercoil isrectifiedandbecomesuseable for
the load.

26
Figure 20: Basic Coil Diagram
In orderto effectivelybuildandtestthe wirelesspowersystem, several parametersmustbe identified
inorder to assistwithtroubleshootingandproducingthe mostefficientendresultpossible.
CouplingCoefficient
A transformerisa pairof conductive windingslinkedtogetherwithapermeable ferromagnetic
core.A magneticfield producedbyanalternatingcurrentinthe primarywindingproducesamagnetic
fieldwhichtravelsthroughthe secondarywindingandinducesavoltage inthe coil.The permeablecore
betweenthesetwocoilsensuresthatnearlyall of the magneticflux generatedbythe primaryreaches
the secondarycoil.
In a wirelesspowertransfersystem,thisadvantage islostasan airgap is necessaryinorderfor
the systemto be consideredwireless.The transformercore isremoved,whichresultsinasignificantly
reducedamountof magneticflux linkingthe twowindings. Inordertoidentifyhow strongof acoupling
there existsbetweenthe primaryandsecondarywindings,acoefficient“k”isdeveloped.
The mutual inductance,whichisdefinedasthe ratioof current change in one coil to the voltage
inducedinthe othercoil,can be foundbythe followingformula.
𝑀 =
𝜇0 𝜇 𝑟 𝑁1 𝑁2 𝐴
𝑙
Where μ0 isthe permeabilityof free space (4π× 10-7
), μr is the relative permeabilityof the softironcore,
N isthe numberof coil turnswhere N1 isfor the primarycoil and N2 is for the secondarycoil, A isthe
cross-sectional areainm2
,andl isthe coil’slengthinmeters.Ina wirelesspowertransfersystem,μr can
be regardedas 1, and the total permeabilityissimplyfreespace permeability. Self-Inductance,whichis
determinedbythe ratioof a change incurrent ina windingtoa voltage inthat same winding,isgivenby
the followingformulas,where L1 andL2 are the self-inductancesof eachcoil respectively.
𝑉 = 𝐿
𝑑𝑖
𝑑𝑡

27
𝐿1 =
𝜇0 𝜇 𝑟 𝑁1
2
𝐴
𝑙
𝐿2 =
𝜇0 𝜇 𝑟 𝑁2
2
𝐴
𝑙
By combiningthe equationsforself andmutual inductance,the followingformulaisderivedwhich
describesthe linkbetweenmutual andself-inductance.
𝑀 = √𝐿1 𝐿2
As describedearlier,thisequationistheoretical andisaccurate for an ideal situationwhere all fluxis
linkedbetweenthe twocoils.Inorderto make the formulamore accurate for practical use,the
coefficient“k”mustbe included.
𝑀 = 𝑘√𝐿1 𝐿2
The coefficient“k”rangesbetween0and 1 to indicate how muchof the total flux islinked.While
transformersdon’tlinkall of theirflux,mostof itislinkedandthe “k”value froma transformercanbe
measuredat0.98 or higherinsome cases.Thisiswhythe voltage dropacross a transformercanalways
be approximatedbyobservingthe turnsratiowhile inapplicationswithalow couplingcoefficient,this
methodcannotbe used. For our application,the couplingcoefficientwouldlikelybe below 0.1
approximating1inchbetweenthe transmitterandreceiver coil.Resonantinductivecouplingimproves
thiscouplingcoefficient.
Because we will be constructinginductorsfromscratch,self-inductance will ultimatelybe
neededinordertofindmutual inductance.Toassistinthe process,the Wheelerapproximation canbe
usedas a startingpointfor creatinginductorsandestimatingself-inductance of anair-core inductor.
𝐿 =
𝑟2 𝑛2
9𝑟 + 10𝑙
The variablesinthe equationindicateparametersasfollows:“r” isthe radiusof the coil, “n” is the
numberof turns,and “l” isthe lengthof the coil fromfirstwindingtofinal winding.
InductorQuality Factor
While aninductorisoftenmodeledasonlyacoil of wire ina circuitsimulation,aninductoris
actuallymore accuratelymodeledasaninductorinserieswitharesistor.The resistorrepresentsthe
overall resistance of the conductorlengthwhichthe inductorismade outof. By observingthe ratio
betweenthe reactance andresistance of aninductorusingthismodel,aqualityfactor“Q” can be
determined.

28
Figure 21: Actual Inductor Model
𝑄 =
2𝜋𝑓𝐿
𝑅
=
𝑋 𝐿
𝑅
Thisshowsthat as frequencyincreases,the qualityfactorof the inductorincreases. Because of the need
for alternatingcurrentinthe inductorcoils,the skineffectmustalsobe takenintoaccountwhichresults
inan increase incoil resistance Ras frequencyincreasesaswell.The skineffectpenetrationdepth“δ”is
formulatedthrougharelationwiththe conductor’sresistivityandthe frequencyof current.
𝛿 = √
2𝜌
𝜔𝜇0 𝜇 𝑟
ω = 2πf andρ isthe resistivityof the material of the conductor,whichismostcommonlycopperforthis
type of application(1.68 × 10-8
Ωm).As the frequencyof the currentinthe conductorincreases,the
penetrationdepthdecreases.Thisisknownasthe skineffectwherebymostof the currenttraveling
throughthe conductor ismostlyrestrictedtothe outerlayersof the conductor. This meansthatas
frequencyincreases,the reactance of the inductorincreaseswhichcausesQto increase.Atthe same
time,the resistance of the inductorincreaseswhichcausesQto be adverselyaffected.Thisresultsin
difficultywhentryingtocreate the highestqualityinductorsforwirelesspowertransfer.Inorderto
remedysome of these problems,aninductorwithalargercross-sectioncanbe usedinorder to increase
the amountof area onthe surface of the conductor.
While itmayseemlike ahigherqualityfactorisbetter,thisisnotalwaysnecessarilythe case.
Improvingthe qualityfactorbyincreasingthe frequencycangreatlyimprove the transferdistance of
wirelesspower,butthe bandwidthof the signal decreaseswhichcanresultinlessreliabilityif the
frequencyof the receivercoil isbroughtawayfromresonance. Thiseffectisdisplayedinthe plotbelow.
For thisreason,itseemsillogical toexceedthe KHzrange forour resonantfrequencyselectionasour
currentplansare to levitate the globe approximately1inchfromthe base.

