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DESIGN AND IMPLEMENTATION OF A STOCHASTICWIRELESS SENSOR NETWORK
BY
JOEL CHRISTOPHER JORDAN
B.S., University of Illinois at Urbana-Champaign, 2003
THESIS
Submitted in partial fulfillment of the requirementsfor the degree of Master of Science in Electrical Engineering
in the Graduate College of theUniversity of Illinois at Urbana-Champaign, 2004
Urbana, Illinois
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ACKNOWLEDGMENTS
I thank my adviser Roy Campbell for providing me with an interesting project to
work on. Also, I thank Doug Jones and Dan Sachs for introducing me to an interesting
direction to take the project in. Don Schmidt initially informed me of the possibility
of this project. Jacky Leungs long hours of soldering made this project possible. The
student chapter of the ACM provided me with laboratory space and test equipment.
I thank my family for their understanding and encouragement, and especially my
father Glenn Jordan, who set a fine example for me to follow in my studies.
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TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER 2 STOCHASTIC SENSOR NETWORK DESIGN . . . . . 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Stochastic Sensor Network Properties . . . . . . . . . . . . . . . . . . . . 42.3 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Test Network Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
CHAPTER 3 SENSOR NODE DESIGN CONSIDERATIONS . . . . . 83.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Power Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1 Circuit overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2.2 Circuit implementation . . . . . . . . . . . . . . . . . . . . . . . . 113.2.3 Reservoir capacitor selection . . . . . . . . . . . . . . . . . . . . . 12
3.3 Energy Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.1 Solar panel selection . . . . . . . . . . . . . . . . . . . . . . . . . 133.3.2 Alternate power sources . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.4.1 Sound-level transducer . . . . . . . . . . . . . . . . . . . . . . . . 173.4.2 Light level detection . . . . . . . . . . . . . . . . . . . . . . . . . 173.4.3 Other sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Wireless Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5.1 Radio module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5.2 Antenna considerations . . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Control Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.6.1 Microcontroller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.7 Timekeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
CHAPTER 4 SENSOR NODE OPERATION . . . . . . . . . . . . . . . 234.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.1 Hardware overview . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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4.2.2 Expansion connector . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.3 Reprogramming the nodes . . . . . . . . . . . . . . . . . . . . . . 264.2.4 Prototype circuit boards . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.4 Design Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.5 Base Station and Debugging Circuit . . . . . . . . . . . . . . . . . . . . . 31
CHAPTER 5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . 335.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
APPENDIX A SOLAR CELL DISCUSSION . . . . . . . . . . . . . . . . 35
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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LIST OF TABLES
Table Page
3.1 Low-light performance for identically rated solar panels. . . . . . . . . . . 153.2 Solar panel power production per unit area. . . . . . . . . . . . . . . . . 16
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LIST OF FIGURES
Figure Page
3.1 Solar stochastic sensor node block diagram. . . . . . . . . . . . . . . . . 83.2 Conceptual solar cell IV curve. . . . . . . . . . . . . . . . . . . . . . . . 93.3 Solar battery charger circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Power supply circuit schematic. . . . . . . . . . . . . . . . . . . . . . . . 113.5 Aerogel, left, and double layer, right, 0.47-F supercapacitors. . . . . . . . 133.6 Four solar panels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.7 Sound-level detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.8 Radio transceiver circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1 Stochastic sensor node schematic. . . . . . . . . . . . . . . . . . . . . . . 244.2 Expansion header pinout. . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 In-circuit serial programming header pinout. . . . . . . . . . . . . . . . . 264.4 Stochastic sensor node prototype. . . . . . . . . . . . . . . . . . . . . . . 274.5 Software operation flowchart. . . . . . . . . . . . . . . . . . . . . . . . . 284.6 Schematic of debugging circuit. . . . . . . . . . . . . . . . . . . . . . . . 31
A.1 Solar cell equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 36
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CHAPTER 1
INTRODUCTION
Wireless sensor networks have generated much research interest in recent years as
advances in electronics technology have made them feasible. In general, such a network
consists of many nodes scattered over an area to provide distributed sensing and data
processing [1]. These networks can enable unattended monitoring of physical quantities
over large areas on a scale that would be prohibitively expensive to accomplish with
humans. Many uses have been suggested for wireless sensor networks, including habitat
[2] and medical monitoring [3].
Many groups have designed sensor nodes. These include Berkeleys Mica motes [4] and
PicoRadio projects [5], MITs Amps [6], and Rices GNOMES [7], as well as many others.
All of these sensors have similar goals, such as small physical size, low power consumption,
and rich sensing abilities. In addition, the TinyOS project [8] provides a framework for
designing flexible distributed applications for data collection and processing across asensor network.
Many sensor network applications require the collection of data over long periods of
time. Sensor nodes are generally powered with batteries, putting a limit on how small the
node can be made for a given lifetime. Unfortunately, it is unlikely that battery capacities
will increase dramatically in the near future. Historically, battery charge density has
increased by a mere 2% per year over the last 50 years [9]. As an example, a CR2032
lithium coin cell, about the size of a quarter, would provide an average of only 75 W if
used completely over a year.
As an alternative to batteries, sensor nodes can scavenge energy from their envi-
ronment. Ambient light, mechanical vibrations, or even acoustic sources could provide
power to operate a sensor. Research suggests that up to 100 W/cm3 can be obtained
from vibrational sources [10]. A thin-film solar cell may provide 5 mW/cm2 of power
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in bright sunlight, but only about 15 W/cm2 at desk level in office lighting. Unlike
batteries, these ambient sources are often unreliable. A solar-powered node could no
longer operate if a power outage turned off the lights in a building.
Sensor nodes, then, must operate with extremely low power dissipation. However,
consider that a typical commercial radio transceiver requires 10 mW of power in receive
mode and 35 mW while transmitting [11]. Recent research has produced a transceiver
design which needs only 1 mW in its receive mode [12] and 25 mW while transmitting
[13]. Even this is more power than a small sensor node can produce.
A solution to this problem is low-duty-cycle operation, where sensors spend a large
percentage of the time in a low-power sleep mode. Because the power source is often
unreliable, the duty cycle will be unreliable, varying with the amount of power available.
Others have constructed self-powered sensor nodes with low-duty-cycle operation [14].However, existing routing algorithms have problems when operating on such hardware.
