Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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21-92 Mechatronic Systems, Sensors, and Actuators

The following magnitudes are differentiated (the subscripts 1 and 2 refer, respectively, to the rear 1

and front 2 chambers of the pistons):

A piston thrust section

disturbance of force acting on the piston rod

G mass flow rate of air entering the chamber

M mass of the translating parts of the piston

n air polytropic coefficient

P cylinder chamber pressure

initial cylinder chamber pressure

amb

ambient pressure

R air constant

initial cylinder chamber air temperature

x rod position measured starting from x

piston half stroke

dead band

coefficient of viscous friction

The continuity and equilibrium equations are given by:

(21.58)

(21.59)

(21.60)

The flow proportional valve V

is modeled as a variable section pneumatic resistance. The equations

used for calculating mass flow rate G through a pneumatic resistance, characterized by a conductance C

and by a critical ration b, in accordance with ISO 6358, which connects two environments A and B, with

respective pressures of P

and P

, taken to be positive in the A → B direction, are

(21.61)

(21.62)

(21.63)

(21.64)

--------

nRT

x++()P

()

1 n–()/ n

-------------------------------------------------------------------------

x++()

--------------------------------

------

–=

--------

nRT

x–+()P

()

1 n–()/n

------------------------------------------------------------------------

− x+()

---------------------------------

------

--------

amb

–()A

amb

–()A

dx/dt–––

---------------------------------------------------------------------------------------------------------

sonic flow: G

C for 0

-----

b≤<=

subsonic flow: G

C 1

b–

1 b–

-----------------------

– for b

-----

1≤<=

sonic flow: G

–

C for 0

-----

b≤<=

subsonic flow: G

–

C 1

b–

1 b–

-----------------------

– for b

-----

1≤<=

9258_C021_Sect002-005.fm Page 92 Wednesday, October 10, 2007 7:10 PM

Actuators 21-93

Hypothesizing a bipolar reference signal, it can be assumed that the range V

ref

> 0 corresponds to the

supply–user connection, while the field V

ref

< 0 corresponds to the user–discharge connection. The

appropriate equation of flow above must be rewritten in the same way.

Calculation of the conductance of the flow proportional valve is made considering the static and

dynamic link between the reference voltage V

ref

and the opening of the passage aperture A

in accordance

with modeling of the second order of the type:

(21.65)

where

is the damping factor,

is the valve’s natural frequency, and K

is its area static gain.

Assuming a static relation of the linear type between the opening A

and the conductance C, as an

initial approximation, we get

(21.66)

where K

is the flow static gain of the valve, function of the maximum conductance C

max

, and of the

maximum value of the reference voltage V

ref max

(21.67)

The complete dynamic relation between reference voltage and conductance is, therefore,

(21.68)

The nonlinear model of the pneumatic servosystem with the position reference x

set

and the force

disturbance F

as inputs, is made up of a nonlinear system of nine equations, of order eight overall, of

the type:

a) C

= C

ref 1

, t) order 2 conductance of valve V

(see (21.68))

b) C

= C

ref 2

, t) order 2 flow rate of valve V

(see (21.68))

c) G

= G

, P

) order 0 flow rate of valve V

(see (21.61)–(21.64))

d) G

= G

, P

) order 0 flow rate of valve V

(see (21.61)–(21.64))

e) G

= G

, x, ) order 1 continuity chamber 1 (see (21.58))

f) G

= G

, x, ) order 1 continuity chamber 2 (see (21.59))

g) = (F

, P

, ) order 2 piston equilibrium (see (21.60))

h) V

ref 1

= V

ref 1

set

, x

ret

) order 0 V

valve control

i) V

ref 2

= V

ref 2

set

, x

ret

) order 0 V

valve control

If we want to carry out a linear analysis, it can be assumed that the equations a), b), g), h), i) are already

written in linear form.

