Battery Charger Report 3

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    Business Plan and Design Proposal:12 Volt Universal Battery Charger

    Group 3Final Report

    December 17, 2003

    Michael EskowitzECE Box # 99

    Eric HallECE Box # 133

    Chris HammanECE Box # 135

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    Table of Contents

    Executive Summary 1

    Section 1: Introduction 2

    1.1 Problem Statement 2

    1.2 Planned Approach 3

    Section 2: Product Specifications 4

    2.1 Market Research 4

    2.2 Customer/ Product Requirements 8

    2.3 Product Specifications 9

    Section 3: Product Plan 11

    3.1 Development Schedule 11

    3.2 Budget 13

    Section 4: Design Approach 14

    4.1 Design Options 14

    4.1.1 Signal Conditioner 15

    4.1.2 Charge Monitor 15

    4.1.3 Charge Status Display 16

    4.2 Value Analysis 17

    4.2.1 Power Supply 17

    4.2.2 Charge Monitor 18

    4.2.3 Charge Status Display 20

    4.3 Competitive Value Analysis 21

    4.3.1 Solar Chargers 22

    4.3.2 AC Chargers 24

    4.2.3 Pedal Chargers 26

    4.4 Module Definitions 27

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    4.5 Manufacturability 34

    4.6 Cost Analysis 35

    4.7 Hazard Analysis 37

    4.8 Legal Considerations 38

    Section 5: Product Results 39

    5.1 Product Functionality 39

    5.2 Product Form 39

    5.3 Expected ROI 40

    Section 6: Recommendations 42

    Appendix A: Circuit Diagram 44Appendix B: Assistance and Contact Info 45

    Appendix C: LM 555 Equation Derivations 46

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    Table of Figures

    Figure 1: Map of Mali 4

    Figure 2: Solar Panel Charger 6

    Figure 3: AC-Charger 7

    Figure 4: System Block Diagram 14

    Figure 5: Solar Charger 22

    Figure 6: AC Charger 24

    Figure 7: AC Battery Charger 25

    Figure 8: Signal Conditioner 28Figure 9: Charger Circuit 30

    Figure 10: Charge Status Display 32

    Figure 11: Switching Oscillator 33

    Figure 12: Kinkajou Charger Casing 40

    Figure 13: Battery Charge Display 40

    Figure 14: Side View of Charger Case 40

    Figure 15: Return on Investment 40

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    Table of Tables

    Table 1: High-Level Gantt Schedule 11

    Table 2: Itemized Task Gantt Schedule 12

    Table 3: Power supply value analysis 18

    Table 4: Charge monitor value analysis 19

    Table 5: Charge status display value analysis 21

    Table 6: Competitive Value Analysis 27

    Table 7: Component Pricing 36

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    Executive Summary

    A recent report published by the United Nations1 has indicated that there are

    currently 860 million illiterate adults world-wide and 100 million children who have

    no access to education. They cite literacy programs as a crucial means of breaking the

    poverty cycle.

    Design that Matters (DtM), a nonprofit corporation, has developed a low-cost

    projection system called the Kinkajou that will deliver teaching materials to

    instructors who are desperate for teaching resources. In light of this, our company

    has been contracted to design a portable, multi-input battery charging device that willcharge 12 Volt lead-acid car batteries, which are used to power the Kinkajou device.

    After a consultation session with the principals, Tim Prestero and Neil Carter, we

    were instructed to investigate the viability of introducing the product to a target

    market. The country of Mali will be the focus of our feasibility study.

    In the following paper, we will present an overview of our prototype

    development process, justify our design decisions, make a set of recommendations for

    future actions, and propose a business plan that could later be developed for our

    product.

    1 United Nations, The State of Global Literacy (Online: www.unusa.org)

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    Section 1: Introduction

    1.1 Problem Statement

    You are to design a universal 12 Volt battery charger that can take various

    forms of electrical energy and charge a typical 12 Volt lead-acid

    (automotive) battery. The charger must be able to handle the following

    inputs: a solar panel, a pedal generator, and standard AC power (both

    American and European standards). The charger must not overcharge the

    battery, and must indicate the state of charge. In addition, the circuit should

    not drain the battery. The charger must be affordable in the community it is

    used in, and should be suitable for applications such as the Kinkajou

    Projector. (http://kinkajou.designthatmatters.org) Prototype cost should

    not exceed $50.

    1.2 Planned Approach

    The process of developing a quality product that meets the demands

    of a potential market involves a great deal of forethought and design work.

    Our first course of action was to perform market research to anticipate the

    needs of our target market and to formulate a set of product specifications and

    requirements. After we had gained good insight as to what the productspecifications were we were able to formulate a course of action in which to

    carry out the design project. We brainstormed numerous design options and,

    based on a value analysis of these options, finalize a design approach.

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    Due to the extensive nature of this project and the short time allotted for

    completion, we found it necessary to subdivide the various tasks and assign

    each group member with a specific set of responsibilities. The assignments

    were given depending upon the willingness and ability of each team member.

    Additionally, we decided that certain tasks such as writing reports, giving

    presentations and doing research were the responsibility of everyone in the

    group. By taking a modular approach we were able to design, build, test, and

    troubleshoot several subsystems independently and combine them after each

    was working as a stand alone device.

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    Fi ure 1: Ma of Mali

    Section 2: Product Specifications

    2.1 Market Research

    A. Methods

    In developing our market report, we utilized a variety of resources to quantify

    our market, research products, and determine design considerations. In addition to

    the information session led by the founders of Design that Matters, some of our

    research materials included The Stanford Business Journal, Reports from the United

    Nations Educational, Scientific and Cultural Organization (UNESCO), the United

    States Patent website as well as several product websites.

    B.Market Research

    From extensive research we were able to

    identify and anticipate the needs two markets

    both the stated market of Mali and other parts of

    the Developing World. A dual market exists in

    that the charger could also be sold separately

    from the Kinkajou.

    Mali is among one of the poorest nations in

    the world as 65% of its land is desert or semi-

    desert. The yearly per-capita GDP is about U.S.

    $2982 and much of the country lacks economic developmentas a result,

    constructing a device that is inexpensive to produce and sell is essential. Since

    transportation and shipping are expensive endeavors due to the lack of paved

    2 International Service for National Agricultural Research, Mali: A Typical Sahelin Country (Online:www.insar.org)

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    roads, it is also essential that the device be as light-weight as possible since it will

    likely need to be carried over long distances. Our market primarily consists of those

    who reside in village communities, which typically lack electricity. Therefore the

    charging device would need to accommodate multiple sources of input. Only about

    50% of people in Mali can afford the luxury of batteries to power electric devices

    and the cost to recharge a battery is up to 700 CFA (Communaute Financiere

    Africaine or the African Financial Community) which equates to roughly U.S. $1.24

    per battery. This is a substantial cost to people in such an impoverished area.