Some, such as GEAR [15], include power reserves in the route selection heuristic so
that routes prefer nodes with more power available. Unfortunately, it requires nodes
to constantly listen for transmissions from neighbors, so low-duty-cycle operation is not
possible. Other algorithms, such as LEACH [16], rely on time division multiple access
(TDMA) schemes to acheive low duty cycle operation. In this type of algorithm, a master
node assigns communication time slots to slave nodes, which only turn on their radios
during these time slots. Because self-powered nodes may have unreliable power sources,
however, they cannot be guaranteed to wake up as scheduled.
To deal with these problems, stochastic sensor networks have been proposed [17]. In
such a network, nodes store power while in an inactive mode, then become active until
the stored energy is depleted, at which point they return to the inactive state. This
process is unsynchronized between the sensor nodes, thus forming a stochastic sensor
network. Also, no routing is used. Instead, data is propagated to its destination using
much simpler stochastic flooding. Such a network can be made reliable under certainassumptions about the active node density [17], [18]. Furthermore, high-level protocols
can be layered onto the network to enable rich applications [19]. While simulations have
verified that these networks should work, no real-world testing has taken place. If this
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theory can be demonstrated in real nodes, it would have great advantages for enabling
simple, robust networks of self-powered sensors.
Such testing requires a wireless sensor node with rich power management features that
no existing architectures offer. Therefore, a new sensor architecture has been designed
with extremely low power consumption in mind. This sensor uses solar cells to collect
energy and store it in a large reservoir capacitor. While in the inactive state, the sensor
can check its stored power levels to determine whether to enter the active mode or to
continue storing energy.
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CHAPTER 2
STOCHASTIC SENSOR NETWORK DESIGN
2.1 Introduction
A stochastic sensor network makes certain assumptions about the capabilities of the
nodes. These are reviewed here, along with a network model that determines the condi-
tions for proper network operation. Finally, details of a planned network implementation
are presented.
2.2 Stochastic Sensor Network Properties
For the development of stochastic sensor networks, three important assumptions are
made about the operation of the nodes [19]. First, each node has a sleep/wake cycle
determined by local environmental conditions, which are not known to other nodes. At
any given time, there is a probability, denoted Pa, that a node will be in its active state.
Second, because they will not necessarily always have enough energy to maintain the
contents of volatile memory, the nodes are assumed to be memoryless. Upon entering
the active state, a node may not have any knowledge of the rest of the network or even of
the local environment. Finally, nodes do not necessarily know their locations, in either
absolute or relative terms. This assumption simplifies node design and also allows for
mobile nodes to participate in the network.
Taken together, these assumptions severely limit a sensor network architecture. Sto-chastic wireless sensor networks use a simple design capable of providing robust operation
even with these contraints. In such a network, a collection of unsynchronized nodes
alternate between active and inactive states. While operating in its active state, a node
will monitor its transducers for events, perform calculations, and listen for network traffic.
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When any node receives a message not intended for it, that node stores it in a message
queue. As stored power is about to run out, the active node broadcasts one or all of
the messages in its queue to its neighboring nodes and enters the inactive state. In
the inactive state, the node operates in a low-power sleep mode and collects energy,
periodically waking up to see if it has enough stored power to re-enter the active state.
The design of a simple stochastic sensor network involves only slightly more planning
than tossing nodes down randomly over an area. To ensure that the network performs
somewhat robustly, an average active node density must be maintained. Recent work
has developed a model which can determine this critical density for a given network [18].
The same model has been used here for the design of a test network for the proposed
stochastic sensor platform.
2.3 Network Model
The network consists of Q nodes, each with exactly N neighbors. A node is said
to be a neighbor if it is within the range of the first nodes wireless transceiver. Since
each node is only awake for a fraction of the total time, the probability PA denotes this
fraction of time in the mean.
A discrete-time analysis is used, where one time slots length is the amount of time
it takes to transmit messages to other nodes. This is assumed to be fixed even for
varying numbers of messages. Once a node enters the active state, it remains awake
for K 2 time slots. In the first K 1 time slots of this active period, the node will
listen for incoming packets. If any are received, they are added to a message queue and
rebroadcast in the Kth time slot of the active period. In the next time slot, the node
enters the inactive state. During each subsequent time slot, the node will enter the active
mode with probability PW or stay asleep with probability 1 PW. Provided the nodes
wake up independently, this provides a Poisson model for the active-inactive cycle, and
the distribution of the inactive time is geometric.
Using this model for a steady-state analyis, it has been shown that a quasi-stable
state exists where enough nodes are active to hear and rebroadcast messages to keep the
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messages in circulation indefinitely with high probability. Quasi-stability can occur when
N PA >K
K 1(2.1)
This quasi-stability criterion has been shown to hold in the presence or absence of colli-
sions and with single or multiple packet types circulating [18].
The wake probability PW is intended to ensure that the active-inactive cycle of each
node is asynchronous with respect to the other nodes. In the case where PW = 1, the
active-inactive cycles of all nodes will maintain a fixed phase relationship, and therefore
the awake probabilities of the nodes will not be independent. When PW < 1, nodes
operate asynchronously and can be considered independent.
In actual energy-scavenging nodes, the use of an uncertain inactive period length
models the uncertainty of the time necessary to store enough energy for an active cycle.
Mostly, the uncertainty is due to the different amounts of energy available to each node,
but it is also partly due to component tolerances. Therefore, PW should be chosen such
that the expected value of the awake time is the average time required to store enough
energy for a single active cycle.
Though simulations using this model show encouraging results, some discussion is
necessary about real-world issues of building such a network. It has been demonstrated
that even in controlled conditions, the reliability of radio links of similar nodes falls offrapidly with distance [20]. Neighborhood size is limited by the maximum transmit power,
which is determined by government regulation. Because transmission occurs only during
a small fraction of the active time, transmit power can often be increased with little effect
on the sensor duty cycle. However, once the neighborhood size limit has been reached,
the active node density can only be increased by increasing the duty cycle or the total
node density.
2.4 Test Network Design
Because real sensors will have to operate on fairly low duty cycles, the quasi-stability
criterion requires many nodes per neighborhood for a successful network. During system
prototyping, however, a test network is needed to characterize the performance of a group
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of nodes of a quantity small enough that design modifications can still quickly be made
if needed.