29
Figure 22: Increasing Q effect on Resonant Frequency Bandwidth
FindingMutualInductance
In orderto findthe mutual inductance betweenapairof coupledwindings,the entire equation
for voltage acrossan inductormustbe found.There are three componentsof the total voltage acrossa
winding:the voltage due tothe resistance of the windings,the voltagecausedby self-inductanceand
the voltage causedbythe mutual inductance betweenthe twowindings.Thisisshownbythe formulas
for winding1and winding2:
𝑉1 = 𝑖1 𝑅1 + 𝐿1 (
𝑑𝑖1
𝑑 𝑡
) + 𝑀 (
𝑑𝑖2
𝑑 𝑡
)
𝑉2 = 𝑖2 𝑅2 + 𝐿2 (
𝑑𝑖2
𝑑 𝑡
) + 𝑀(
𝑑𝑖1
𝑑 𝑡
)
If the secondcoil becomesopened,the equationscanbe simplifiedasthere willbe nocurrentflowi ng
throughcoil 2 and thiswill cause nomutual inductance incoil 1:
𝑉1 = 𝑖1 𝑅1 + 𝐿1 (
𝑑 𝑖1
𝑑 𝑡
)
𝑉2 = 𝑀 (
𝑑𝑖1
𝑑 𝑡
)
By solvingfori1 usingintegration:
𝑖1 =
𝑉1
𝑅1
(1 − exp (
−𝑡 ∗ 𝑅1
𝐿1
))
𝑉2 =
𝑀 ∗ 𝑉1
𝐿1
(exp (
−𝑡 ∗ 𝑅1
𝐿1
))
By analyzingt= 0:

30
𝑉2 = 𝑀 ∗
𝑉1
𝐿1
By applyingastepvoltage acrosscoil 1, andby knowingthe self-inductance of coil 1,the voltage atthat
instantacross coil 2 can be usedto determinewhatthe mutual inductance betweenthe twocoilsis. This
informationcanbe usedinour experimentsbyorientingthe coilsinthe desiredfinalposition.Afterwe
are able tofindthe mutual inductance,we canset upcouplingparametersinside of aSPICEsimulation
inorder to assistwithmaximizingpowertransferefficiency.
Oscillator
In orderfor an EMF to ultimatelybe inducedacrossthe receivercoils,analternatingcurrent
mustbe deliveredthroughthe transmissioncoil.ByFaraday’sLaw, a change in the magneticflux
environmentof acoil will produce anEMF inthat coil.
Figure 23: Faraday's Law of Induction
A currentthrougha conductorwill produce amagneticfieldbasedonthe amountof current.By
alternatingacurrentthrough the transmissioncoil, achangingmagneticfieldatthe receivercoil is
produced.
While the mainselectricityprovidesanACpowersource, the frequencyof 60Hz istoo lowto
produce a sufficientwirelesspowertransfer.Mostcommonly,frequenciesinthe KHztoMHz range are
used.While MHzrange frequenciesare knowntoproduce the mostefficientwirelesspowertransfer
overthe greatestdistance,the circuitrynecessarytoprovide astable long-termACsource atthese
frequenciesisunreasonableforthe scope of thisproject.Ultimately,the wirelesspowertransfersystem
isbeingusedtopowera DC motor,thusa frequencyinthe KHzrange was chosen.Inorderto produce a
stable KHzfrequency,anoutputfromour DC powersupplywill actasan inputto an oscillatorcircuit.

31
Hartley and Colpitts Oscillators
Two typesof oscillatorswere examined.The Hartleyoscillatorandthe Colpittsoscillatorsare
twotypesof LC tank circuitswhichcan be usedinconjunctionwithagaindevice suchas a transistoror
an op amp inorderto maintainoscillations.While regulartankcircuitoscillationswill eventually
dampenoutdue to inevitablelossesincircuitry,thesetwooscillatoroptionscontainatappedoutput
whichcan be returnedto the gaindevice asfeedback.The Hartleyoscillator’sdefiningcharacteristicisa
tappedinductor,whichcanbe derivedasatap betweentwoinductorsoras a wire outputfromthe
middle of aninductor.The Colpittsoscillatorissimilarinoperation,butwiththe tapbeingplaced
betweentwocapacitors.
Figure 24: Hartley Oscillator Characteristic
Figure 25: Colpitts Oscillator Characteristic
The oscillatorwhichwaschosenisthe Colpittsoscillator.While bothtypesgivesimilarresults,
the Colpittsoscillatoriseasiertotestand modifyasneededdue tothe ease of replacementof
capacitorsversusthe replacementof inductors.Mutual inductance causedbythe couplingof two
inductorsinthe Hartleyoscillatorcanalsocause expectedresultstobecome skewed.

32
Colpitts OscillatorCircuitSimulation
For the preliminary circuitdesign,a12 voltDC signal fromthe powersupplyisused.Spice based
simulatorshave difficultybeginningoscillationsdue tothermal noise notbeingincludedinthe
simulation.While performingthe simulationinPSpice,the oscillationsdidnot beginatall.InLTSpice,
the oscillationswouldbeginanddie off afterafew milliseconds.There are several methodswhichcan
be usedto start these oscillators,butthe methodwe chose wastosenda small 0.5V pulse shortlyafter
the simulationbegins.Thispulseonlylastsfor10 microseconds,andwasenoughtogenerate astable
waveform.
The 2N2222 transistorwas usedforthe simulation,butamore powerful transistorcapable of
high-speedswitchingismore ideal whenorderingparts. ResistorsR1andR2 are usedinorderto set the
biasof the transistor,while resistorR3stabilizesthe operatingpointof the transistor.CapacitorC3
providesapath to groundforparasiticinductance whichcouldotherwiseinterfere withthe oscillation
waveform. CapacitorC4is usedto blockDC fromthe final outputwaveform. CapacitorC1and C2 along
withinductorL1 producesthe LC oscillatorwhose frequencycanbe determinedfromthe following
formulawhere the total capacitance isfoundbycombiningC1and C2 inseries.
Figure 26: Resonant Frequency Formula for Colpitts Oscillator
Figure 27: Colpitts Oscillator Circuit (~150 KHz)

33
For thissimulation,the outputwaveformfrequencywascalculatedtobe approximately150kHz:
1
2𝜋√2.2 ∗ 10−6(
1 ∗ 10−6 ∗ 1 ∗ 10−6
1 ∗ 10−6 + 1 ∗ 10−6)
= 151.7𝐾𝐻𝑧
The simulationinLTSpice producedthe followingwaveforminthe outputof the circuitfollowingthe DC
blockingcapacitor:
Figure 28: Colpitts Oscillator Output Waveform
As seen,the signal takesapproximately160microsecondsinordertoreach itsstable amplitude of
roughly7 volts.Thisamplitude canbe modifiedinanumberof ways.ResistorR3 can be increasedor
decreasedwhichwillaffectthe gainof the circuit.Some simulationswereperformedaslow as100
ohmsfor R3 whichproducedsinusoidswithlargeramplitudes.CapacitorsC1and C2 can alsobe
modified. While the outputof the transistorisretrievedfromthe collector,aportionof the output
signal,more specificallythe voltage fromthe tapbetweenC1and C2, issentas feedbackintothe
emitterof the transistor.Thisfeedbackprovidesthe continuousoscillationsthatare normallylostin
more basic LC circuits.Bymodifyingthese capacitorvalues,the amountof feedbackcanbe alteredand
the amplitude of the oscillationscanbe changed.