    Therefore producing such a device would result in long term savings to

    communities.The Kinkajou Device has world-wide appeal to promote literacy in regions that

    lack adequate teaching resources. Organizations such as the World Literacy

    Foundation, UNESCO, and the World Literacy Crusade would likely be interested

    in purchasing the device for use in their campaigns to fight illiteracy.

    There is a world-wide demand in the developing world for a low-cost means

    of charging 12 Volt batteries. Power is essential for most modern devices. A

    charger with a myriad of inputs could be used for the following:

    Adapting charging technology to meet the demands of communities that lack

    electricity will likely prove to be a very profitable market. Additionally the

    charger could be used in the developed world to accommodate alternative sources

    of energy in order to lessen dependence on fossil fuels.

    Communication Systems

    Refrigeration

    Health Services

    Disaster Recovery

    Residential and Commercial Applications

    Utility Applications

    Water Pumping

    Lighting

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    Figure 2: SolarPanel Charger

    C. Competing Products

    In an effort to evaluate our competitors we performed extensive product

    research to determine typical production costs, feature sets, and sales price. Since

    a charger that handles multiple power sources does not exist, we examined each

    type of charger individually.

    Solar Chargers

    There are several commercially available solar battery

    chargers. Camping and automotive retail stores providedinformation on various models that are currently for sale.

    Prices ranged from U.S. $ 29-$50 for low-end battery savers

    that provide a low-current, slow charge. There are also a

    variety of solar devices that will fully charge a battery with

    prices ranging from U.S. $64 - $900 depending on the extra features. Output

    wattage of these chargers seemed to be the biggest price differentiator. After

    comparing several different chargers, we were able to identify distinguishing

    characteristics among competing products.

    Distinguishing Features of Solar Chargers:

    Rollable-mat solar collectors

    Daisy-chain capability for multiple chargers

    Built-in diode for reverse current protection

    Bypass for charger to Run 12 Volt Device without battery

    Pedal Chargers

    From our market research, we determined there is not a wide variety of

    commercially available pedal chargers. Most of our inquires led us to believe that

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    Figure 3: AC-Charger

    nearly all pedal chargers are homemade devices that are pieced together from various

    parts, typically bicycles and car alternators. There does not appear to be a standard

    consensus on how pedal chargers are built; a pedal generator will have various

    outputs depending on the RPM being produced, the gear-ratio of the chain drive, and

    the actual device being used in the generator to convert mechanical to electrical

    energy. Due to the lack of competing products available in the market place, our

    company will need to determine a set of requirements for the pedal charging feature.

    AC- Outlet Chargers

    Our product will need to be able to interface with both European (110 Volt) and US (220 Volt) power

    standards. To address this, we researched various products

    internationally. Prices for AC-Outlet Chargers ranged from

    U.S. $25- $200 depending on the feature set and the output

    current, which will determine the rate at which a battery is charged. After comparing

    several competing products we were able to synthesize a list of desirable features.

    Distinguishing Features for AC-Outlet Chargers:

    Reverse Polarity Indicator

    Short-Circuit/Surge Protection

    Easy-To Read Color Terminals

    Charge Rate, Charge Status, Charge Done Indicators

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    2.2 Customer/ Product Requirements

    From our market research we were able to determine the following set of customer

    requirements and product specifications:

    Affordability - Our market research shows that to most people, price is the

    first thing considered when buying a product. Since the Kinkajou projector is

    designed to be used primarily for literacy classes in the developing world, its

    components need to be as inexpensive as possible.

    Durability - It is reasonable to expect that the device will be bumped and

    dropped from time to time, so it is essential that the charger is strong

    structurally. Furthermore, our market research shows that Africa is known for

    having large power spikes and brownouts, so surge protection is a necessity as

    well. It is also essential that the product last as long as possible and need few

    repairs over time.

    Compact Size/ Light Weight - Many of the users of this product will live in

    small communities far from cities where they might purchase such a device.

    Thus the product will need to be carried some distance. For this reason, it

    needs to be as compact and lightweight as possible so that the average person

    can carry it a reasonable distance.

    Efficiency - As seen in our customer requirements, the product will need to be

    as efficient as possible in its use of power. The device may be powered by a

    person using either a hand crank or a bicycle generator and thus it is infeasible

    to expect a long duration of supplied power. It is thus critical that all power be

    used efficiently.

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    Versatility - Our research shows that the population that the product will be

    marketed toward has variety of available power sources. Some may have

    access to AC power, but many areas will not and thus need to make use of

    alternate power sources. It is for this reason that the product needs to be able

    to charge a battery with power from three different sources, an AC outlet (both

    110 and 220 Volt outlets), solar panels, or a pedal generator.

    Simplicity - The product will be used by people who are most likely not

    technically educated. Therefore, to appeal the largest market possible, it mustbe simple to operate and switch between the three possible power sources.

    2.3 Product Specifications

    Once we had developed a good understanding of the needs of our customers, we

    were able to merge the findings of our customer requirements and market research

    into a general set of product specifications:

    110/220 AC power supply input

    Solar panel power supply input

    Bicycle or hand crank generator power supply input

    Non-alpha-numeric output display

    Cost per unit of less than U.S. $50

    Portable and durable

    High Mean Time Before Repair (MTBR)

    High efficiency

    Charges a 12V lead acid car battery

    Does not overcharge the car battery

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    We were required to adhere to these underlying product specifications throughout

    the course of our design process. By using these product specs as an initial, non-

    technical guideline, we were able to hasten the design process and make effective

    decisions.

    As stated by our contractor, Design That Matters, affordability is a critical aspect

    of this device. The target market for this product will be developing nations that will

    not be able to absorb a high per unit cost. Specifically, Design That Matters has set a

    price target of less than U.S. $50 total for the battery charger and Kinkajou drive

    circuitry.

    In the course of our market research, we determined that the probable inputvoltage range from the three power sources will range from 6V-22V DC. Due to the

    variability of system input, it is necessary to construct a signal conditioning system to

    supply a constant input to the charging mechanism. To make this system possible,

    low voltage signals will need to be amplified to a constant value just as high voltage

    signals will need to be regulated. By ensuring that the charging device receives a

    constant input, we can guarantee the operation of the charger.