The planned application is a sound-level detector in a hallway. Nodes with omnidi-
rectional microphones will be placed around a hallway near flourescent lights. Initially,
all of the nodes will be placed within transmit range of a constantly powered base station
which will record all messages received. This should allow simple monitoring of stochastic
flooding behavior.
This test network, not yet complete at the time of this writing, will consist of 25 sensor
nodes. Though a stochastic sensor network will typically consist of many more nodes,
this small number was chosen to allow for quick modifications to the nodes. With so few
nodes, however, a high duty cycle must be acheived for quasi-stability to be observed.
After node operation is verified in this limited network, more nodes can be constructedfor testing denser networks.
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CHAPTER 3
SENSOR NODE DESIGN CONSIDERATIONS
3.1 Overview
The design presented here is a solar-powered stochastic sensor node (SSN). At a high
level, such a node consists of a power supply, sensor transducers, wireless communication
hardware, and control logic. Figure 3.1 shows a block diagram of these high-level blocks.
This chapter presents each of these units in terms of its constituent parts. The parts
chosen for this particular design are discussed with suggestions for possible replacements.
3.2 Power Conversion
Scavenging power from the environment and converting it into usable energy proved
to be fairly difficult. The voltage must be converted to a standard logic voltage level,
and the current is often too small to be directly used. Energy must be stored until a
Figure 3.1 Solar stochastic sensor node block diagram.
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Figure 3.2 Conceptual solar cell IV curve.
sufficient amount is available to run the sensor node circuit. Then, the power supply
must convert the stored energy to a usable voltage and current.
3.2.1 Circuit overview
Scavenging power via solar panels proved to be a difficult task. For example, an
inexpensive thin film solar panel produced about 2.5 mW/cm2 in full sun, but only about
15 W/cm2 indoors under flourescent lighting. Also, its operating voltage dropped from
3 V outdoors to around 1 V indoors. Thus, any usable power circuitry must efficiently
store energy with a wide range of input voltages and currents.
A conceptual IV curve for a solar cell is shown in Figure 3.2. At some point on
the curve with voltage Vm and current Im, the solar cell produces maximum power Pm.
Ohms law gives the load resistance necessary to operate at this maximum power point.
Circuits driven by the solar cell should present this resistance to the solar cell so that
power is not wasted. A more detailed discussion of solar cell operation can be found in
Appendix A.
The initial power circuit design was suggested by a solar battery charge circuit [21].
Figure 3.3 shows a simplified version. This circuit uses the capacitor to keep the solar
panel operating at near its maximum power point for high efficiency. A comparator
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Figure 3.3 Solar battery charger circuit.
constantly monitors the capacitor voltage, comparing it to a reference voltage Vref. When
the capacitor voltage reaches Vref, the comparator enables a DC-DC boost converter
that produces the battery charging voltage. Due to hysteresis, the comparator turns off
the boost converter when the capacitor voltage has dropped to some minimum voltage.
Additional circuitry not shown in the figure monitors the battery voltage and adjusts the
DC-DC converter output voltage for proper charging.
The comparator relies on the battery to provide its supply voltage. Since most com-
parators do not guarantee proper operation with an inadequate supply voltage, the circuit
may have strange behavior if the batterys voltage drops too low. For example, if the DC-
DC converter can operate at a lower voltage than the comparator, it might erroneouslyturn on before the comparator is producing a valid output. Therefore, a battery, at least
partially charged, is an essential component of the circuit. If the battery were allowed
to discharge to a voltage below the comparators minimum operating voltage, the circuit
would not necessarily be able to recharge it.
The SSN power supply circuit is conceptually similar to this battery charger. In the
SSN, a comparator enables the DC-DC converter to power the logic when the reservoir
capacitor reaches a voltage near Vm, the maximum power voltage. Instead of using a
rechargeable battery, however, the SSN uses a nonrechargeable lithium coin cell, which
has much higher energy density. Also, instead of using a discrete comparator, the SSN
monitors the capacitor voltage in software using the microcontrollers analog-to-digital
converter (ADC) and a programmable threshold. Because the SSN has full control over
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Figure 3.4 Power supply circuit schematic.
the power supply in software, more exotic power management schemes than simple thresh-
olding could be implemented without changing the hardware.
The addition of a nonrechargeable battery does limit the operational lifetime of the
SSN. Because the circuit was designed for low power consumption, however, a standard
CS2032 coin cell can easily power the circuit in its inactive mode for several years.
3.2.2 Circuit implementation
Figure 3.4 shows the SSN power supply circuit. The boost converter is U3, a Maxim
MAX1675. It creates a higher voltage than its input by switching current on and off
through inductor L1, then filtering the resulting voltage spikes. When used as configured
for the SSN, it boasts efficiency near 90%. The inductor L1 is a Murata LQH4N220,
chosen primarily for its small size, and the capacitor C2 is a Sprague 593D476X0010C2T,
chosen for its low series resistance. Diodes D1D3 are Vishay SD103AW Schottky diodes.
This specific part was selected mainly for its low forward voltage drop.
Connection of the boost converters feedback (FB) pin to the output voltage pin
selects its 3.3-V output mode. When in shutdown mode, which the microcontrollerselects through U3s SHDN pin, the DC-DC converters output voltage is slightly below
the input voltage applied to the inductor connection (LX) pin. Also, the boost converter
has no overvoltage regulation. When not in shutdown mode, if its input voltage is higher
than 3.3 V, the output voltage will follow the input voltage.
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Because changing light levels will drop the solar cell voltage, diode D1 protects it from
capacitor discharge currents. Diodes D2 and D3 select between the DC-DC converter and
battery B1 to power the sensor node logic. When B1, a 3-V lithium coin cell, has a higher
voltage than the boost converter output, diode D3 will be forward biased and D2 reverse
biased, and the battery will power the circuit. Because the DC-DC converters output
voltage of 3.3 V is higher than the batterys, the opposite occurs when it is enabled.
Using this scheme, the circuit can run from the battery in inactive mode, then enable
the boost converter during its active cycle.
3.2.3 Reservoir capacitor selection
The reservoir capacitor serves the dual purpose of storing scavenged energy and allow-
ing the solar panel to run close to its maximum power point. A larger capacitance value
allows more charge to be stored at a given voltage level. This means that the circuit can
be run for longer within a voltage range near Vm, increasing power scavenging efficiency.