34
The followinggraphdisplays1wavelengthof the outputwaveformafterstable amplitude isreached.
Figure 29: 1 Wavelength of Output Waveform
The resultingFourierTransformof the signal showsthatthe frequencyof the generatedsignal issimilar
to our calculatedresultof 151.7kHz.
Figure 30: Output Fourier Transform

35
In the eventthatloadingthe receivercoil negativelyaffectsthe ACwaveformgeneratedbythe
oscillator,analternate designisshownbelow whichbuffersthe oscillatorfromthe transmissioncoil.In
thiscircuit,the transmissioncoil isnolongerthe inductorinvolvedinthe resonanttankcircuit.A
separate inductorisaddedtothe circuitat the outputof the BJT acting as a voltage follower.The high
inputimpedance of the secondBJTwill helptopreventchangesinthe loadingof the receivercoil from
affectingthe oscillationfrequency.The amplitude of the voltage acrossthe new transmittercoil is
slightlysmallerthaninthe previouscircuitdue tothe dropin voltage acrossthe base-emitterjunction.
Figure 31: Buffered Colpitts Oscillator Circuit
Figure 32: Buffered Colpitts Oscillator Output

36
DC Motor Controller
Figure 33: Level 2 Functional Decomposition of the Motor
H-bridge forLevel 2 Functionality
Module Motor Driver
Inputs Power:V DC
PWMand DIO Signals
Outputs Speedanddirectioncontrol
Functionality ReceivesDCvoltage topowerthe brushlessDCMotor. ReceivesPWMandDIO
informationfromthe Xbee inordertocontrol motorspeedanddirection.

37
Brushed DC Motor for Level2 Functionality
Module Motor Driver
Inputs Speedanddirectioncontrol
Outputs Undesiredrotationspeed
Angle
Functionality Receivesspeedanddirectioncontrol voltage fromthe motordriverandrotates
accordingly.Rotatesatan undesiredhighspeedwhichisreducedbyattachinga
gearbox.Angle of the DCmotor isusedinpositioncontrol processing.
Gearbox for Level 2 Functionality
Module Gearbox
Inputs Undesiredrotationspeed
Outputs Rotation
Functionality Lowersthe final outputrotationspeedwithatrainof gears.
Xbee Transmitter for Level2 Functionality
Module Xbee Transmitter
Inputs MCU GPIO Signals
Outputs Serial Data
Functionality Receives digital inputsfrom4GPIOpinsfromthe RaspberryPi and1 PWM input
analogsignal andtransmitsthisinformationtothe receiverXbee.
Xbee Receiver forLevel 2 Functionality
Module Xbee Receiver
Inputs Serial Data
Outputs PWMand DIO signals
Functionality Convertsthe serial datafromthe Xbee transmitterinto Digital 3.3V outputsanda
PWMoutput fromthe PWM0 pinin orderto control motordirectionandspeed.

38
DC MotorSelectionandParameters
Figure 34: 6 RPM Gear Motor from ServoCity
OperatingRange: 3-12 VDC
Torque @ Max Efficiency:126 oz-in.@12 VDC
Torque @ Stall: 613 oz-in.@12VDC
Stall Current: 500mA @ 12VDC
No load current: 45mA
No load current @ Max Efficiency:95mA (12VDC)
No load speed@ Max Efficiency:4.78 RPM
Gear Ratio: 500:1
Weight:4.7 oz.
ThisbrushedDC motorfrom servocity.com featuresa3-12VDC range whichisusedinorder to
control the speedof the motor.A largerappliedDCvoltage producesfasterrotation.A 500:1 ratio gear
trainis appliedtothe outputshaftof the motorin orderto reduce the final outputtothe desired6 RPM
maximumwhichproducesanappropriate visual of the rotatingglobe.The maximumstall currentof the
motor isratedat 500mA when12VDC is applied.The importance of thisvalue isitsrepresentationof
start-upcurrentof the motor whenzeroback-emf isgenerated.If thismaximumstallcurrentcannotbe
met,there isa risk of damage to the gear trainwhichwill stopthismotorfrom operating.
Counter-electromotiveForce
A brushedDCmotor containsa coil of wire whichacts as itsrotor or armature.A voltage applied
across the motor terminalsproducesacurrentthroughthese windingswhichcreatesamagneticfield.
Thismagneticfieldinteractswiththe permanentmagnetsonthe motor’sstatorwhichcausesrotation.

39
Figure 35: Illustration of Brushed DC Motor Rotation Mechanics
As the coil rotates,the magneticfieldenvironmentof the coil of the armature is constantlychanging,
whichbyFaraday’sLaw inducesan emf (voltage) inthe coil.Asthe rotational speedof the armature
increases,thischange withrespecttotime increases.Thisinducedemfisknownasthe counter-
electromotive force whichisoftenreferredtoas the back-emf.The back-emf of amotorcan be
modelledasinthe figure belowasa voltage source whichproducesacurrentto oppose the current
appliedbythe external voltage source tothe motor.
Figure 36: Equivalent Model of Back-emf
In orderto accuratelyrepresentamotorin a circuitsimulation,back-emf andthe resistance of
the armature must be accountedfor.This isbestrepresentedbyavoltage source whichrepresents
back-emf,aresistorwhichrepresentsthe resistanceof the armature windings,andaninductorwhich
representsthe energystoreddue tothe magneticfieldof the currentcarryingarmature windings.As
mentionedinthe chosenDCmotorparameters,the 500mA stall currentrepresentsthe large current

40
draw the motorrequireswhenitisnotrotatingand no back-emf isgeneratedandanexternal voltageis
originallyapplied.
Figure 37: Equivalent Model of a DC Motor
Transmitter Xbeeand Circuit
In orderfor motorspeedanddirectiontobe manipulated,the motorcontrollermustbe
communicatedwithwirelesslyasthe controllerisseparatedfromthe microprocessorhandlinginput
commands.Anideal methodisthe Xbee communicationmodule,whichallowssimple point-to-point
communicationbasedonthe IEEE 802.15.4 standard.
Figure 38: Xbee Module by Digi

41
Figure 39: Xbee Pinout Diagram
The Xbee module allowsforserial transferof informationviaradiofrequency.Thiscanoccur
throughthe device’stransmitterandreceiverpinsorthroughdirectinput/output.Indirectinput/output
mode,a pairof Xbeeswill communicate asif there isavirtual serial dataline travellingfromeachof the
DIO pinsonthe transmittertoa correspondingDIOonthe receiverXbee. Inorderforthe twoXbeesto
communicate viaDIO,some settingsmustbe configured usingDigi X-CTUsoftware orcommandline:
 PAN ID – Thisisan arbitraryhex value rangingfrom0000 to FFFF.This value mustbe the same
on bothtransmitterandreceiverXbeesinorderforthe twodevicestocommunicate andmust
be unique if there are otherpersonal areanetworksestablishedinthe area.
 Baud Rate – Both Xbeesmustbe setto the same Baud rate for communication.Defaultis9600.
 DestinationAddressHigh and Low – Thissetsthe Xbee broadcastaddress.
 Analog-to-Digital or Digital Input/output – These pinsare capable of digital oranaloginputas
well asdigital output.Eachpinmust be configuredbasedonthe particularapplication.