    The charge controller is another module that has several design considerations. In

    addition to supplying an efficient and timely charge to the 12 Volt Battery, it will be

    essential that the charge controller provide an output of its charge status as well as

    stop itself from continuing to charge once the battery has reached full capacity.

    Due to the fact that the target market for this device will be in developing

    countries with a low literacy rate, an alpha-numeric display is impractical. In order to

    make the device as readily understandable as possible, a series of LEDs will be used

    to display battery charge status. Additionally, because the Kinkajou system itself will

    be primarily used in darkened classrooms, the LEDs will allow the battery charger to

    be utilized in such environments as well.

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    Section 3: Product Plan

    3.1 Development ScheduleDue to the extensive nature of this project we found it necessary to subdivide the

    various tasks and assign each group member with a specific set of responsibilities.

    The assignments were given depending upon the willingness and ability of each team

    member (refer to the R column of Table 2). Additionally, we decided that certain

    tasks such as writing reports, giving presentations and doing research were the

    responsibility of everyone in the group. We have also divided the project into phases

    with dates corresponding to the completion deadline. Please refer to our Gantt charts

    below (Tables 1 & 2) for specific task assignments and project phases.

    Table 1: High-Level Gantt Schedule

    By developing both high-level and itemized task schedules we were able to ensure

    that our group was on task and well prepared for future deadlines. The Gantt chart

    method was used to plot individual responsibilities and their corresponding due

    dates. We made sure to allow a margin for contingency; recognizing that no matter

    how much forethought was given, everything would not go as planned.

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    Table 2: Itemized Task Gantt Schedule

    Key:

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    3.2 Budget

    One of the most important initial stipulations of the original problem statement

    was that .the charger must be affordable in the community it is used in, and should

    be suitable for applications such as the Kinkajou Projector. Prototype cost should not

    exceed $50. In addition to having a $50 dollar initial prototyping budget, it was also

    necessary to ensure that the total production cost when produced in bulk not exceed

    roughly $25. This budget constraint played a major role in making design decisions as

    economical as possible and also made it obligatory to take calculated risks when trying

    potential design methodologies. Throughout the process of devising our product, we

    often had to fully consider cost-benefit analysis as well as examine the trade offs

    between better specification fulfillment vs. reduction of overall expense.

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    Section 4: Design Approach

    4.1 Design Options

    Given the set of product specifications previously described, we found that

    the most effective way to design the device was as a set of several interconnecting

    subsystems. The block diagram shown below highlights the three main

    subsystems identified during the design process: a signal conditioner, a battery

    charge monitor and a charge status display. The signal conditioner in our product

    is used to format any applied voltage from the three types of potential inputs (wall

    outlet AC, solar panel or pedal generated voltage) and to apply a voltage on the

    battery in order to charge it. The charge monitor is needed to regulate the current

    flow into the battery so that the battery does not become overcharged or otherwise

    damaged during the process of charging. Additionally, the charge status display

    is necessary to indicate the level of charge on the battery and, in particular, to alert

    when the battery has been fully charged.

    Figure 4: System Block Diagram

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    4.1.1 Signal Conditioner

    The power supply subsystem of our design is responsible for converting an

    AC source into DC and accepting two additional DC sources. In brainstorming

    this subsystem we determined two ways of handling the AC/DC conversion

    process. Converting the 110/220 AC voltage into a DC voltage could either be

    done internally through the use of a transformer, bridge rectifier and zener diode

    or the conversion could be done externally through the use of an AC adapter rated

    for the appropriate voltage range.

    4.1.2 Charge MonitorWhile brainstorming the charge monitor we identified several design

    strategies for this subsystem. Because the charge monitor must tell the charge

    status display what to indicate, we considered using an A/D converter in a

    sample-and-hold configuration to quantify the batterys voltage. The digital

    output could then be passed through several combinational logic circuits in order

    to generate both the appropriate input for the charge status display and the

    control signals for the power supply. Another digital approach would be to utilize

    a PIC microcontroller with an internal A/D converter. The PIC could then read the

    battery voltage and internally generate the output for the charge status display

    and control signals for the power supply. This particular design strategy would

    eliminate the need for additional combinational logic circuitry.

    Having considered digital solutions we next considered an analog strategy

    for implementing the charge monitor. One possible analog design consists of

    generating a reference voltage (possibly the voltage at which the charger stops

    charging) and comparing it to the batterys voltage using a comparator. The

    output signal from the comparator would then be sent back to the power supply

    in order to control the charge placed on the battery by means of a negative

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    feedback loop. Another analog design would be to use the LED array in the

    charge status display to measure a specific voltage on the battery and then feed

    that voltage back to the power supply in a negative feedback loop. This design

    approach has the advantage of merging the charge monitor and charge status

    display into a single functional subsystem.

    The design approach that we eventually settled on utilizes a UC3906 linear

    lead-acid battery charge management IC to implement a three stage charging

    algorithm. The IC accomplishes this by controlling both voltage and current

    output based upon feedback from the battery. Additionally, this IC will monitor

    battery temperature and adjust the output signal accordingly. This componentgreatly simplifies our task of charging the battery in the most efficient way

    possible.

    4.1.3 Charge Status Display

    Several design options exist for the charge status display. An analog

    display with an arrow that either ranges between 0 and 100% charge or indicates

    the battery voltage (a voltmeter) could be used. A single LED or group of LEDs

    could also be used for this task. The single LED design would have the LED lit

    when the battery reached full charge, while the LED array design would feature a

    progressive update of the charge status. Another option would be to use a 7-

    segment LED display to output a numeric charge percentage. Additionally, in

    terms of non-visual display systems, a buzzer could be used to generate an

    audible signal that the battery has finished charging. The buzzer also need not be

    standalone as it could be used in conjunction with one of the other design

    strategies.

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    4.2 Value Analysis

    In order to determine the most feasible implementation we performed

    value analysis on the design concepts presented in Section 4.1. We used value

    analysis matrices to aid in deciding which options will make our product the most

    marketable.

    4.2.1 Power Supply

    Product Requirements

    Handles 110/220V AC as input

    Supports solar panels and pedal generator as input

    Produces a DC voltage suitable for charging a 12V lead acid car battery

    Options Available and Advantages/Disadvantages

    External AC/DC conversion using an AC adaptor:

    Easy to implement, more expensive.

    Internal AC/DC conversion:

    Harder to implement, less expensive.

    Value Analysis

    Cost: Price of subsystem.

    Inexpensive 3

    Reasonably Priced 2

    Expensive 1

    Simplicity: Ease of construction.