A smaller capacitance value, however, allows for a physically smaller and cheaper capac-
itor. Smaller values also decrease the initial charge time to reach the turn-on threshold
voltage. The reservoir capacitor chosen must balance the total size of the sensor against
the power conversion efficiency.
Double layer capacitors, available in values from 0.1 F to 100 F, were initially tested forthe circuit. They are extremely compact and seemed ideal for the application. However,
the high equivalent series resistances (ESR) of these parts meant that a higher turn-on
threshold would be needed to compensate for the voltage drop in the capacitor itself. For
example, the peak load current in a stochastic sensor node is about 20 mA. A double
layer capacitor with an ESR of 30 charged to 2 V will output at most 1.4 V for this
current due to the voltage drop across this equivalent series resistor. Also, ESR increases
throughout the lifetime of the capacitor, so low ESR is even more important for sensors
with long operational lifetimes.
The SSN instead uses aerogel supercapacitors, which are larger than their double
layer equivalents but have much lower ESR. A Cooper Bussman PA-5R0V474 aerogel
supercapacitor rated at 5 V and 0.47 F occupies about 4.7 cm3. Its ESR, measured at
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Figure 3.5 Aerogel, left, and double layer, right, 0.47-F supercapacitors.
1 kHz, is 0.20 . On the other hand, a Panasonic EEC-F5R5U474 electric double layer
capacitor rated at 5.5 V and 0.47 F occupies only about 2.9 cm3. Its ESR, also measured
at 1 kHz, is 30 . Figure 3.5 shows the two capacitors side by side.
3.3 Energy Source
Several sources of ambient energy could be used for the SSN energy source. Vi-
brational energy [10], acoustic energy, and thermal energy could all be used, but none
provides as much energy in the same amount of space as a solar panel. Solar panels
also are available cheaply from standard electronics distributors. These advantages madethem the logical choice for powering the SSN.
3.3.1 Solar panel selection
Several different types of panels were evaluated for relative performance in varying
lighting conditions. Figure 3.6 shows four of these. Two of the panels, (a) and (b), were
thin-film amorphous silicon panels produced by Iowa Thin Film Technologies. The first,
an SP3-37, is rated for operation at 3 V and 22 mA in full sunlight, and it measures1.5 2.5 in. The second, a TX3-25, is rated for operation at 3 V and 25 mA in full
sunlight, and it measures 1 4.5 in. The third, shown in (c), was a generic silicon solar
module, probably monocrystalline, purchased from Edumund Scientifics. It measures
1 1.8 in and is rated for operation at 3 V and 20 mA in full sunlight. Finally, a
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(a) (b) (c) (d)
Figure 3.6 Four solar panels: (a) 3-V, 22-mA module; (b) 3-V, 25-mA module; (c) 3-V,20-mA module; and (d) CuInSe2 module.
laboratory sample copper indium diselenide (CuInSe2) panel, measuring 4 4 in, was
tested. Its expected operating voltage and current were not known.
In an outdoor setting with bright sunlight, even small solar panels can provide the
necessary voltage and current to operate a sensor node. In indoor lighting, however,
power output drops to a fraction of the outdoor value. Both the operating current and
voltage fall to nearly unusable levels.
A particularly troublesome problem was that, in indoor lighting, supposedly identicalpanels produced very different output voltages. Five of the SP3-37 and TX3-25 panels and
three of the generic modules were tested in indoor fluorescent light at three levels. The
results are shown in Table 3.1. While the short-circuit current remained approximately
equal for different samples of each type of panel, the open-circuit voltage varied greatly
between otherwise identical thin-film panels. The manufacturer of the thin-film cells
indicated that this was due to parasitic effects within the panels. Some cells in the third
generic solar panel were cracked, causing a lower output voltage than expected. Because
of these problems, the panels used should each be validated for output voltage with the
lighting in which they will be used.
Another useful quantity is the power production per unit area for each panel. The
values for the SP3-37, TX3-25, and generic modules were averaged over all the panels
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Table 3.1 Low-light performance for identically rated solar panels.SP3-37
Panel High light Medium light Low lightVOC (V) ISC (A) VOC (V) ISC (A) VOC (V) ISC (A)
1 2.74 152 2.24 94 1.79 592 1.93 155 1.53 96 1.21 613 1.74 150 1.28 93 0.94 594 1.25 149 0.88 92 0.65 575 1.03 145 0.74 89 0.54 57
TX3-25
1 2.31 168 1.81 103 1.40 652 2.06 167 1.63 100 1.31 683 1.90 182 1.62 116 1.32 734 1.60 161 1.16 100 0.78 625 1.03 164 0.64 101 0.45 69
Generic 3 V, 20 mA
1 1.23 38 1.09 25 0.88 142 1.20 37 1.01 23 0.88 153 0.90 38 0.74 23 0.59 15
tested, while only one CuInSe2 panel was tested. As before, power production was
measured inside the lab under flourescent lighting at three different intensity levels. Table
3.2 shows the results.
While the CuInSe2 panel performs the best, this may be because it was a high-
quality laboratory sample. Unfortunately, no low volume supplier could be found for
these panels. Because the thin-film solar cells could be obtained for half the price of the
generic monocrystalline modules while producing much more power indoors, these were
selected for the SSN. The SP3-37 was chosen because it fit onto one side of the sensor
node circuit board.
The problem of low-light voltage drops could be solved by using a panel with ahigher open-circuit voltage in full light. However, since the radio module will not operate
at a supply voltage higher than 4 V, the power supply must ensure that its output
voltage cannot go any higher. This might be accomplished with a buck-boost converter
or integrated boost converter and linear regulator such as the Maxim MAX1672.