As far as the flow rates of valves c) and d) are concerned, it is hypothesized that the flow rate for each

of them is subsonic in feed, with V

ref

> 0, and sonic in discharge, with V

ref

< 0. This means that for valve

, for example, the pressure P

must be within the range bP

< P

≤ P

in feed and in the range P

≥ P

amb

-----------

ζσ

---------

++ K

ref

== =

max

ref max

---------------

---------

ζσ

-------

C++ K

ref

··

9258_C021_Sect002-005.fm Page 93 Wednesday, October 10, 2007 7:10 PM

21-94 Mechatronic Systems, Sensors, and Actuators

in discharge. This hypothesis is physically acceptable; hypothesizing b = 0.3, P

= 10 bar, P

amb

= 1 bar, we

get that P

can vary between 3.33 bar and 10 bar. It is the same for P

Linearizing the subsonic feed flow rate curve with a secant passing through the points P

= P

, G

= 0

and P

= P

, G

= G

1 sonic

, of angular coefficient K

, we get

(21.69)

where

(21.70)

(21.71)

In the neighborhood P

= P

and C

= C

= 0 (the subscript r indicates of reference), we get

(21.72)

Equation 21.72 is valid for V

ref1

> 0, to which C

> 0 corresponds analytically.

The flow rate discharge is expressed by

(21.73)

which in the neighborhood P

= P

becomes

(21.74)

Equation 21.74 is valid for V

ref1

< 0, to which C

< 0 corresponds analytically.

Calculating a mean of slopes K

and K

we get a mean slope K

mean

given by

(21.75)

The linearized flow rate as a function of C

therefore becomes

(21.76)

∗

–()=

1sonic

∗

–

--------------------

1 b

∗

–()

-----------------------

1 b

∗

–

-------------

== =

–()

1 b

∗

–()

--------------------------

–()

1 b

∗

–()

----------------------------

mean

---------------------

∗

–()

21 b

∗

–()

---------------------------------

∗

–()

21 b

∗

–()

---------------------------------

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Actuators 21-95

In the same way for the valve V

we get

(21.77)

The continuity equations of the mass in the piston chambers e) and f ), linearized in the reference

neighborhood defined by

become

(21.78)

(21.79)

The block diagram of the linearized model is shown in Figure 21.124.

By applying the Laplace transforms of the system of linearized equations, assuming identical valves,

we get:

(21.80)

where C.I. indicates the initial conditions, K

OLV

is the static gain in speed, K

OLF

is the gain of the force

disturbance,

and

are, respectively, the actuator’s natural frequency and the damping factor, and G

is the compensator law.

This result is shown in the block diagram in Figure 21.125. Figure 21.126, on the other hand, shows

the closed loop block diagram with position feedback. Obvious similarities can be seen when this plan

is compared with that for a hydraulic servosystem.

FIGURE 21.124 Block diagram of the linearized model of a pneumatic servosystem with position control.

SET

RET

–

_______________

__________

_______________

)

–

2 1 –

__________

)

–

2(1 –

)

_____

amb

– A

)

–

_____

)

_______

–

_______

– x

)

–

xx x

–

+ 2

()

–

∗

–()

21 b

∗

–()

---------------------------------

, P

,== =

0 P

, P

0== == ==

0, n 1== =

-------------

---------------

−

-------------

–

---------------

ζσ

++()

-----------------------------------------

++()

---------------------------------------------

OLV

++()

---------------------------------------------

OLF

C.I.+–=

9258_C021_Sect002-005.fm Page 95 Wednesday, October 10, 2007 7:10 PM

21-96 Mechatronic Systems, Sensors, and Actuators

In particular, hypothesizing that:

= P

with

∈ 0.6 – 0.9

= A

= A double ended actuator

n = 1 isothermal transformation

we can express the significant parameters of the pneumatic servosystem:

(21.81)

(21.82)

(21.83)

(21.84)

On the basis of the design specifications, it is possible to choose the size and characteristics of the

servosystem components, operating first on the linearized model, and then checking the complete

effectiveness of the choice made with a complete nonlinear system model.