    Easy 3

    Moderate 2

    Hard 1

    Availability: Widely available components

    Good 3

    Average 2

    Poor 1

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    Weight Assignments

    A completed value analysis for the power supply is shown in Table 3

    below.

    Table 3: Power supply value analysis

    4.2.2 Charge Monitor

    Product Requirements

    Does not overcharge the battery

    Outputs to the display

    Controls the power supply

    Options Available and Advantages/Disadvantages

    Digital with combinational logic:

    Harder to implement, easily expandable/robust, high power

    consumption.

    PIC microcontroller:

    Software expandable (handles logic internally), replacement parts

    unavailable in developing countries.

    Analog with comparator:

    Harder to implement, readily available replacement parts.

    Integrated with charge status display:

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    Efficient design, low power consumption.

    UC3906:

    Efficient design, replacement parts unavailable in developing

    countries.

    Value Analysis

    Cost: Price of subsystem.

    Inexpensive 3

    Reasonably Priced 2

    Expensive 1

    Efficiency: Power consumption of the subsystem

    Good 3Average 2

    Poor 1

    Simplicity: Ease of construction.

    Easy 3

    Moderate 2

    Hard 1

    Weight Assignments

    A completed value analysis for the charge monitor is shown in Table 4

    below.

    Table 4: Charge monitor value analysis

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    4.2.3 Charge Status Display

    Product Requirements

    Easy to understand

    Inexpensive

    Low power consumption

    Options Available and Advantages/Disadvantages

    Analog display:

    Harder to interpret, more expensive.

    Buzzer:

    Easy to implement, does not indicate charge status.

    Seven segment display:

    Harder to implement, more expensive, requires literacy.

    Single LED:

    Inexpensive, low power consumption, easy to implement, does not

    indicate charge progress.

    LED array:

    Inexpensive, low power consumption, harder to implement than

    single LED, indicates charge progress.

    Value Analysis

    Cost: Price of subsystem.

    Inexpensive 3

    Reasonably Priced 2

    Expensive 1

    Simplicity: Ease of construction.

    Easy 3

    Moderate 2

    Hard 1

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    Understandability: The clarity of the display.

    Good 3

    Average 2

    Poor 1

    Weight Assignments

    For the display subsystem, we considered understandability to be the most

    important criteria and, as a result, it was assigned a weight of 3. Of the remaining

    two criteria, cost was assigned a weighting of 2 and simplicity a weighting of 1.

    Table 5: Charge status display value analysis

    4.3 Competitive Value Analysis

    After searching widely, we were able to find many competitors in the

    market of recharging batteries. Typical applications for battery charging included

    Marine, camping/outdoor, and automotive uses. It was determined after

    thorough research that our product would be unique to the marketplace due to the

    fact that currently no charging device available is designed to accept multiplepower sources. Despite this, we will evaluate similar products for each type of

    input source; AC, Solar, and Pedal Generated. Table 4 shows the competitive

    value analysis of our product vs. the four competitors described below.

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    4.3.1 Solar Chargers

    When solar panels are used to charge storage batteries, their limited output

    under low sunlight conditions leads to seriously shortened battery life and

    performance. Trying to protect against this creates higher costs, as the typical

    solution seems to be increasing the size / number of both the panels and batteries.

    In addition, typical solar controllers, although able to protect batteries from

    under/over charge, fail to optimize the charge rate capabilities of the solar panels.

    They also do not remove sulphate build-up on the batterys storage plates, causing

    longer recharge time, boil out and significantly shortened life.

    There are a variety of solar devices that will fully charge a battery with pricesranging from U.S. $64 - $900 depending on the extra features. Output wattage and

    solar panel size of these chargers seemed to be the biggest price differentiator.

    After looking at several models, we what seemed to be two of the better

    commercially available solar chargers out there.

    PRO-KIT 15-WATT SOLAR BATTERY CHARGER ICP Global Technologies

    The Pro-Kit Charger was similar to many other solar products

    available. At U.S. $189 the device is far more expensive than

    our product, but the photovoltaic cell is what drives the cost of

    the charger up and because our charger relies on an external

    solar cell, it is reasonable to assume that our product would be

    a competitor3.

    3BatteryMart, Solar Battery Chargers (Online: http://www.batterymart.com/battery.mv?c=solarchargers)

    Figure 5: SolarCharger3

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    Specifications:

    Wattage: 15 watts Peak Output: 1 amp@15 volts

    Approx. Watt-Hrs / Day *: 60 75 Approx. Amp Hrs / Day *: 4 - 5

    Dimensions: 38" x 13" x 1" / 965 mm x 330 mm x 25 mm Weight: 9.2 lbs / 4.2 kg

    Temperature Range: -40F to 176F / -40C to 80C Warranty: 5 years @ 80% of output

    Ratings:

    Operating Conditions: 5, Diverse Temperature Range and Weatherproof Design

    Display: 2, Very Limited User Display

    Extra Features: 1, Has a few added features like overcharge protection

    Range: 4, Can operate on many input voltages- dependent upon sunlight

    Ease of use: 4, Intuitive to Use

    Charge Time: 2, Depends on available sunlight, 15 W Max Output

    Modular Design: Unknown- Dont know internal design

    Components: Unknown- Dont know internal components

    Versatility: 1, Operates on 1 Input

    Weight: 3, Light-weight

    Price: 0, $189

    BATTERYMINDER 12 VOLT 5 WATT SOLAR CHARGER- VDC ELECTRONICS

    The BatteryMINDer, produced by VDC Electronics is another typical

    product that beats most other competitors price significantly for its output specs.

    The device distinguishes itself in particular because it optimizes the solar panels

    charge rate, ensuring batteries are charged in the shortest possible time, keeping

    them at full-charge indefinitely, without ever overcharging.4

    Specifications:

    Wattage: 5 watts Peak Output: 333 mAmps@15 volts

    Approx. Watt-Hrs / Day *: 20 - 25 Approx. Amp Hrs / Day *: 1.4 - 1.75

    Dimensions: 19 5/8" x 13 5/8" x 5/8" Weight: 7 lbs

    Temperature Range: 0F to 130F Warranty: 5 years

    4 BatteryMart, Solar Battery Chargers (Online: http://www.batterymart.com/battery.mv?c=solarchargers)

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    Ratings:

    Operating Conditions: 4, Diverse Temperature Range and Weatherproof Design

    Display: 0, No User Display

    Extra Features: 2, Battery Minder Component Optimizes Charge

    Range: 4, Can operate on many input voltages- dependent upon sunlight

    Ease of use: 2, Moderate Difficulty

    Charge Time: 1, Depends on available sunlight, 5 W Max Output

    Modular Design: Unknown- Dont know internal design

    Components: Unknown- Dont know internal components

    Versatility: 1, Operates on 1 Input

    Weight: 3, Light-weight

    Price: 0, $99.95

    4.3.2 AC Chargers

    There were an extensive number of portable, commercially available

    battery chargers, with prices ranging from about U.S. $30 - $500. The price was

    largely a variable of extra features, number of batteries that could be charged at

    one time and the output amperage, which determines the rate at which a battery is

    charged. The Competitors also had different ways of implementing what seemed

    to be different charging algorithms to achieve optimal charge. There are two

    options examined in this section, a typical, fully-finished consumer model and an

    exposed AC charger circuit made for industrial/customized applications. Because

    most consumer models were essentially the same, we chose the two models that

    best represent the needs and specs of our market.