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Table 3.2 Solar panel power production per unit area.Panel High light
Voltage (V) Current (A) Power/area (W/cm2)
Generic 1.13 37.9 10.7SP3-37 1.74 150.2 10.8TX3-25 1.78 168 10.3CuInSe2 2.83 297 16.2
Panel Medium lightVoltage (V) Current (A) Power/area (W/cm2)
Generic 0.95 23.7 5.6SP3-37 1.34 95.5 5.1TX3-25 1.37 103.9 4.9CuInSe2 2.55 180.9 8.9
Panel Low lightVoltage (V) Current (A) Power/area (W/cm2)
Generic 0.78 14.8 2.9SP3-37 1.03 58.6 2.5TX3-25 1.06 66.5 2.4CuInSe2 2.26 118.9 5.2
3.3.2 Alternate power sources
The SSN power supply is not limited to solar panels. Power sources delivering between1 and 4 V at low currents can be connected in place of the solar panel. Depending on
the power source, the turn-on threshold voltage and reservoir capacitor size may need to
be adjusted. A battery could also be used if the large reservoir capacitor were removed.
3.4 Transducers
The microcontroller chosen for the SSN has a built-in ADC and several standard
digital interfaces. Using these, it could conceivably support many different types oftransducers. Because the prototype was intended to be used for monitoring activity in
a building, a sound-level transducer was chosen for the test sensor. The SSN is solar
powered, so it can also use the solar panel to measure the relative light level.
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Figure 3.7 Sound-level detector.
3.4.1 Sound-level transducer
The SSN includes a simple sound-level sensor for testing. This circuit, shown in Figure
3.7, uses an electret microphone and a high-gain operational amplifier. The microcon-
troller samples the amplified output with its integrated ADC. The amplifier chosen, a
Texas Instruments TLV2460, uses only 500 A of current when enabled.
Resistors R9 and R4 configure the amplifier for a gain of 1000. Because the gain-
bandwidth product of the TLV2460 is specified at 5.2 MHz for a supply voltage of 3 V,
this places the 3-dB frequency of the amplifier at 5.2 kHz. Frequencies above this will
be significantly attenuated. Because this depends on the low-pass characteristic of the
amplifier which may vary from chip to chip, it is not guaranteed to be a reliable antialias-
ing filter. If it is desired to perform digital signal processing on a sampled waveform, an
antialiasing filter should be explicitly designed for this purpose. This simple high-gain
amplifier design is intended to be used primarily for detecting sound level.
3.4.2 Light level detection
The solar panel output can be used to roughly determine the light level. Since the
short circuit current is roughly proportional to the brightness of the incident light, the
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microcontroller can monitor the rate of change of the reservoir capacitor voltage to de-
termine the relative amount of light present. The solar panel output current depends on
a variety of factors such as the spectral composition of the light, the panel voltage, and
the ambient temperature. Therefore, this method will only be accurate for measuring
relative light levels when all sensors are in similar light at the same temperature.
3.4.3 Other sensors
The SSN provides support for additional sensors via an expansion header. The use
of this connector is discussed in detail in Chapter 4. Typically sensors that might be
connected this way include temperature, humidity, acceleration, and many other types.
3.5 Wireless Communication
Recent developments in low-power radio communications have produced several com-
peting wireless communications standards. For example, 802.11a/b/g wireless networks
have become fairly common. They provide high data rates of up to 54 Mb/s and ranges
up to 100 m. Unfortunately, chipsets supporting this standard also have fairly high power
requirements. Other alternatives, such as Bluetooth and ZigBee, use much less power
than 802.11a/b/g but still require more than the SSN is expected to provide. For ex-
ample, one ZigBee-ready chipset, the EM2420, uses about 30 mW when transmitting or
receiving [22]. The SSN required a radio designed for much lower power consumption
than any of these could offer.
3.5.1 Radio module
Each sensor node includes a radio module for communicating with other nodes. The
radio is typically the largest power user in the system, so power trade-offs must be con-
sidered when choosing a transceiver. For example, the radio module will have some static
power consumption, which is independent of the bandwidth. An increase in bandwidth
will decrease the time to transmit a message. If the radio has a low-power sleep mode,
shorter message transmit times allow the radio to spend more time asleep, reducing static
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power requirements. In the SSN, the microcontroller on the receiver must constantly run
at a higher speed than the radio bit period to perform baseband data decoding. Because
the receiver will spend most of its time performing this task, reducing the power used in
this state may be more beneficial than saving transmit power. Also, an increased bitrate
lowers the radio range for a given transmit power.
The radio used in the SSN is an RF Monolithics TR1004 914-MHz transceiver, which
is pin compatible with the 916.5-MHz TR1000 module. This was chosen primarily for its
low power consumption, which is typically about 10 mW in receive mode and 40 mW in
transmit mode. Unfortunately, it provides only a bit-level interface without any timing
information, so clock recovery must be performed by a microcontroller instead. Other
radio modules which provide higher-level interfaces, such as the Chipcon CC1000, typi-
cally use more power than the microcontroller and TR1004 combined. This transceiveralso has a low power sleep mode, consuming only about 2 W of power. Because it
can enter and exit this mode in a fraction of a bit period, power can possibly be saved
by putting the chip to sleep between received bits during start symbol detection, but
experimentation has shown that this tends to increase the error rate.
The SSN operates the transceiver at 19 200 Bd in on-off keying (OOK) mode. Though
the transceiver can operate at differnent bitrates and in amplitude shift keying (ASK)
mode, passive components in the circuit were selected specificially for Manchester-encoded
data at 19 200 Bd. Operation at other baud rates or in the ASK mode is not possible
without modifying the circuit. The radio circuit, adapted from the TR1004 data sheet
[11], is shown in Figure 3.8.
Though relatively slow, 19 200 Bd was chosen primarily to make it simple for the
microcontroller to perform start-symbol detection. At the start of each data packet, the
transmitting node sends a training preamble of alternating zeros and ones to calibrate
the DC blocking capacitor, followed by a 20-bit start symbol. While it is waiting for this
start symbol, the receiving node must constantly sample the incoming data so that itcan synchronize its serial port with the transmitter. A slower bitrate allows the receiver
to operate at a lower clock speed, saving power.
Transmit power can be decreased by replacing RTXM with a larger resistance. More
information about specific values is available in the TR1004 data sheet.
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Figure 3.8 Radio transceiver circuit.
3.5.2 Antenna considerations
Antenna selection is fairly important for radio performance. A wire cut to a length of
one quarter wavelength, known as a whip, placed perpendicularly over a ground plane,
provides acceptable performance at a low cost. Such antennas are omnidirectional in the
plane perpendicular to the antenna wire. Attenuation will occur, however, out of this
plane, including a null directly above the antenna. This makes quarter-wave antennas
appropriate only when all of the sensors are close to coplanar. Antenna polarization will
also affect transceiver performance. If nodes with whip antennas are oriented such that
the antennas are perpendicular to each other, the polarizations will not match and the
received signal will be heavily attenuated.