References

Andersen, B. W., The Analysis and Design of Pneumatic Systems, Wiley, New York, 1967.

Bouteille, D., Belforte, G., Automazione Flessibile, Elettropneumatica e Pneumatica, Tec niche Nuove,

Milano, 1987.

FIGURE 21.125 Block diagram of the open loop model.

FIGURE 21.126 Block diagram of the closed loop model.

OLV

–

OLF

+ 2

s +

ζσ

+ 2

s +

ζ σ

RET

OLK

OLF

–

SET

+ 2

ζσ

–

+ 2

ζ σ

OLV

-------------

1 b

∗

–()

------------------

---

∗

–()

1 b

∗

–()

------------------------

OLF

1 x

()

–[]

-------------------------------------

m 1 x

()

–[]

------------------------------------------=

1 x

()

–[]

-------------------------------------=

9258_C021_Sect002-005.fm Page 96 Wednesday, October 10, 2007 7:10 PM

Actuators 21-97

Belforte, G., D’ Alfio, N., Applicazioni e Prove Dell’automazione a Fluido, Levrotto & Bella, Torino, 1997.

Belforte, G., Manuello Bertetto, A., Mazza, L., Pneumatica: Corso Completo, Tecniche Nuove, Milano,

1998.

Blackburn, J. F., Reethof, G., Shearer, J. L., Fluid Power Control, MIT Press, Cambridge, 1960.

Dransfield, P., Hydraulic Control Systems—design and Analysis of their Dynamics, Springer, Berlin, 1981.

Esposito, A., Fluid Power with Applications, 5th ed., Prentice-Hall, Upper Saddle River, NJ, 2000.

Gotz, W., Hydraulics. Theory and Applications, Robert Bosch Automation Technology Division Training,

Ditzingen, 1998.

Hehn, A. H., Fluid Power Troubleshooting, 2nd ed., Dekker, New York, 1995.

Introduction to Hydraulic Circuits and Components, The University of Bath, Bath, 2000.

Introduction to Control for Electrohydraulic Systems, The University of Bath, Bath, 1999.

Jacazio, G., Piombo, B., Meccanica Applicata Alle Macchine 3: Regolazione e servomeccanismi, Levrotto &

Bella, Torino, 1994.

Johnson, J. E., Electrohydraulic Servo Systems, 2nd ed., Penton IPC, Cleveland, 1977.

Johnson, J. L., Design of Electrohydraulic Systems for Industrial Motion Control, Penton IPC, Cleveland,

1991.

Johnson, J. L., Basic Electronics for Hydraulic Motion Control, Penton IPC, Cleveland, 1992.

Lewis, E. E., Stern, H., Design of Hydraulic Control Systems, McGraw-Hill, New York, 1962.

Mang, T., Dresel, W., Lubricants and Lubrications, Wiley-VCH, Weinheim, 2001.

McCloy, D., Martin, H. R., The Control of Fluid Power, Longman, London, 1973.

Merritt, H. E., Hydraulic Control Systems, Wiley, New York, 1967.

Moog, Technical Bulletins, 101–152, Moog, New York.

Muller, R., Pneumatics. Theory and Applications, Robert Bosch Automation Technology Division Training,

Ditzingen, 1998.

Nervegna, N., Oleodinamica e Pneumatica, Politeko, Torino, 1999.

Parr, A.,

Hydraulics and Pneumatics: A Technician’s and Engineer’s Guide,

2nd ed., Butterworth Heinemann,

Oxford, 1998.

Shetty, D., Kolk, R. A., Mechatronics System Design, PWS publishing company, Boston, 1997.

Tonya n, M . J. , Electronically Controlled Proportional Valves: Selection and Application, Dekker, New York,

1985.

Viersma, T. J., Analysis, Synthesis and Design of Hydraulic Servosystems and Pipelines, Elsevier, Amsterdam,

1980.

Yea ple, F. , Fluid Power Design Handbook, 3rd ed., Dekker, New York, 1996.