    CLIPLIGHT 12 VOLT 10 AMP PORTABLE CHARGER MOBIL LINE

    The Mobil Line Deep Cycle Battery charger is typical of most

    portable chargers in that it can recover deeply discharged batteries as

    well as prevent overcharging. The charger also has overload and

    reverse polarity protection as well as an intuitive,

    Figure 6: ACCharger5

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    simple to understand LED display5. At U. S. $49.95, the device is competitively

    priced for the variety of features that it offers in comparison to other models.

    Specifications:

    Output: 12 Volt Nominal; 10 Amp DC Set Voltage: 14.7 +/- 0.1 Volt

    Float Voltage: 14.0 +/- 0.1 Volt Input: 105 VAC - 120 VAC ; 60 Hz

    Dimensions: 3-1/2" x 2-1/4" x 4-1/2" Weight: 3 lbs.; 1.36kg

    Ratings:

    Operating Conditions: Unknown

    Display: 2, LED Array

    Extra Features: 2, Several Extra features like polarity indicator and surge protection

    Range: 0, Only Rated for American Power Standard

    Ease of use: 4, Very Easy to Use

    Charge Time: 3, 10 Amp Output, uses charging algorithm for optimal time

    Modular Design: Unknown- Dont know internal design

    Components: Unknown- Dont know internal components

    Versatility: 1, Operates on 1 Input American AC Standard

    Weight: 4, Light-weight

    Price: 1, $49.95

    L12-0.5/115AC LEAD ACID CHARGER IBEX INC.

    Ibex Inc. offers a wide variety of industrial application

    battery chargers that can handle both American and European

    AC power sources as well as being manufactured to operate in

    harsh and extreme in environments. Their line of devices are

    rugged and made to last for many years without failure or need

    for repair. The Ibex chargers range in cost from U.S. $45- $806.

    4 Battery Mart, 12 Volt AC Chargers (Online: http://www.batterymart.com/battery.mv?c=12voltchargers)

    6 Ibex AC Battery Chargers (Online: http://www.ibexmfg.com)

    Figure 7: ACBattery Charger6

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    Specifications:

    Output: 14.8 V 10 Amps Input: 103 252 V AC

    Dimensions: 5 x 4 x 3 Weight: 4 lbs

    Temperature Range: 0F to 130F

    Ratings:

    Operating Conditions: 4, Designed to Handle Extreme and Harsh Environments

    Display: 0, No User Display

    Extra Features: 1, Has some internal extra features

    Range: 2, Accommodates American and European Power Standards

    Ease of use: 0, Not housed, controls dont come with circuit

    Charge Time: 2, Uses 3-Stage Temperature Dependent Charging Algorithm

    Modular Design: 1, Circuit is modular

    Components: 2, Uses common parts like transformers, diodes and capacitors

    Versatility: 2, Operates on 2 Inputs US and European Standards

    Weight: 4, Light-weight

    Price: 1, $45

    4.2.3 Pedal Chargers

    From our market research, we determined there is not a wide variety of a

    commercially available pedal charger. Most of our inquires led us to believe that

    nearly all pedal chargers are homemade devices pieced together from various

    parts, typically bicycles and car alternators. There does not appear to be a

    standard consensus on how pedal chargers are built; a pedal generator will have

    various outputs depending on the RPM being produced, the gear-ratio of the

    chain drive, and the actual device being used as the generator to convert

    mechanical to electrical energy. Due to the lack of competing products available

    in the market place, our company will need to determine our own set of

    requirements for the pedal charging feature.

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    4.4Module Definitions

    Signal Conditioner

    The Signal conditioning phase is designed ensure that any input signal

    above or below the desired operating voltage is regulated before being passed to

    the UC 3906. This is accomplished by a boost converter and voltage regulator in

    series, which boost or step-down the input signal as necessary.

    After evaluating several boost converters, we found the LM2577, a TO-263-

    5 package based solution that meets our design requirements. The LM2577 is able

    to reliably boost low DC voltages in the range of 3.5 40 volts to a constant output

    voltage that can be synthesized by a simple LC configuration.The voltage regulator used for this subsystem is an LM350. This IC will be

    used to provide a constant current and smooth voltage signal to the UC3906. As

    long as the boost converter raises the any low input signal to above 15 volts, the

    Table 6: Com etitive Value Anal sis

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    LM350 will be able to ensure that the UC3906 receives a constant supply of 15

    volts.

    Figure 8: Signal Conditioner

    The appropriate components in the boost converter section of the signal

    conditioner were chosen using the following equations for VVin 5.3min =

    and VVout 17= .

    MAX

    MAXINMIN

    D

    DVVL

    =

    1

    )12)(6.0(4.6 min

    VVV

    VVV

    DFOUT

    INFOUT

    MAX 6.0

    min

    +

    +

    =

    2

    min

    2750

    IN

    OUTLOADC

    V

    VIR

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    OUT

    LOADV

    VinAI minmax

    1.2

    OUTIN

    LOADCOUT

    VV

    IRLC

    min

    max19.

    min

    2

    25.58

    INC

    OUTOUT

    CVR

    CVC

    1V23.12

    1 = OUTV

    R

    R

    The resistors used in the voltage regulator were synthesized using the equation

    2

    1

    2 *125.1 RIR

    RV ADJOUT +

    += .

    Linear Charger IC

    The heart of our design is the UC3906, a linear lead-acid battery charge

    management IC which implements a three stage charging algorithm in order to

    maximize battery lifespan. (See Figure 9) The IC accomplishes this by controlling

    both voltage and current output based upon feedback from the battery.

    Additionally, this IC will monitor battery temperature and adjust the output

    signal accordingly. This component greatly simplifies our task of charging the

    battery in the most efficient way possible.