At 914 MHz, one quarter wavelength is approximately 8.2 cm. If a smaller antenna is
required, compact helical coil and chip antennas are available, but these generally have
lower gain than the quarter-wave antennas and can be more sensitive to ground-plane
design. Antennas can also be etched directly onto the edge of a circuit board, but these
require careful design and testing with a network analyzer [23].
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A small helical antenna, the Linx Technologies JJB-RA, was selected for the SSN
because of its small size. If desired, it could easily be replaced with a quarter-wave whip.
3.6 Control Logic
3.6.1 Microcontroller
A microcontroller controls the operation of the entire sensor node. Among its many
tasks, it must be programmed to wake the rest of the sensors circuits when it decides
to enter the active mode. It must take readings from all available transducers and
decide whether it is necessary to send a message with these readings in it. Also, the
microcontroller needs to monitor incoming messages and handle them as appropriate.
A PIC18LF4320 microcontroller was chosen to control the SSN. Though it only has
4096 words of program ROM and 512 bytes of RAM, the simplicity of the stochastic
sensor node design means that this is far more than sufficient. One of its key features
is an internal 8-MHz oscillator with a programmable divider. Besides reducing external
parts requirements, this allows the microcontroller to scale its clock frequency to match
the current task, lowering power usage. Transducers can be connected directly to the
internal 10-bit ADC. A standard PIC18F4320 does not have guaranteed operation when
the supply voltage is less than 4.2 V, so a slightly more expensive PIC18LF4320 was
used.
The PIC18LF4320 could easily be replaced with other microcontrollers if they have
an internal ADC and comparable speed with a 3 V power supply.
3.7 Timekeeping
The microcontroller needs a way to determine relative time so it can label its messages
with time information. This task is given to the real-time clock module.The SSN uses an Epson RTC-4574 real-time clock (RTC) module with a built-in
32.768-kHz crystal oscillator. Besides keeping time, the RTC also has a programmable
interval interrupt that can be used to wake the microcontroller instead of using its less
flexible watchdog timer. Also, the RTC can be programmed to output square waves at a
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given frequency, and this can be used to calibrate the microcontrollers internal oscillator.
Finally, the quiescent current used by this RTC is typically less than 1 A.
This part could easily be replaced with another low-power RTC. Also, a real-time
clock could be implemented in software in the microcontroller, deriving its frequency
either from an external crystal oscillator or the less accurate internal oscillator. The
power consumption for a software RTC would be roughly equivalent to the hardware
version. The software-based approach was not used here so the SSN software could be
kept simpler.
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CHAPTER 4
SENSOR NODE OPERATION
4.1 Introduction
While the previous chapter focused on the design issues considered while building
the SSN, this chapter gives a detailed look at the nodes operation. First, the hardware
platform as a whole is discussed. This is followed by an explanation of the SSN software.
Finally, a circuit for debugging the nodes is described.
4.2 Hardware
4.2.1 Hardware overview
Figure 4.1 shows the full schematic for the SSN. The microcontroller, U1, controls
the rest of the circuit. The microcontrollers internal oscillator, which operates at several
frequencies from 31.25 kHz to 8 MHz, provides the clock signal.
4.2.2 Expansion connector
The nodes provide a 25-pin expansion connector for connecting additional sensor
boards. Connected to unused microcontroller pins, it provides up to 13 digital I/O chan-
nels, 3 of which can also be used as analog input channels. Two of the pins can directly
cause interrupts on changes. Both interintegrated circuit (I2
C) and serial peripheral inter-face (SPI) communications channels are available, though not simulateously. Pulse width
modulated (PWM) inputs and outputs can be handled with two capture/compare/PWM
(CCP) pins.
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Figure4
.1
Stochasticsensornodeschematic.
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Figure 4.2 Expansion header pinout.
Figure 4.2 shows the pinout of the expansion connector. The pin names correspond
to those in the PIC18LF4320 data sheet [24].
The PIC, as well as most other microcontrollers, has I/O pins designed for high
current drive. A single pin can in most cases source or sink 25 mA. This means that
the microcontroller can directly power sensors and other circuitry with a digital output
set high, then turn them off by driving the pin low. Using this technique, even circuits
without sleep modes can be operated at low duty cycles. However, some chips have
long startup times that make this technique less useful, since the microcontroller must
power the chip for milliseconds before measurements can be taken. Such chips should be
avoided unless they provide a low-power sleep mode with a much faster startup time.
The DF9-25P-1V connector used provides only 7 mm of clearance between the two cir-cuit boards. To avoid problems, all parts should be mounted on the top of the expansion
board.
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Figure 4.3 In-circuit serial programming header pinout.
4.2.3 Reprogramming the nodes
A 10-pin programming header, J1 in the schematic, is provided for in-circuit pro-
gramming of the PIC microcontroller. When the sensor is operational, shunts are placed
across the pins to connect the PIC to the rest of the circuit. For programming, the shunts
are removed and a programming cable is attached. Figure 4.3 shows the pinout for this
connector, chosen to correspond to the in-circuit programming cable of the EPIC Plus
PIC programmer made by microEngineering Labs. With an appropriate adapter cable,
it should be compatible with other programmers which support in-circuit programming.
4.2.4 Prototype circuit boards
Several SSN prototypes have been built. Figure 4.4 shows the front and back of an
SSN. Each is 2.5 2.5 in, though future iterations could be made much smaller with
some optimization. An SP3-37 thin-film solar panel can be affixed to the back side of
the board. Each costs about $75 when purchased in quantities of 25.
4.3 Software
The initial sensor node software has been written entirely in assembly language. This
design decision was made due to the authors familiarity with PIC assembly as well as
the need for low overhead in many code sections. The use of tightly optimized assembly
language in critical loops allows for the use of low operating frequencies, saving power.
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(a) (b)
Figure 4.4 Stochastic sensor node prototype: (a) front side, and (b) rear side.