42
Figure 40: Transmitter Xbee Wiring Diagram
The diagram above showsthe wiringof the transmitterXbee tothe RaspberryPi 2.Five different
GPIO pinsonthe RaspberryPi are connectedto pinson the Xbee.The firstfourof these GPIOpinsare
responsible forcontrollingthe H-bridge functionsof the motorsuchas forward,reverse,andbrake.
These GPIOpinsare connectedtoDIO pins1, 2, 3 and 6 on the Xbee.These DIOpinsare assignedas
digital inputs.The RaspberryPi GPIOoutputswill be settoeither0V or 3.3V basedonuser inputsfor
motor control.The series1Xbee is capable of readingvaluesupto 3.3V,but if a series2Xbee isused,
the maximumpossiblevoltageis1.2V.Thiswouldrequire amethodof reducingthe voltage fromthe
outputof the RaspberryPi to the Xbee inputsuchas a resistive voltage divider.
The fifthand final GPIOpinusedformotorcontrol fromthe RaspberryPi 2 ispin12 whichisthe
hardware PWMoutputpin.By connectingthistoAD0/DIO0 on the Xbee andassigningthispintoanalog
input,the analog-to-digital converterof the Xbee willconvertthe PWMintoa digital signal for
transmission.The signal canthenbe recoveredatthe PWMoutputof the receiverXbee andusedto
drive a transistorwhichwill control the motor’sspeed.Userinputswill determinethe dutycycle of the
PWMsignal.

43
Convertingthe PWM signalto Analog
The GPIO pinson the RaspberryPi are capable of digital outputsonly.Eachpiniseithersetto
high(3.3V) or low(0V).In orderfor the microprocessortoemulate ananalogoutput,hardware PWMis
available onpin12 and software PWMisavailable onanyGPIOpin.While PWMiscapable of handling
functionssuchas a motor’sspeedoran LED’s brightnessonitsown, sometimesatrue analogvoltage
level isrequired.Thisisthe case forthe Xbee’sanalogtodigital converter.Forthisreason,itisnecessary
to convertthe PWM outputintoitscorrespondinganalogsignal whichcanthenbe processedbythe
Xbee.
The base clockfor PWMgenerationonthe RaspberryPi is19.2 MHz. The periodisfoundusing
the equation:
𝑇 =
1
𝑓
Thisgivesusa periodof 52.1ns. Asan example,a50% duty cycle signal ischosen,whichmeansthatthe
PWMsignal ishighfor half of each period,andlow forhalf of eachperiod.The correspondinganalog
value of the digital signal isrepresentedbythe followingformula.Thisleadstothe equivalentvoltage of
a 3.3V PWMsignal witha 50% duty cycle to be simply1.65V
𝐴𝑛𝑎𝑙𝑜𝑔 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 =
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑥 𝐷𝑢𝑡𝑦 𝐶𝑦𝑐𝑙𝑒
100%
The signal wassimulatedasa voltage source inLTSpice:
The parameterschosenwere:
 Initial Voltage:0V
 On Voltage:3.3V
 Time Delay:0s
 Rise Time: 1ps
 Fall Time:1ps
 Time “on”:26.05ns
 Period:52.1ns
 N-cycles:500

44
Rise time andfall time were chosenas1ps as the voltage isunable tochange instantaneously.The high
time isexactlyhalf of the periodchosen.The numberof cycleswaschosenarbitrarilyandisonlyneeded
to be a greaterlengthof time thanwhatwe intendtoview inthe simulation.The followingplotshowsa
segmentof a 1us transientsimulation.
Figure 41: Raspberry Pi 19.2 MHz PWM
The Fast-FourierTransformshowsthatthe signal parameterschosenaccuratelyrepresentthe Raspberry
Pi 2 PWM clockfrequencyof approximately19.2MHz:
Figure 42: Fourier Transform of PWM

45
In orderto convertthisPWMsignal intoitscorrespondinganalogvoltage,the voltage source is
connectedtoa low-passfilter.Fora simple RClow-passfilter,the cutoff frequencyformulaisgivenas:
𝑓𝑐 =
1
2𝜋𝑅𝐶
Knowingtwoof the variablesisnecessary.The frequencyof the PWMpinclock is19.2MHz. We chose a
value of 1k for the resistoras resistance valuestoolarge increase the time neededforthe filtertoadjust
to changesinPWM dutycycle. Solvingthe equationforthe capacitance yieldsthe results:
𝐶 =
1
2𝜋𝑓𝑐 𝑅
𝐶 =
1
2𝜋(19.2 × 106) × 1000
= 8.29𝑝𝐹
Simulatingthe circuitandperformingthe transientanalysisresultsinthe following:
Figure 43: First Order Low-pass Filter

46
Figure 44: Slightly Attenuated PWM Signal
From the plot,the ripple voltage remainstoohigh asthe highfrequencyhasjustbegunattenuating.In
orderto adjustthis,largercapacitance valueswere testedandavalue of 500pF was usedtoresultinthe
followingwaveform:
Figure 45: Further Attenuated PWM Signal
While the waveformisbecomingclosertoourdesiredoutput,asecondstage filterwhichisidentical to
the firstwas connectedinorderto create a second-orderlow passfilter:

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Figure 46: Second Order Low-pass Filter
Figure 47: Comparison of First Order and Second Order Outputs
The resultingtransientanalysisshowsastable inputforthe Xbee.The greenplotindicatesthe first-
orderlowpass outputwhile the blue signalindicatesthe second-orderlow passoutputwhichisfedinto
the Xbee.The final ripple voltage isapproximately1mV andthe highfrequencyof the PWMsignal has
beenlargelyattenuated.A DCsignal isleftwhichcanbe usedasthe Xbee analoginput AD0.
Figure 48: Ripple Voltage Transient
Receiver Xbee
The receiverXbee isthe device withoutputsdirectlyconnected intothe DCmotorH-bridge
transistorsinorderto operate the directionof rotation.The receiverXbee isconnectedwithvoltage

48
pinsof 3.3V andground fromthe wirelesspowerrectifiedvoltage.The VCCpinmustalsobe connected
to the voltage reference pin(Vref).Thisassignsthe maximumvalueof the Xbee pinoutputs.Anexample
of thisis whenVref isconnectedto3.3V the PWM signal fromthe outputof the Xbee will have a3.3V
peak-to-peakvalue.The PWM0 pinisconnectedintotransistorM1 inorderto control the overall
voltage of the motor.The PWMdoesnot needtobe correctedby a low-passfilterasPWMis sufficient
inapplicationsrequiringDCmotorspeedcontrol.DIO1,DIO2, DIO3,and DIO6 control transistorsM2,
M4, M3, and M5 respectively. The motorcircuitdiagramcontainingthesetransistorsandconnectionsto
respective pinsonthe Xbee isfoundinthe nextsub-section,whileawiringdiagramof the Xbee receiver
module isshowninthe figure below.
Figure 49: Xbee Receiver Module Wiring Diagram
DC Motor Circuit(H-bridge)
The H-bridge circuitisthe methodwe chose for alternatingthe directionof currentthroughthe
motor.This allowsthe motortorotate bothclockwise andcounter-clockwise.The diagramof the H-
bridge circuitisshownbelow.