    The UC 3906 accepts an input voltage of 10-40 Volts DC. In our design, the

    voltage regulator will provide a regulated voltage in the range of 10-20 Volts DC

    to the UC3906. Depending on the input voltage and the charge of the battery, the

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    IC will provide a voltage and current as specified by the charging algorithm. In

    order to accomplish this the configuration shown in Figure 9 was implemented.

    The resistor values used in the circuit were derived from the set of equations

    below.

    k463.2 ==D

    CI

    R

    k2123.2

    1

    =

    +=

    T

    XSUM

    A

    V

    RRR

    k18== ASUMB RRR

    Figure 9. Charger Circuit

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    k881*3.2

    =

    =FOC

    SUM

    DVV

    RR

    k2303.2=

    =

    D

    FSUMI

    VR

    A3.010

    == MAXOCI

    I

    k7.43*

    =+

    =DC

    DCX

    RR

    RRR

    1.025.0

    ==MAX

    SI

    R

    34.0

    5.2=

    =

    T

    TIN

    T V

    VV

    R

    Additionally, the equations above contained specific voltage and current level that

    are specified below.

    A50=DI

    mA5.1=TI

    A5.2=MAXI

    V4.14=OCV

    V16=INV

    V8.13=FV

    V2.10=TV

    These equations come from the UC3906 datasheet found on Texas Instruments

    website.

    It should also be noted that standard components may be used for all of the

    parts in this diagram except for RS and the transistor. RS must be a 1W resistor and

    the pnp transistor must be rated for the maximum current that will be fed to the

    battery (2.5A).

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    Charge Status Display

    We have elected to feature a continuously updated user display. In order

    to accomplish this an LM3914 was used to drive an array of ten LEDs. Our design

    is shown in Figure 10.

    Figure 10. Charge Status Display

    In this configuration pin 4 is used to specify the low end of the display

    range (10.5V) and pin 6 is used to specify the high end of the range (13.8V). The

    input signal (pin 5) is then scaled linearly across the range specified. The resistor

    attached to pin 7 is used to determine the luminosity of the LEDs by pulling a

    specific amount of current.

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    Switching Oscillator

    As we have elected to feature a continuously updated user display it is

    necessary to repeatedly switch between charging the battery and monitoring the

    batterys charge. In order to accomplish this effectively the switch must

    disconnect the charger IC from the battery when refreshing the display. An

    LM555 configured as an astable oscillator will be utilized to repeatedly switch

    between the two systems. Using an LM555 will allow us to specify the refresh rate

    of the display (the LM555s frequency) as well as the amount of time available toupdate the display (the duty cycle).

    The specific configuration we utilized is shown below in Figure 11. This

    configuration implements a duty cycle of approximately 1%. That is, the battery is

    being charged 99% of the time.

    Figure 11. Switching oscillator

    The inclusion of a diode across RB allows for a duty cycle below 50%. During the

    charging cycle the current path will bypass RB yielding the following performance

    equations.

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    ( ) ( ) sec69.02ln*k100*F102ln** === AH RCt

    ( ) ( ) sec3.692ln*M10*F102ln** === BL RCt

    sec24.76Period =+= LH tt

    mHz13Period

    1Frequency ==

    It should be noted, however, that these equations are based on the

    functioning of an ideal diode and, as such, the actual results in implementation

    will vary according to the characteristics of the device.

    4.5 Manufacturability

    Our product implements both discrete components and common integrated

    circuits. All parts are readily available and produced by multiple companies. We

    took this into consideration when choosing our parts in the event a company went

    out of business, we would still be able to follow our design. One exception is the

    UC 3906. This IC is designed specifically designed to charge lead acid batteries,

    and will likely be uncommon in typical electronic shops in Mali or other

    developing areas.

    The battery charger will require a case that is lightweight, attractive, and

    durable. The most important aspect of the casing however, is good dissipation of

    heat. Our design implements 4 voltage regulators, all of which produce

    significant heat when in use. Clearly efficient transfer heat to the outside will be

    essential. Durability is also an important aspect of the case design. This product

    will undergo frequent use and be transported; therefore it will need to be

    structurally sound enough to protect the components from everyday bumping

    and jarring. In addition we have made our case design is watertight by caulking

    all seems and cracks.

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    Our design is modularized on several levels. For example our signal

    conditioning subsystem is broken up into two smaller modules, voltage boost and

    voltage regulation. This method of using several levels of system subassemblies

    makes manufacturing and troubleshooting more simple and efficient.

    While our product does have excellent functionality, some improvements

    could be made in the manufacturing stage. Firstly, all of the circuitry would

    certainly be mounted on a PCB. Another change that should be made in the

    manufacturing stage from our prototype design is the use of more standard parts

    to reduce part variety. This pertains specifically to resistors and capacitors. In

    several instances we connected several components in series or parallel to attain aspecific value which we did not have in a single component. Clearly some

    changes need to be made before mass production, but our modular design lends

    itself well to manufacturing.

    4.6 Cost Analysis

    Standard Cost

    For the first year, we have projected research and development costs to be

    approximately $10,800, as shown in section 5.3. This value is substantially lower

    than expected, primarily because we have done a large part of the design and

    testing at no charge to Design that Matters. Future development of our design

    will likely be conducted by students similar to us who will not be paid either.

    However before the product becomes open on the market, we expect that Design

    that Matters will hire professional consultants to check our work and perform

    safety testing, to ensure the final product is ready for the consumer. For the

    second year of production, research and development costs will be approximately

    $5,000. This amount is certainly lower than costs for the first year, but still

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    necessary because modifications and improvements will undoubtedly occur in the

    early stages of product development and implementation.

    We expect design that matters will outsource the manufacturing of the

    charger. Since at the start of this endeavor, Design that Matters only plans to

    produce 800 of these devices. Therefore it does not make sense for them to

    purchase the factory and machinery necessary to mass produce a product line

    when the market for the device is still untapped and unknown.

    The only notable price change between our prototype and the final

    manufactured product will be the AC adaptor. For prototyping and testing, we

    opted to purchase an inexpensive AC adaptor which could take an input of120VAC and output 17VRMS. This worked fine for testing here in the U.S., but

    one of our customer requirements was that the charger needed to accept both

    American and European AC power standards. Therefore, in our manufactured

    cost analysis we take into account a more expensive adaptor to convert 220VAC to

    the proper DC voltage.