The code is also extremely compacta recent build used less than 400 words of the
microcontrollers program memory. Several vendors sell C compilers for the Microchip
PIC platform, so it would be entirely possible to rewrite noncritical sections of the code
in C for future maintainability.
The program flow is straightforward. Figure 4.5 shows a flowchart of its operation.
To initialize, the microcontroller turns off all unneccessary peripherals to save power. It
also puts all unused I/O pins into output mode for additional power savings. After ini-
tialization, the sensor puts itself into the inactive mode to charge the reservoir capacitor.This is accomplished by turning off the internal oscillator and programming the real-time
clock to periodically wake the processor. When awoken, the microcontroller checks the
capacitor voltage to determine whether it has enough power to enter the active mode.
If it does, it can either wake up into active mode unconditionally or based on the wake
probability PW. Probabilistic wake-up is useful for ensuring independence between nodes
when they are powered from a constant power source such as batteries.
Once in the active mode, it enables the microphone and listens for acoustic events.
If one is found, it creates a new message packet and stores it in the message buffer. It
then waits in receive mode for incoming packets for a set time period. Packets addressed
to it are handled, and all other packets are queued for rebroadcast. Finally, it sends all
packets in the message queue and returns to the inactive mode to recharge.
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Figure 4.5 Software operation flowchart.
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The microcontroller uses its hardware serial port to send and receive data through
the radio transceiver. Each outgoing byte is split into two 4-bit nybbles which are then
Manchester encoded and sent via the serial port. The encoding provides DC balance,
which is required for proper transceiver operation. Because the serial port hardware adds
a start and stop bit to every byte sent, this means that every 8 bits of information are
encoded as 20 bits for transmission.
4.4 Design Evaluation
Preliminary testing with the SSN prototype has shown encouraging results. The
average power consumption of a node was measured as it performed several common
tasks. The experimental setup consisted of simply a multimeter connected in series with
the SSN. A variable power supply, adjusted to 3.3 V, was connected directly to the VCC
rail. The tests were performed on a node without a real-time clock installed, but its
negligible power consumption should not have much of an effect.
A program was written to cycle between several common circuit tasks when a button
was pressed. The first, sleep mode, put the microcontroller and radio transceiver into
their low-power sleep modes. This mode consumed only 0.8 A of current, for a total
power consumption of 2.6 W. Second, the current consumption of analog-to-digital
conversions was tested. The microcontroller enabled its ADC and constantly sampled
from it while running at 31.25 kHz. This required 120 A of current, for a total power
consumption of 400 W. Next, receive mode was tested. In this mode, the microcontroller
put the radio transceiver into its receive mode, then sets its own oscillator to 1 MHz
and performed a start-symbol detection loop. This mode consumed 3.3 mA of current,
for a total power consumption of 10.9 mW. Finally, transmission mode was tested. To
transmit, the microcontroller placed the radio transceiver into OOK transmit mode, then
enabled its onboard serial port and transmitted DC-balanced data. While transmitting,
the microcontroller operated at a clock speed of 4 MHz. This was tested for two transmit
power levels. The first, using an 8.2-k resistor for RTXM, required 4.2 mA of current,
for a total power consumption of 13.9 mW. The second, using a 4.7-k resistor for RTXM,
required 5.9 mA of current, for a total power consumption of 19.5 mW.
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These numbers align closely with expectations. The sleep mode currents are negligi-
ble, and will allow operation from a lithium coin cell battery for years. Analog-to-digital
conversion requires much more current, but still not very much. Since only about 20 s
are required to capture a sample, this power consumption is not a large problem. Trans-
mit and receive mode currents are closely aligned with the numbers in the TR1004 data
sheet [11]. Though the measured transmit current is about half the typical value in the
data sheet, this is easily explained. Because DC-balanced data are being transmitted,
the radio transmits nothing exactly half of the time, leaving an average current of half
the maximum.
These numbers give some idea of the expected duty cycle of the nodes. Transmitting a
20-byte packet of information (Manchester encoded with start and stop bits at 19 200 Bd)
would require 20.8 ms. If a node listens for nine times that length of time, or 188 ms,the total energy used during the active period is
(20.8 ms)(19.5 mW) + (188 ms)(10.9 mW) = 2460 J (4.1)
If the sensor is to have a duty cycle of 5%, for a total period of 4.18 s, the solar panel
must provide 589 W of power. The actual number will be slightly higher since the
microcontroller spends a small amount of energy checking sensors at the beginning of the
active period and handling received packets.Other informal testing has been performed with prototype sensor nodes built on
solderless breadboards. A small network of three prototype nodes was developed, with
one transmitter, one relay, and one receiver node. The transmitter was placed near
a light and programmed to wake up from its inactive mode at a threshold capacitor
voltage in order to send a single packet. The packet contained a packet count which was
incremented every time the transmitter node entered the active mode. The relay and
receiver were both powered from laboratory power supplies and remained in the active
mode. When it received a message, the relay would resend the message to the receiver
node. This testing verified that this design had the functionality to be a stochastic sensor
node. Testing on the actual SSN hardware was not complete at the time of this writing.
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Figure 4.6 Schematic of debugging circuit.
4.5 Base Station and Debugging Circuit
In the interests of power consumption and size, limited debugging capabilities are
built onto the SSN circuit board. Jumpers JP6 and JP7, when not shunted, are used to
test the battery and boost-converter output currents, respectively. The radio must be
tested by programming the microcontroller with a test program and monitoring received
packets on a base station. A reset switch can be added via the reprogramming header
J1 by connecting pins 2 and 10 through a normally open momentary switch.
For more thorough testing, or for conversion of a regular node into a base station,
a debugging circuit can be connected to the expansion header. This circuit provides
a standard RS-232 serial interface for connection to a PC. It also has several switches
and LEDs useful for modifying and monitoring the processor state. Figure 4.6 shows aschematic of the debugging circuit.
A microcontroller, U1, is connected to an external computer through the RS-232
serial port, CONN2, and to the SSNs microcontroller through a standard I2C bus. The
program on the microcontroller simply translates data between the two busses so the
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SSN can relay information to a PC. Switch S1 resets the debug microcontroller, while S2
and S3 are connected to input ports on the SSN microcontroller. These particular input
lines can be configured to generate interrupts. Diodes D1D8 are LEDs which can be
programmed to display status information.