21.5 MEMS: Microtransducers Analysis, Design,

and Fabrication*

Sergey Edward Lyshevski

21.5.1 Introduction

In many applications (from medicine and biotechnology to aerospace and security), the use of nano-

and microscale structures, devices, and systems is very important [1–4]. This chapter discusses the

analysis, modeling, design, and fabrication of electromagnetic-based microscale structures and devices

(microtransducers controlled by ICs). It is obvious that to attain our objectives and goals, the synergy

of multidisciplinary engineering, science, and technology must be utilized. In particular, electromagnetic

*This section is a part of the book: S. E. Lyshevski, MEMS and NEMS: Systems, Devices, and Structures, CRC Press,

Boca Raton, FL, 2001.

9258_C021_Sect002-005.fm Page 97 Wednesday, October 10, 2007 7:10 PM

21-98 Mechatronic Systems, Sensors, and Actuators

theory and mechanics comprise the fundamentals for analysis, modeling, simulation, design, and opti-

mization, while fabrication is based on the micromachining and high-aspect-ratio techniques and pro-

cesses, which are the extension of the CMOS technologies developed to fabricate ICs. For many years,

the developments in microelectromechanical systems (MEMS) have been concentrated on the fabrica-

tion of microstructures adopting, modifying, and redesigning silicon-based processes and technologies

commonly used in integrated microelectronics. The reason for refining of conventional processes and

technologies as well as application of new materials is simple: in general, microstructures are three-

dimensional with high aspect ratios and large structural heights in contrast to two-dimensional planar

microelectronic devices. Silicon structures can be formed from bulk silicon micromachining using wet

or dry processes, or through surface micromachining. Metallic micromolding techniques, based upon

photolithographic processes, are also widely used to fabricate microstructures. Molds are created in

polymer films (usually photoresist) on planar surfaces, and then filled by electrodepositing metal (elec-

trodeposition plays a key role in the fabrication of the microstructures and microdevices, which are the

components of MEMS). High-aspect ratio technologies use optical, e-beam, and x-ray lithography to

create trenches up to 1 mm deep in polymethylmethacrylate resist on the electroplating base (called seed

layer). Electrodeposition of magnetic materials and conductors, electroplating, electroetching, and lift-

off are extremely important processes to fabricate microscale structures and devices. Though it is recog-

nized that the ability to use and refine existing microelectronics fabrication technologies and materials

is very important, and the development of novel processes to fabricate MEMS is a key factor in the rapid

growth of affordable MEMS, other emerging areas arise. In particular, devising, design, modeling,

analysis, and optimization of novel MEMS are extremely important. Therefore, recently, the MEMS

theory and microengineering fundamentals have been expanded to thoroughly study other critical prob-

lems such as the system-level synthesis and integration, synergetic classification and analysis, modeling

and design, as well as optimization. This chapter studies the fabrication, analysis, and design problems

for electromagnetic microstructures and microdevices (microtransducers with ICs). The descriptions of

the fabrication processes are given, modeling and analysis issues are emphasized, and the design is

performed.

21.5.2 Design and Fabrication

In MEMS, the fabrication of thin film magnetic components and microstructures requires deposition of

conductors, insulators, and magnetic materials. Some available bulk material constants (conductivity

resistivity

at 20°C, relative permeability

, thermal expansion t

, and dielectric constant—relative

permittivity

) in SI units are given in Table 21.7.