    COST PER UNIT

    QUANTITY1 100 500 1000

    UC 3906 $5.36 3.332 3.094 3.0345

    LM317 $0.60 0.3375 0.21 0.1995

    AC Adaptor $6.95 4.95 4.75 4.5

    LM 555 $0.50 0.3525 0.225 0.18

    Rocker Switch $0.76 0.46 0.42 0.39

    Steel Clips $0.73 0.4526 0.35 0.28

    LM 2577 $5.42 3.4314 3.225 3.1992

    LED Array $2.10 1.4 1.225 1.12

    LM 3910 $2.91 1.598 1.222 1.2032

    LM 350 $1.65 0.99 0.891 0.858

    Large Heat Sinks $1.25 0.775 0.65 0.5Small Heat Sinks $0.30 0.186 0.12 0.09

    Screw Terminals $1.00 0.62 0.48 0.37

    Miscellaneous Hardware $3.00 2.24 $2.15 $2.00

    LM317 $0.60 0.3375 0.21 0.1995

    Large Heat Sinks $1.25 0.775 0.65 0.5

    Small Heat Sinks $0.30 0.186 0.12 0.09

    Casing $1.50 $1.37 $1.19 $1.05

    TOTAL: 36.18 23.79 21.18 19.76

    Table 7: Component Pricing

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    Retail Pricing

    We have estimated the cost of parts to constitute 40% of the total retail price

    since Design that Matters is a not for profit organization. In addition,

    approximately 15% of the total retail price will be taken by the wholesaler and

    distributor. Finally 5% will be allotted to advertising costs since the market is

    already defined. This leaves 40% profit after all fixed costs are met. To calculate

    the retail price, we simply multiplied the cost of parts by 2.5 to get 100% of the

    retail price. Manufacturing in quantities of 1000 yields a retail price of $49.40, or

    approximately $50. The above percentages reflect standard fractions of the retail

    price.

    4.7 Hazard Analysis

    Before releasing our product on the unsuspecting people of Mali, it will be

    necessary to perform rigorous tests on how well the device will perform under

    long-term operation. The casing has not been tested for shock or heat resistance,

    leaving a potential hazard with the components becoming overly hot and burning

    the user or melting the case. Also the materials have not been tested for toxicity if

    ingested or placed in a bodily orifice. In the event that the case might burn or melt

    there could be potential hazard associated with the fumes as well. The voltage

    regulator and boost converter circuits pose the greatest threat to burning the user.

    Were the AC Adapters cord to become unraveled or exposed, it could potentially

    pose a great shock risk to the user. At 110 or 220 volts, coming into contact with

    the hot wire could be harmful and even fatal.

    For the most part though, it can be reasonably concluded that except for a

    very small number of possible instances, our product is relatively safe and

    contains for the most part, hazard-free parts.

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    4.8 Legal Considerations

    Patent/ Intellectual Property

    All intellectual property, tangible articles of manufacture, and design

    methods represented by initial prototypes and design notebooks are the sole and

    proprietary work of the members of this design team: Mike Eskowitz, Eric Hall

    and Chris Hamman. In the event that, at a later date, something in the design is

    determined to be patentable, the group has agreed to abide by the WPI Intellectual

    Property Policy. (http://www.wpi.edu/Pubs/Policies/intell.html) Since all

    development and design was done using WPI facilities with WPI equipment, the

    University would be entitled to ownership rights and would absorb all costs

    associated with patenting the invention. WPI would be entitled to no more than

    50 percent of any royalties incurred from the patent.

    Product Liability

    We waive all liability claims to Design that Matters due the fact that time

    did not permit extensive safety and reliability testing. The prototype developed

    by our group is not guaranteed on any grounds whatsoever. It is the

    responsibility of DtM to accept any failures, injury, or loss of life associated with

    this design prototype. It is our hope that this section will negate any implied

    warranties and sufficiently protect us from involuntary negligence and all

    liabilities.

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    Section 5: Product Results

    5.1 Product FunctionalityAt present, our device is fully functional from end to end. As tested on

    prototyping board, each module functions independently as well as with the other

    components. To date, our group is still migrating the display circuit module to the

    solder board and will have the circuit wired and enclosed by mid-January. By

    ordering the components surface mounted and placed on a PCB, the size of the device

    could decrease significantly; however, the heat sinks in the boost converter and

    voltage regulator must be sufficiently large to dissipate the heat produced when the

    circuit is drawing a high current.

    5.2 Product Form

    In the harsh weather and climate conditions of Mali, it will be necessary for the

    products casing to be water resistant, dust-proof, shock and heat resistant, as well as

    withstand jarring and drops. For the purposes of our prototype we have enclosed our

    circuit in a handmade case, the next design should most likely have a case made of a

    strong and resilient composite plastic.

    Our user interface is extremely simple to use and understand. The user need only

    to plug in the AC Adapter or Input Clips to the proper polarity (red +, black -), attach

    the output clips to the battery, and flip the rocker switch into the on position. If the

    charger is receiving input voltage, the Green LED will light. The user display

    quantizes a range of battery charge in terms of ten different possible battery output

    voltages. Our case and interfaces are shown in the following set of pictures:

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    Figure 12 and 13: Kinkajou Charger Casing and Battery Charge Display

    Figure 14: Side View of Charger Case

    5.3 Expected ROI

    Our market research has revealed that the market for this type of device is

    16,000 units world wide. Assuming that a battery charger will accompany each

    kinkajou projector, we feel that our product will be able to capture 5% of this

    market, or 800 units. The capital investment required to achieve this production

    goal will include costs of research and development, as well as manufacturing.

    RDE will be minimal since most of the designing and testing is being conducted

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    by unpaid students. Professional consultants will need to be hired to test the final

    product for safety and functionality. These calculations are as follows.

    (3 engineers) x (15 hours/week) x (4 weeks) x ($60/hour) = $10,800

    Manufacturing costs will include contracting production plants as well as

    the necessary equipment and machinery. We have estimated initial

    manufacturing costs to total $50,000. Therefore, the initial capital needed to begin

    production of battery chargers is $60,800.

    Since we plan to sell 800 units at a retail price of $50 for the first year, our

    first year revenues will be $40,000. Assuming an equal number of chargers are

    sold each month during the first year, approximately 67 chargers will be sold eachmonth. Therefore, the monthly revenue will be $3350. Since our calculated retail

    price is 40% profit, our monthly expenses will be $2010. At this rate, our break

    even point will be at 48 months or 4 years. R0I at 5 years is calculated to be 9.53%.

    Clearly this is a substantial amount of time to be in debt. This should most

    defiantly be revisited in future project additions. A chart displaying the Return on

    investment over time is shown in figure 15.