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Figure 50: H-bridge Circuit
As the example inthe diagramshows,the DIO1andDIO6 pinsfromthe Xbee receiverare setto high
(3.3V) while the DIO2and DIO3 pinsare setto low (0V).Thisallowsthe currenttoflow fromthe source
of the M2 MOSFET through the motorrepresentedbyaresistor,andintothe drainof the M5 MOSFET.
Alternatively,M4and M3 can be enabledinaseparate sequence toalternate the directionof the
currentand motor rotation.The diodesare installedinthe circuitinorderto protectthe MOSFETs from
discharge whenthe motoristurnedoff. Othercombinationsof MOSFETScan alsobe turnedhighand
lowinorder to “brake”the motor and quicklydischarge it.The truthtable isshown.
M2 M3 M4 M5 Output
Low Low Low Low No rotation
High Low Low High
Rotation in
direction A
Low High High Low
Rotation in
direction B
High Low High Low Brake
Low High Low High Brake
The PWM0 pin isdirectlyconnectedtothe motor’soverall voltagesource.The maximumcurrentoutput
of the Xbee (approximately2mA) isnotenoughtorotate the motor and will cause damage toXbee if
attempted.Inorderto remedythis,the PWMpinis connectedtoanotherMOSFET whicheffectively
convertsthe 3.3V peak-to-peakPWMof the Xbee intoalarger 12V peak-to-peakPWMfromthe wireless

50
powerrectifiedvoltage.The transientanalysisplotsbelow show the PWMcurrentstravelingthrough
the motor inthe simulationabove forbothdirectionA andB as showninthe truth table.
Figure 51: PWM Current in Direction A
Figure 52: PWM Current in Direction B

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Rotational PositionTracking
Figure 53: Level 2 Functional Decomposition of Rotational Positioning
IR LEDfor Level 2 Functionality
Module IR LED
Inputs VDC:1.28V
Outputs IR wavelength
Functionality ReceivesDCvoltage. Convertsthisvoltage toanIR wavelengththatisoutput.
Reflectivesurface for Level2 Functionality
Module Reflectivesurface
Inputs InfraredWavelength
Outputs InfraredWavelengthReflected
Functionality ReceivesIRwavelength. Thiswavelengthisthenreflectedback withthe same
properties.
IR Photodiode forLevel 2 Functionality
Module IR Photodiode
Inputs InfraredWavelengthReflected
Outputs Sensoroutput
Functionality Receivesaninfraredwavelengthtothree equallyspacedinfraredphotodiodes. With
circuitrythisoutputsto a controllerforpositioning

52
InfraredLED,InfraredPhoto-Diode,Op-amp,Reflectionmaterial
The rotational positioningsystemservesasaway forus to track the globesmovementand
location. Bytakingan infraredlightsource andreflectingitoff the bottomof the globe areadingcan be
createdby the infraredphoto-diodes. The reading,beingavoltage source,willbe takeninbythe
RaspberryPIand decoded. Accordingtothe sensitivityof the photo-diodesamore accurate readingcan
be producedthusallowingustotrack more locationsandprecise movementsof the Globe. When
coupledwithinternetconnectivitywhenaproperplace ischosenthe globe shall rotate tothat exact
positionviathe createdsystem. Insteadof justhearingaboutthatlocationthe individualwillalsobe
pointedtowardsitandexperiencingvisually.
Infrared LED’s
An InfraredLED isa lightsource createdby a diode. Thisparticularlightsource isusedfor
thermal readingsandinteractions. Itisalsoinvisibletothe humaneye makingita perfectconceptfor
our project.
Figure 54: Infrared LED
WhendealingwithLED’san appropriate voltage andcurrentsource are neededtopowersucha
system. Forthisparticularsystemwe planon takinga 5v source and thendroppingthe voltage toa
reasonable level forapropercurrentgeneration andvoltage output. Overallif done correctlywe will
achieve asystemwhere anInfraredLED emitsa wavelengthof around950nm witharounda 20 degree
bandwidth. Withmultiple LEDstructureswe can compensate forsucha small bandwidthandcreate a
greaterintensityfiledof strength.

53
The followingdiagramisasimple LEDcircuitthat will be incorporatedintothisproject. Forthis
simulationIuseda5v DC source witha 36.5 ohm resistor. Thisinturn gave us the appropriate current
and voltage runningthroughthe InfraredLED.
Figure 55: Circuitry for Infrared LED operation
Figure 56: Output response of current flowing through LED
For our projectwe planon takinga single oran array of InfraredLED’sand positioningthemin
the centerof the globe. Multiple infraredLED’smaybe usedfor intensitypurposes. These LED’swill
thenbe positionedupwardtocreate alightsource emittingfromthe base of the structure.

54
Figure 57: Infrared LED Array
Infrared Photo-Diode’s
An InfraredPhoto-Diode isalightsensitiveelectrical componentthatwhenplacedunderalight
source will become excitedandtake ona currentrating. Thisparticularphoto-diodeiscoatedwith a
polarizedlens. Thislensonlyallowsforthe Infraredwavelengthtoenterwhile blockingoutall other
lightsources,wavelengths.
Figure 58: Infrared Photo-Diode
For our projectwe planon takingthree infraredphoto-diodesandpositioningthemall around
the base 120 degreesawayfromone another. Withthismethodthe Infraredwavelengthbeingemitted
by the InfraredLED’sshouldbe relativelyeasytotrack. Thispositioningof the photodiodesaroundthe
base alsoallows fora methodof trilateration.
Belowisa diagramrepresentingthispositioning. We have three Infraredphoto-diodes
representedinblueall equallyspaced120degreesawayfromeachother. Locatedat the centerof the
structure isan array of LED’s representedwithgreencircles.

55
Figure 59: Example of Infrared Photo-diode placement
These InfraredPhoto-Diodeswillrequire anappropriate circuitforsensoroutputresponse. The
circuitpertainingtoan infraredphoto-diodeisasseenbelow. Beingthatthe simulationprogramdid
not have an appropriate photo-diodeamimicwasmade usinga currentsource,a resistor,anda
capacitor.
Figure 60: Example of Photo-diode
But insome caseswe may needan operational gain. Withthisgainthe outputfromthe photodiodes
wouldbe boostedsothat a clearerreadingcouldbe made. Insteadof onlyreceivingarounda3v input
readingthiscouldbe boostedtoaround9v. Anexample of thiscircuitwiththe infraredphoto-diode
attachedis shownbelow.

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Figure 61: Circuitry for Infrared Photo-diode operation
A current “Ip” will runthroughthe photodiode whenitisexcitedthisinturnwill lowerthe
overall voltage beingobtained atthe outputthusgivingusa way to track position. The systembeing
developedworksmore alongthe linesof aninvertedsystem. The lessvoltage beingobtainedatthe
outputthe closerthe objectisto that photodiode andvice versa. The equationforfindingthe phase
currentis shownbelow.
𝐼 𝑝 = 𝐵(𝐸 𝑒)
We alsoneededanequationtofindthe outputof the system. Since aphotodiode actslike a
phototransistorsoutputthisequationwasrelativelyeasytofind.
𝑉𝑜𝑢𝑡 = 𝑉𝑐𝑐 − ( 𝐵1 𝐿1 + 𝐵𝑓 𝑖 𝐵) 𝑅 𝐿
Trilateration
Trilaterationisamethodusedbycellphone companiestotrackindividualsviatheircell phones.
Thismethodworksbytakingthree pointsandfindingthere central overlappingarea. Thisareais closely
relatedtowhere thatindividualis locatedasa marginof erroris natural. Our groupplanson takingthis
methodandimplementingitintoourproject. The processfor measuringthe radiuswill be converted
fromlightintensityintoavoltage. Thisvoltage readingwillthengive usthe appropriate rotational
positionof the globe. The designforthisissimple asseenbelow.