The debug board provides its own independent power source from a 9-V wall DC
power supply. A standard 7805 voltage regulator, U5, generates the 5 V needed for the
logic, while U4, a 3.3-V voltage regulator, generates the voltage necessary for interfacing
with the SSN. An I2C level shifter uses two NMOS transistors, Q1 and Q2, to convert the
bidirectional logic lines between the two different logic voltages. These specific NMOS
transistors were chosen for their low threshold voltages. Jumper J1, when connected, al-
lows the SSN to be powered from the debug board. When this jumper is left unconnected,
the debug board can be used to verify energy scavenging operation.
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CHAPTER 5
CONCLUSIONS
5.1 Conclusion
In the absence of plentiful or reliable power, stochastic wireless sensor networks offer a
viable alternative to routed networks. The ability to support self-powered nodes provides
great advantages where nodes cannot easily be serviced. Stochastic sensor nodes can be
built relatively cheaply using off-the-shelf parts. Existing electronics are power-efficient
enough to support the use of low-quality commodity solar cells. The software to control
the sensor nodes is small and simple enough to fit into an inexpensive microcontroller
with much room to spare.
Many applications could use this technology. Solar-powered sensors could be deployed
in outdoor environments where it would be difficult or impossible to change batteries
but long-term operation is required. Using stochastic sensor network design techniqueswould allow robust network operation even in situations where very little ambient energy
is available for scavenging.
5.2 Future Work
While the stochastic sensor node works, much more can be done. The current design
is large and expensive. Software functionality is still very basic. The solar panels are far
too large and inefficient.Future design iterations could easily shrink the sensor to half its current size or less.
Because the nodes were assembled by hand, many parts were chosen to be easily soldered,
making them take up much more space than otherwise necessary. The microcontroller was
chosen to make development easier. A smaller, less capable chip, however, could easily be
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substituted. The circuit board layout is suboptimal, and great size improvement could
be had simply by optimizing this better.
The software needs much improvement. As of the time of this writing, it barely
provides basic packet forwarding abilities. While the node is unsuited to relatively heavy-
weight sensor operating systems such as TinyOS [8], a richer development environment
could facilitate application design.
The solar panels selected, while adequate for the large prototype, should be replaced
with smaller monocrystalline silicon panels. These provide higher efficiencies than the
thin film panels chosen for the SSN. However, they are difficult to obtain cut to size
in small quantities. Alternatively, other power sources, such as vibrational or thermal
energy, may be utilized.
Beyond these suggestions, the sensor could be more radically redesigned as new hard-ware becomes available. Low-power processors are being developed specifically for use
in sensor networks, significantly reducing the energy required to execute an instruction
[25]. As new radio technologies become commercially available, these can also be incor-
porated into the design. Alternatively, a low power, low overhead radio could be designed
specifically for this type of node.
Another interesting topic is the issue of network sensing coverage and reliability.
Because nodes are only on some percentage of the time, it may be possible to bound
the probability of sensing an event within some neighborhood based on the awake sensor
density. Work focused on insuring sensing coverage in networks of unreliable sensor
nodes [26] seems directly applicable to the stochastic network. Network reliability could
possibly be characterized using such a method.
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APPENDIX A
SOLAR CELL DISCUSSION
Understanding how solar cells work is important for designing a sensor node which
relies on them for power. This appendix summarizes solar-cell operation and applies it
to the SSN power-supply design.
Solar cells utilize the phenomenon of optical carrier generation at a semiconduc-
tor p-n junction [27]. Photons with energy greater than the band gap energy generate
electron-hole pairs. Some of these diffuse across the junction and create a net current
Iph proportional to the junction area, electron and hole diffusion lengths, and the optical
generation rate. This current flows from the p-side to the n-side, opposite of the normal
diode current ID which is also present. From the diode equation
ID = IS
eqVDkT 1
(A.1)
where IS is the saturation current, q is the charge of an electron, k is the Boltzmann
constant, T is the junction temperature, and VD is the junction voltage. Thus, the total
current through the solar panel is
I = ID Iph (A.2)
In the SSN, a reservoir capacitor with capacitance C is connected across the output
of the solar cell. Including this capacitor and the series resistance of the leads, thisproduces the equivalent circuit of Figure A.1. Ignoring the capacitor, when the outputs
are connected together, the short-circuit current is approximately Iph. A little algebra
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Figure A.1 Solar cell equivalent circuit.
shows that the open-circuit voltage VOC is
VOC =kT
qIph
IS + 1
(A.3)
If the voltage across the capacitor is VC and the current through it is I, the charging
characteristic of the circuit can be determined. While it is difficult to solve for VC, some
insight can still be obtained. Summing the currents produces
ID = Iph I (A.4)
Substituting from Equation (A.1) produces
IS
eqVDkT 1
= Iph I (A.5)
Also, using the equation for capacitor current,
I = CdVC
dt(A.6)
Combining these two equations and rearranging produces
dVC
dt=
1
C
Iph IS
eqVDkT 1
(A.7)
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Noting that
VC = VD IRS (A.8)
Substituting for I from Equation (A.5) and rearranging gives
VC = VD RS
IS
eqVDkT 1
Iph
(A.9)
Differentiating both sides with respect to time,
dVC
dt=
dVD
dt
q
kTRSISe
qVDkT
dVC
dt(A.10)
Simplifying this givesdVC
dt=
dVD
dt1
q
kTRSISe
qVDkT (A.11)
Finally, combining with Equation (A.7) and rearranging gives
dVD
dt=
Iph IS
eqVDkT 1
C
1 q
kTRSISe
qVDkT
(A.12)
Finally, when ID Iph, this can be approximated as
dVDdt
= IphC
(A.13)
Since VD VC when RS is small, this shows a linear charging characteristic for the
capacitor at voltages below the diode turnon voltage. As the diode turns on, the voltage
on the capacitor suddenly begins increasing much more slowly since much of the photo
current is being shunted through the diode.
This is useful because parasitic effects in the solar panel, not modeled here, may
decrease the open-circuit voltage of the panel in low light. Because of the extremely
linear charging characteristic which abruptly flattens as the diode turns on, the sensor can
detect when it has approached the open-circuit voltage and adjust its turn-on threshold
accordingly. This allows the sensor to operate closer to the maximum power point of the
solar cell in any light condition.
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