TABLE 21.7 Material Constants

Material

σρ µ

× 10

−6

Silver 6.17 × 10

0.162 × 10

−7

0.9999998 NA

Copper 5.8 × 10

0.172 × 10

−7

0.99999 16.7

Gold 4.1 × 10

0.244 × 10

−7

0.99999 14

Aluminum 3.82 × 10

0.26 × 10

−7

1.00000065 25

Tungsten 1.82 × 10

0.55 × 10

−7

NA NA

Zinc 1.67 × 10

0.6 × 10

−7

NA NA

Cobalt NA NA 250 NA

Nickel 1.45 × 10

0.69 × 10

−7

600 nonlinear NA

Iron 1.03 × 10

1 × 10

−7

4000 nonlinear NA

Si 2.65 11.8

SiO

0.51 3.8

2.7 7.6

SiC 3.0 6.5

GaAs 6.9 13

Ge 2.2 16.1

9258_C021_Sect002-005.fm Page 98 Wednesday, October 10, 2007 7:10 PM

Actuators 21-99

Although MEMS topologies and configurations vary (see the MEMS classification concept [2]), in

general, electromagnetic microtransducers have been designed as the closed-ended, open-ended, and

integrated electromagnetic systems. As an example, Figure 21.127 illustrates the microtoroid and the

linear micromotor with the closed-ended and open-ended electromagnetic systems, respectively. The

copper windings and magnetic core (microstructures) can be made through electroplating, and Figure

21.129 depicts the electroplated circular copper conductors which form the windings (10

m wide and

thick with 10

m spacing) deposited on the insulated layer of the magnetic core.

The comprehensive electromagnetic analysis must be performed for microscale structures and devices.

For example, the torque (force) developed and the voltage induced by microtransducers depend upon

the inductance, and the microdevice’s efficiency is a function of the winding resistance, resistivity of the

coils deposited, eddy currents, hysteresis, etc. Studying the microtoroid, consider a circular path of radius

R in a plane normal to the axis. The magnetic flux intensity is calculated using the following formula:

where N is the number of turns. Thus, one has

The value of H is a function of R, and therefore, the field is not uniform.

Microwindings must guarantee the adequate inductance in the limited footprint area with the minimal

resistance. For example, in the microtransducers and low power converters, 0.5

H (or higher) inductance

is required at high frequency (1–10 MHz). Compared with the conventional minidevices, the thin film

electromagnetic microtransducers have lower efficiency due to higher resistivity of thin films, eddy

currents, hysteresis, fringing effect, and other undesirable phenomena, which usually have the secondary

(negligible) effect in the miniscale and conventional electromechanical devices. The inductance can be

increased by ensuring a large number of turns, using core magnetic materials with high relative perme-

ability, increasing the cross-sectional core area, and decreasing the path length. In fact, at low frequency,

the formula for inductance is

where

is the relative permeability of the core material, A is the cross-sectional area of the magnetic

core, and l is the magnetic path length.

FIGURE 21.127 Closed-ended and open-ended electromagnetic systems in microtransducers (toroidal microstruc-

tures with the insulated copper circular conductors wound around the magnetic material and linear micromotor)

with magnetic cores (stator and rotor electroplated thin films).

Electroplated magnetic core

with copper microwindings

r, L

Silicon substrate

Magnetic core

Microwindings

Magnetic core

Copper windings

Closed-ended

Electromagnetic system

Open-ended

electromagnetic system

Insulator

displacement

H ds⋅

RH Ni==

----------

---------------------

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21-100 Mechatronic Systems, Sensors, and Actuators

Using the reluctance ℜ = l/(

A), one has L = N

/ℜ. For the electromagnetic microtransducers, the

flux is a very important variable, and using the net current, one has Φ = Ni/ℜ.

It is important to recall that the inductance is related to the energy stored in the magnetic field, and

Thus, one has

We found that the inductance is the function of the number of turns, flux, and current.

Making use of the equation

one concludes that the inductance increases as a function of the squared number of turns. However, a

large number of turns requires the high turn density (small track width and spacing so that many turns

can be fitted in a given footprint area). However, reducing the track width leads to an increase in the

conductor resistance, decreasing the efficiency. Therefore, the design trade-off between inductance and

winding resistance must be studied. To achieve low resistance, one must deposit thick conductors with

the thickness in the order of tens of micrometers. In fact, the dc resistance is found as R =

, where

is the conductor resistivity, l

is the conductor length, A

is the conductor cross-sectional area. Therefore,

the most feasible process for deposition of conductors is electroplating. High-aspect-ratio processes

ensure thick conductors and small track widths and spaces (high-aspect-ratio conductors have a high

thickness to width ratio). However, the footprint area is limited not allowing to achieve a large conductor

cross-sectional area. High inductance value can also be achieved by increasing the magnetic core cross-

sectional area using thick magnetic cores with large A. However, most thin film magnetic materials are

thin film metal alloys, which generally have characteristics not as good as the bulk ferromagnetic materials.