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Figure 62: Trilateration example figure
WhendealingwithTrilaterationseveral equationscome intoplayinordertofindthe
appropriate location. The x-axisrequiresthatthe radii of twoof the circlesare takenas well asthe
distance betweenthe two. Withthisinminda pointalongthe x-axiscanbe foundusingthe following
equation:
𝑥 =
𝑟1
2
− 𝑟2
2
+ 𝑑2
2𝑑
Nowthat a pointon the x-axishasbeenfoundapointforthe y-axiswill alsoneedtobe found. Byusing
the radiusof the firstand secondcirclesandthe distancesbetweenthemanappropriate equationcan
be formed. Thisequationisasfollows.
𝑦 =
𝑟1
2
− 𝑟3
2
+ 𝑖2 + 𝑗2
2𝑗
−
𝑖
𝑗
𝑥
To go alongwithfindingthe rotational positionof the globe areflectivesurface willbe needed.
By havinga reflectivesurface slightlyoff centerof the globesbase arotational movementwill be formed
wheneverthe globe rotates. Thiswill hopefullyallowforthe trilaterationformulatotake effectand
calculate the exactpositionof the globe.
Op-amps
For the purpose of rotational positioningaNon-invertingop-ampwill be needed. Thisdesign
will playarole in boostingthe voltage outputgeneratedfromthe infraredphotodiode. Whendesigning
thiswe had to forman appropriate gainso thatthe inputvoltage wouldnotbecome saturatedbythe

58
voltage poweringthe op-amp. Thereforealow inputvoltage willbe usedandpassedthroughthe
photo-diodewheneveraninfraredinputtakeseffect.
One mainequationwasbroughtintoplayforthe designof thissystem. The gainequationwas
usedto calculate the voltage outputof the Non-invertingop-ampsystem. The equationusedtosolve
the gain is as follows.
𝐺𝑎𝑖𝑛 = 1 +
𝑅2
𝑅1
By decreasingthe resistance atR1 we can obtaina greatergain. Thisequationdirectlycorrelatesinto
findingthe outputvoltage. Whenfindingthe outputvoltage of the systemwe have tomonitorthe input
voltage toachieve anappropriate reading. By takingthe inputvoltage tothe Non-invertingop-ampand
multiplyingitbythe inputvoltage we were able tofindthe outputvoltage of the system.
𝑉𝑜𝑢𝑡 = 𝑉𝑖𝑛(1 +
𝑅2
𝑅1
)
An example of thiscircuitisshownbelow.
Figure 63: Non-inverting Op-amp
Afterall issaidand done all of these systemswill be incorporatedintoone finalexecutable
function. The wavelengthemittedbythe infraredLED’swill be focusedupward. Once these waves
reflectoff of the Globesreflective surfaceavoltage readingwillbe outputtedbythree infrared
photodiodes. The methodof trilaterationwillthenbe usedtodepictwhere the Globe islocatedonits
axisof rotation. Our final designforrotational positioningwill resemble the model below.

59
Figure 64: Final design for rotational positioning
Levitation Control
Figure 65: Level 2 Functional Decomposition of the Levitation Control System

60
Relay for Level2 Functionality
Module Relay
Inputs Power:VDC
Controlsresponse
Outputs On/Off
Functionality ReceivesDCvoltage toflow throughthe relays.
Receivesanon/off commandfromcontrolstodictate if a solenoidistoturnon.
Sendsan outputof voltage to saidsolenoids. On/Off.
Solenoids forLevel 2 Functionality
Module Solenoids
Inputs On/Off Voltage fromrelays
Outputs Levitationstabilization
Functionality Receivesanon/off inputfromrelays. Thisallowsthe solenoidstocreate a magnetic
fieldforstabilization.
Permanent magnet (base) forLevel 2 Functionality
Module Permanentmagnet(base)
Inputs None
Outputs Unstable Levitation
Functionality Outputsunstable levitationfrombase usedtocreate a non-contactsurface with
the globe
Permanent magnet (globe)for Level 2 Functionality
Module Permanentmagnet(globe)
Inputs Unstable Levitation:Permanentmagnet(base)
Levitationstabilization:Solenoids
Outputs Stable Levitation
Position
Functionality In takesbasiclevitationwith levitationstabilizationtopromote stablelevitationin
globe. Magneticfieldgeneratedbypermanentmagnetinglobe outputspositonto
hall effectsensors.

61
Hall Effectsensors forLevel 2 Functionality
Module Hall Effectsensors
Inputs Position
Outputs Feedback
Functionality Receivespositionof globe byuse of magneticfieldfrompermanentmagnetinglobe.
Convertsthisinputtovoltage foran outputfeedbacktoa controller
Hall EffectSensors,Relays,Solenoids,andPermanentMagnets
The levitationsystemservesasaway forus to stablyandhopefullypermanentlylevitate the
globe. Byutilizingtwopermanentmagnetslevitationwill existandcontinue toexist. The nextpartof
the equationwasto create a stable fieldof levitation. Since magneticlevitationisneverstable andwill
alwayscease tobe stable the helpof solenoidswill needtobe implemented. These solenoidswillbe
activatedviaa response outputfromthe RaspberryPi. The response systemwill firstbe triggeredby
Hall Effectsensorslocatedaroundthe globe. Dependingonthe voltage outputof these sensorswill
depictwhere the globe islocatedatthatgiventime. Byusingsolenoidspositionedaroundthe globe a
stable fieldwill be created.
Hall Effect Sensors
A Hall EffectSensorisa device thatconvertsmagneticfieldenergyintoelectrical output. A
range of inputfroma magneticfieldistakenintoaccountbythissystemwhichinturn outputsthe
respective voltage output. Thisoutputwhichwill be readbythe microprocessorinsuresthatacorrect
positioncanbe obtainedbythe levitatingneodymiummagnet.
Figure 66: Hall Effect Sensor
Whendesigningsuchasystemto use Hall EffectSensorsthree thingswere takenintoaccount.
The firstand most importantwasplacement. The placementof the sensorswillbe ina square topology.
To achieve thisfoursensorswill be placedeachonthe 90 degreesangle of the square toensure proper
spacing.

62
Figure 67: Hall Effect Sensor placement
The nextfactor we tookintoaccount was the total distance fromthe neodymiummagnetthese
sensorswill be placed. Bytakingintoaccountthe levitationdistance withrespecttothe distance from
the base we were able to achieve adistance of 2.12 inches of separationforthe hypotenuse (redline).
Thisis widelyadjustableasthe nextfactorthat wasstudiedwasthe sensitivityof the Hall EffectSensors.
Figure 68: Right Triangle for distance calculation
To findthe properdistance of the Hall EffectSensorfromthe permanentmagnetinthe globe
PythagoreanTheoremwasneeded.
𝑎2 + 𝑏2 = 𝑐2
The SS490 seriesisaLinearHall EffectSensorthat can detectbothnorth andsouth poles
respectively. Withthe use of thissensorthe magneticrange of detectionwouldbe able torange from -
600 to +600 magneticfield. The sensitivityprovidedbythese sensorsisaround3.125 mv/Gleavingus
witha highrange of inputsmakingpositiondetectionevenmore precise.
Whendealingwiththe SS490 Hall EffectSensora circuitcomesintoplay. These sensorsalready
have a builtinamplifiertoadjustforthe weaksignal cominginandamplifyingittoan appropriate