    Fi ure 15: Return on Investment

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    Section 6: Recommendations

    While our circuit is fully functional, there is still much room for

    improvement and modification due to the incredibly short timeframe within

    which this design process took place. Obviously seven weeks is hardly enough

    time to cautiously and methodically carry out all of the necessary steps when

    designing a product that will be potentially used in the real world. Due to the time

    constraints that were placed on us, we were forced to cut some corners that would

    otherwise have been unacceptable.

    First and foremost is the issue of safety; before releasing our product on the

    unsuspecting people of Mali, it will be necessary to perform vigilant tests on how

    well the device will perform under long-term operation. The casing has not been

    tested for shock resistance, there is a potential hazard with the components

    becoming overly hot and burning a user or melting the case. Also the materials

    have not been tested for toxicity if ingested or placed in a bodily orifice. In the

    event that the case might burn or melt there could be potential hazard associated

    with the fumes as well.

    Another set of tests that will need to be performed are reliability and

    extended operation assessments. It is important to examine the behavior of the

    circuit over long periods of time: what happens when the charging circuit is used

    weekly for two months, or daily for two years? Also can the circuit survive being

    constantly on for 3 days unattended? Another issue is whether the device will fail

    or will need repair rapidly. By considering issues like this, the circuit could later

    be optimized to address the need for a low Mean-Time before Repair and more

    importantly Mean-Time before Failure. It is our opinion that the Boost Converter

    and Voltage Regulator will be the first components to fail with the Transistor in

    the Charging Circuit following sometime after.

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    Also because of a lack of both resources and time we were unable to verify

    our predictions of system performance when the charger is connected to the Solar

    Panel Input. A means of simulating or actually testing the solar panel operation

    were not provided for us, so we can only speculate on the behavior our system

    with the solar panel. A solar panel can be roughly modeled as a constant current

    source; the charge controller is designed to handle input currents of 15 Amps,

    given the proper external transistor configuration. Most likely the UC would let

    the current pass until the battery reaches full capacity whereupon it would stop

    the current flow through the circuit. Later design verification should include a

    great deal of testing with a solar power source.Future courses of action should also include investigating the feasibility of

    incorporating more common components into the design. While many of our

    components like the voltage regulator (LM350), boost converter (LM 2577),

    resistors, and capacitors can be found in everyday consumer electronics, other

    Integrated Circuits like the display driver (LM3914) and charge controller (UC

    3906) are not as widely available in developing nations. On-the-spot repairs are

    required in small rural communities, it is important that the device have as many

    commonly available components as possible.

    Another potential improvement that could be made would be to

    incorporate a less-expensive display module. At a total cost of $5.00 the display

    could be phased out for the sake of cost by using a single resistor to indicate that

    charging has completed. However, making this change would greatly sacrifice the

    functionality of the display. Another component change that could be beneficial

    would be to implement the regulation system using a switching voltage regulator

    as opposed to the linear LM350 and LM317 devices. These linear devices are

    inefficient with some power loss being dissipated in the form of external heat.

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    Appendix A: Circuit Diagram

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    Appendix B: Assistance and Contact Info

    If any or all of this design concept is used in the future by DtM,

    we would be more than happy to offer our assistance in helping to

    further the next design phase. In the event that questions about our

    design process arise or if any future consulting is needed, feel free to

    contact one of the team members listed below:

    Michael Eskowitz

    E-mail: [email protected]

    Cell: 978.430.2681

    Eric Hall

    E-mail: [email protected]

    Cell: 207.939.4449

    Chris Hamman

    E-mail: [email protected]

    Cell: 508.667.7015

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    Appendix A: LM555 Equation Derivations

    In order to derive equations characterizing the behavior of the LM555 when

    configured as an astable oscillator it is best to observe the internal workings of thedevice.

    Figure 8: Internal view of LM555

    We will now present an analytical overview of the LM555s operation.

    1. The most appropriate place to begin analysis in this case is the zero state:

    when the capacitor has zero charge placed on it.

    2. With zero volts placed across the capacitor comparator 1 will assume a low

    state (0) and comparator 2 will assume a high state (1).

    3. This will cause the flip flop to set 1=Q and 0=Q .

    4. An output of 0 from Q will turn the transistor off.

    5. Because the transistor is off the capacitor will become charged. For the

    purposes of calculating a time constant it should be noted that the charge

    path is through both AR & BR .

    6. Once the capacitor reachesCCV

    3

    1comparator 2 will switch low (0).

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    7. When the capacitor reaches CCV3

    2comparator 1 will switch high (1).

    8. This will cause the flip flop to reset to toggle, assuming the state 0=Q and

    1=Q .

    9. The logic high output from Q will activate the transistor.10.This will discharge the capacitor through BR .

    11.The capacitor voltage will discharge to CCV3

    1causing comparator 2 to

    switch high (1).

    12.This will transition the flip flop into state 1=Q and 0=Q .

    13.The process will repeat beginning at step 4.

    As we can determine from the qualitative description above, the oscillator is in the

    high state ( 1=Q ) when the capacitor is charging up to CCV3

    2. It is thus possible to

    calculate the duration for which the output is high ( Ht ) using the universal

    capacitor equation:

    ( ) tINITIALFINALFINALCAP eVVVV=

    A derivation of Ht is presented below.

    Ht :

    Ht

    CCCCCCCC eVVVV

    =

    3

    1

    3

    2

    Hte=3

    21

    3

    2

    Hte=2

    1

    Ht=

    2

    1ln

    =

    21lnHt

    ( )2ln=Ht

    As noted in step 5, the charge path is through both AR & BR , thus the time

    constant is equal to:

    ( )CRRRC BA +==

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    ( ) ( )2lnCRRt BAH +=

    ( )CRRt BAH += 693.0

    A similar set of steps can be taken in order to determine the time Lt . In this case,

    however, the capacitor discharges across BR alone (step 10) yielding a different

    time constant and the result:

    Lt :

    ( )2lnCRt BL = CRt BL 693.0=

    Having obtained both the high and low times for the oscillator output it is possible

    to calculate the output period as:

    HLPERIOD ttT +=

    The reciprocal of which is its frequency:

    HLPERIODHZ ttTf +

    ==11

    Another important attribute is the oscillators duty cycle. The duty cycle is a

    percentage measure of time spent in the high state.

    ( )( ) BA

    BA

    BAB

    BA

    HL

    H

    RR

    RR

    CRRCR

    CRR

    tt

    t

    2693.0693.0

    693.0

    +

    +=

    ++

    +=

    +=