63
reading. Forthiscomponenta 5VDC source wouldbe neededtoobtainanoutputof (Vs-0.2). Thisis
shownbythe followingdiagram.
Figure 69: Hall Effect Sensor Block Diagram and output
Relays
A relayisan electrical deviceusedtoallow asystemtoturn on or turn off. A relaymore or less
isan electrical switch. A systemof fourrelayswill be usedtoinduce alogicsystemof on or off forthe
foursolenoids. Throughthisa control systemdevelopstowhere solenoidscanbe turnedonand off as
neededbythe system.
For the use of relays a designof NPN transistorswillbe utilizedtocontrol solenoids. AnNPN
transistorisa type of BJT. These systemscontainabase,collector,andemitterwhichallowsthemto
functionappropriately. A simple depictionof thissystemisasshown.
Figure 70: NPN Transistor

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As the base currentincreasesthe transistorturnsonallowingvoltage toflow. The calculationforthe
amountof currentflowingthroughthe base of the systemcanbe foundbyusingthe followingformula.
𝐼 𝑏 =
𝑉𝑏 − .7
𝑅 𝑏
By addinga resistor(Rb) we can change the currentto become greateror lesserdependingonwhatis
needed. The currentrunningthroughthe entire systemintothe emittercanbe foundby findingthe
total collectorcurrentor (Ic). This isfoundbytakingthe common-emittercurrentgain andmultiplyingit
time the base current. This formulaisas shown.
𝐼 𝐶 = (𝐵)(𝐼 𝑏)
Whendesigninganappropriate relayforthissystemasafe yetplausible circuitwasneeded.
Thiswas achievedbyfirsttakingthe NPN transistor. A diode wasthenaddedtothe collector’sresistor.
Thiswas done to minimizevoltagebuildupatthispointsothat in an extreme circumstancethe leftover
voltage won’tfrythe transistorandwill allow ittodischarge safelyandefficiently. The nextcomponent
that wasaddedto the NPN circuitwas a capacitor spanningfromthe collectortothe emitter. Thiswas
put intoplace sothat the voltage doesn’tspike inthe collectorsresistance. Italsohelpstosmoothout
the voltage givingthe diode time toturnonand off. Thiswas done to achieve astable plausible relay
systemandis showninthe diagrambelow.
Figure 71: Relay design for solenoid operation
Rc in thissystemisdepictedasthe solenoidorload. Thissystemallowsustoobtaina currentratingof
500mA to flowthroughthe solenoidwhenthe relayisactivated.

65
PermanentMagnets
For our projectthe use of strong permanentmagnetswillneedtobe introduced. A permanent
magnetwill existinthe base of the model aswell asinthe globe. Thiswill insure thatlevitationtakes
place. For the designandtheoryof thissystemweightaswell asthe size of the overall magnetwere
lookedat. We chose to go witha 2 inchdiameter,¼ inchthickmagnetwithanoverall weightof 3.41
ounces.Thisgivesusenoughliftingforce withoutbeingtooheavy. A picture of the magnetisshown
below.
Figure 72: Permanent Magnet
Thismagnetis an NdFeBmaterial of Grade N42. It is an axiallymagnetized magnetmeaning
that bothsidesof the magnetshare a differentpolarization. Thismagnetalsohasa surface fieldof 1601
froma single permanentmagnet. The magneticfieldcreatedbythe tworepellingmagnetsata distance
of 1.5 inchesisaround 239 Gauss.

66
Figure 73: Magnetic Field
Levitationdistance isanotherfactorwhendecidingwhichtype of magnettoacquire. For our projectwe
discussedlevitatingthe globe around1.5inchesfromthe surface of the base. Withthe Grade N42 2inch
magneta distance close tothisis easilyachievable. The force betweenthe twomagnetsisaround0.76
poundsat the heightof 1.5 inches. 1 poundof liftingforce isequal to16 ouncesmeaningwe have
surpassedourstandardof justlifting12 ounces.
Figure 74: Distance with respect to force by magnetic field

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Solenoids
Stabilizationof the levitationprocessisof ourforefrontof concern. Whendealingwithstable
levitationfoursolenoidsarrangedatthe 90 degree pointsof the base will be induced. For the use of
solenoidsseveral equationshadtobe derived. Whenbuildingasolenoidthere are fourmainfactors
that come intoplay:force,magneticstrength,current,andpermeabilityof the material. Foroursystem
we needtoliftaroundtwelve ouncesof weight. The formulapertainingisasfollows.
𝐹 =
(𝑁 ∗ 𝐼)2 ∗ 𝑢0 ∗ 𝐴
(2 ∗ 𝑔2)
∗ sin(𝜃)
The coefficientsforthisformulaare as follows. Byusingan ironcore the permeability μwascalculated
to be .0063 H/m. “N” isthe variable usedtodepictthe numberof turnswhichis60. The current“I” of
the systemwouldonlyneedtobe .5 milliamps. The areaof the solenoid“A”wasdesignedtobe a mere
0.0050671 meterssothat the base couldremainsmall andspace couldbe utilizedefficiently. “g”is the
distance fromthe solenoidtothe metallicobjectwe wantedtoachieve stablelevitation. A distance of
1.5 incheswaschosenwhichcorrelatesintoapproximately 0.0381 meters. Now beingthatthisobject
will notbe directlyabove the solenoidsandangle wasneededtobe takenintoaccountand a
hypotenuse formed. Forourtotal distance fromthe base of the globe tothe solenoidwas
approximately 0.053848 meterswithan angle of 45˚. By usingthisequationwe were able toachieve a
force of .7868 poundsat a distance of 1.5 incheswhichsatisfiesourrequirementof 12 ouncesof lifting
force.
The nextequationneededwasthe magneticfieldgeneratedbythe solenoids. Current,number
of turns,permeability,andlengthall factorintothe strengthof the magneticfieldcreated.
𝐵 =
𝑢0 𝑁𝐼
𝐿
The equationasshowngivesa currentI multipliedbythe numberof turnsN,and the
permeabilityuall dividedbythe lengthof the solenoid. The lengthof the designedsolenoidwas
chosento be 0.0508 meterswhichconvertsto2 inches.
Figure 75: Solenoid

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The circuitryfor these solenoidsisquite simple. Withthe relaysattachedtothe solenoidsan
outputto groundis all that needstobe achieved. The relaysystemtakescare of all the workallowinga
currentto flowthroughthe solenoidthuscreatingamagneticfield. The magneticfieldtocurrentratio
inside of thissolenoidisasseen. Asthe currentincreasesthe magneticfieldalsoincreaseslinearly. This
givesusa maximummagneticfieldataround1.8T.
Figure 76: Magnetic Field of Solenoid
The nextequationthatwastakenintoaccount was the magneticfieldlocatedat1.5 inches
directlyabove the solenoid. Forthiscalculationthe followingequationwasneeded.
𝐵 =
𝜇𝐼𝐴𝑁
2𝜋𝑥3
The coefficientsare asfollowsaboveexceptfor“x”. The variable “x”isthe distance of the solenoidfrom
the metallicobject. Bytaking thisequationintoaccountandadjustingthe currenta graph of the
magneticfieldwasachieved. Thisgivesusamaximummagneticfieldatalmost1T.

69
Figure 77: Magnetic Field directly above Solenoid
The nextequationthatwas takenintoaccount was the magneticfieldlocatedatanangle to1.5
inchesdirectlyabove the solenoid. Forthiscalculationthe followingequationwasneeded.
𝐵 =
𝜇𝐼𝐴𝑁√(1+ 𝑐𝑜𝑠2(𝜃)
4𝜋𝑥3
By takingthe cosine of the angle an appropriate magnetic fieldcalculationcanbe made. To show thisas
the current isincreasedthe magneticfieldincreasesgivingusthe followinggraph. Thisgraph shows
that that maximummagneticfieldatanangle to 1.5 inchesisaround0.55T.

70
Figure 78: Magnetic Field at an Angle to Solenoid
Microcontroller Interface
The belowlevel 2functional decompositionhasfourinputs:feedbackfromHall effectsensors’
voltages,sensoroutputof arotational positionvoltage, usertouchinput,andpower5V DC.The three
outputsare:the response tocontrol the transistorrelaysthatturn the electromagnetsonandoff,the
serial datathat is sentviaRF transmissiontocontrol the motor,andthe displaywhichwillshow the
graphical userinterface,anyinformationfromthe internet,andinformationaboutthe positionof the
globe.Some internal inputsandoutputsare the transferof data viathe WiFi module,the Serial
Peripheral Interface communication,andthe LCDtouch events.

71
Figure 79: Level 2 Functional Decomposition of the Microcontroller
Microcontrollerfor Level2 Functionality
Module RaspberryPi 2 Model B
Inputs Power:5V DC
Tx/Rx:serial communicationwithWiFi module
GPIO pins:SPIfrom A/D,LCD driver
Outputs Tx/Rx:serial communicationwithWiFi module
GPIO pins:response tocontrol relays,encoderbits,LCDdriver
Functionality LCD controlledviaGPIOpins allow userinteraction.Response of relaycontrol creates
stability.SPIcommunicationwithA/Dreceivesinputof analogsensors. General
purpose GPIOas individualbitsallow control of motor.Internetcommunication
shouldbe conductedthroughUSB.

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Analog to Digital Converter for Level 2 Functionality
Module Analogto Digital Converter–MCP3008
Inputs SPI:Serial communicationfromA/Dconverter
Feedback:levitationcontrol systemHall effectvoltages
Sensoroutput:IR beampositiontrackingof angle of the motor
Outputs SPI:Serial communicationwithdigital GPIOpins
Functionality Convertsanalogsignal todigital suchthatthe RaspberryPi can interpretthe sensors’
values. Shouldutilizethe Serial Peripheral Interface standardof communication.
Feedbackisanalyzedbythe RaspberryPi isoutputtedtothe relaysasa response.
LCD Touchscreen forLevel 2 Functionality
Module LCD Touchscreen – PiTFT2.8” 320x240 Capacitive touchscreen
Inputs User input:touchresponse,datarequestssuchasinternetdata
LCD driver:processuserinteraction,displayuserinterface
Outputs LCD driver:senduserinputtoRaspberryPi for processing,requestdatasuchas
internetdata
Display:showuserinterface,show reactiontouserinteraction
Functionality Allowsthe usertointeractwithglobe.Hostsuserinterface withbuttons suchas
“rotate leftcontinuously.”ConnecteddirectlytoRaspberryPi,displayingthe user
interface.
LCD Driver forLevel 3 Functionality
Modulename LCD Driver
Moduletype Inputand output
Inputs Touch input:toucheventflagged,touchposition recorded
RaspberryPi visual data:GUI programinformation,display,animations
Outputs Touch response:sendtoucheventdatatoRaspberryPi and GUI program
Display:actual screenusersees
Functionality InteractswithGUI program. Acceptsuserinputandpassesto RaspberryPi for
processing. Eventsystem.
Relay Control for Stability for Level3 Functionality
Modulename RelayControl forStability
Moduletype Inputand output
Inputs Hall effectsensor: A/Dconverted voltagedescribewhich electromagnetneedsto
be turnedon/off
Outputs Relay:turnon/off
Functionality Three Hall effectsensorsdetectthe (x,y) position of the permanentmagnetinthe
globe.Itsposition outputsavoltage which correspondstowhichdirectionitneeds
to be pushedinorderto stablylevitate.

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WiFi Module for Level3 Functionality
Module WiFi Module – Edimax EW-7811un 150Mbps 11n WiFi USB Adapter
Inputs Rx: data requestfromRaspberryPi
Outputs Tx: informationbasedonlongitude coordinate
Functionality Givesthe RaspberryPi 2 internetcapabilities.ConnectsviaUSB.Communication
protocol isabstracted.
Circuits, Behavioral Models, and Formulas
Microcontroller -RaspberryPi 2Model B
Justification
A RaspberryPi 2 Model B has enoughhorsepowertodisplaya graphical userinterface onsmall LCD
touchscreenandstill runcalculationsbehindthe scenes.Itusesthe BroadcomBCM2836 overthe older
models’ BCM2835. While itretains backwardscompatibility,the BCM2836 isa quad core 900 MHz ARM
processor. The RaspberryPi 2 coststhe same as the RaspberryPi Model B+, but comeswitha purported
six timesthe computational power.
Figure 80: Raspberry Pi 2 Model B
The array of 40 general purpose inputandoutputpins(GPIO) allowsspecificconnectionssuchasSerial
Peripheral Interface (SPI) forfastcommunicationbetweenadigital device and aprocessor. We will
utilize the Inter-IntegratedCircuit(I2C),SPIand genericpinsforthe LCD capacitive touchscreen.SPIwill
alsobe usedforthe analogto digital converter(A/D). RFtransmission andthe relayscanbe controlled

74
viathe genericGPIOactingas switches.Internetcommunicationisaccomplishedviathe USBport with
an Edimax EW-7811un WiFi module.
Analogto Digital Converter – MicrochipMCP3008
The RaspberryPi has no wayof acceptinganaloginputs.Thisiseasilyremediedbyusingthe Microchip
MCP3008 Analogto digital converter.Itallowseightpossible analoginputswhileonlyrequiringfour
GPIO pins.ItutilizesSPItocommunicate withthe RaspberryPi.GPIOpins18,19, 20, and 21 are the chip
select,masterinslave out(MISO),masteroutslave in(MOSI),andclockrespectively.
Figure 81: MCP3008 A/D converter connected to Raspberry Pi breakout
We needanaloginputsforthe fourHall effectsensorsandthe rotational position.Fourchannelsare
dedicatedtothe Hall effectsensors andthree tothe rotational position voltages.The voltagevalues for
the Hall effectsensors will determine whichelectromagnetsare turnedonoroff.The rotational position
voltagesdescribe the facingof the globe withrespecttoLCD touchscreenvia(x,y,z) coordinates.We
can have up to 1024 (2^10) positionsrepresentedinbitsforeachvoltage. The formulatoconvertanalog
to digital is:1024 (10 bit) timesthe analogvoltage in(VIN) dividedbythe reference voltage(VREF).
1024 ∗ 𝑉𝐼𝑁
𝑉𝑅𝐸𝐹

PDR Paper FINAL DRAFT

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