This results in the eddy current and undesirable hysteresis effects, which increase the core losses and

decrease the inductance. It should be emphasized that eddy currents must be minimized.

As illustrated, magnetic cores and microwindings are key components of microstructures, and different

magnetic and conductor materials and processes to fabricate microtransducers are employed. Commonly,

the permalloy (nickel

80%

-iron

20%

alloy) thin films are used. It should be emphasized that permalloy as well

as other materials (e.g., amorphous cobalt-phosphorous) are soft magnetic materials that can be made

through electrodeposition. In general, the deposits have nonuniform thickness and composition due to

the electric current nonuniformity over the electrodeposition area. Furthermore, hydrodynamic effects

in the electrolyte also usually increase nonuniformity (these nonuniformities are reduced by choosing a

particular electrochemicals). The inductance and losses remain constant up to a certain frequency (which

is a function of the layer thickness, materials used, fabrication processes, etc.), and in the high frequency

operating regimes, the inductance rapidly decreases and the losses increase due to the eddy current and

hysteresis effects. For example, for the permalloy (Ni

80%

20%

) thin film magnetic core and copper winding,

-----------

---

B ⋅ H v.d

---

B ⋅ H vd

---

H ⋅ ∇ A×() vd

---

A ⋅ J vd

A ⋅ ld

B ⋅ sd

----

== ====

NΦ

---------

----------------------

9258_C021_Sect002-005.fm Page 100 Wednesday, October 10, 2007 7:10 PM

Actuators 21-101

the inductance decreases rapidly above 1, 3, and 6 MHz for the 10, 8, and 5

m thick layers, respectively.

It should be emphasized that the skin depth of the magnetic core thin film as a function of the magnetic

properties and the frequency f is found as , where

and

are the permeability and

conductivity of the magnetic core material, respectively. The total power losses are found using the

Pointing vector , and the total power loss can be approximately derived using the expression

for the power crossing the conductor surface within the area, e.g.,

It is important to emphasize that the skin depth (depth of penetration) is available, and for the bulk

copper

= 0.066/ .

In general, the inductance begins to decrease when the ratio of the lamination thickness to skin depth

is greater than one. Thus, the lamination thickness must be less than skin depth at the operating frequency

f to attain the high inductance value. In order to illustrate the need to comprehensively study microin-

ductors, we analyze the toroidal microinductor (1 mm by 1 mm, 3

m core thickness, 2000 permeability).

The inductance and winding resistances are analyzed as the functions of the operating frequency. Modeling

results indicate that the inductance remains constant up to 100 kHz and decreases for the higher

frequency. The resistance increases significantly at frequencies higher than 150 kHz (the copper micro-

conductor thickness is 2

m, and the dc winding resistance is 10 Ω). The decreased inductance and

increased resistance at high frequency are due to hysteresis and eddy current effects.

The skin depth in the magnetic core material depends on the permeability and the conductivity. The

100−x%

thin films have a relative permeability in the range from 600 to 2000, and the resistivity is

in the order of 20

Ω cm. It should be emphasized that the materials with high resistivity have low eddy

current losses and allow one to deposit thicker layers as the skin depth is high. Therefore, high resistivity

magnetic materials are under consideration, and the electroplated FeCo thin films have 100–130

Ω cm

resistivity. Other high resistivity materials, which can be deposited by sputtering, are FeZrO and

CoHfTaPd (sputtering has advantages for the deposition of laminated layers of magnetic and insulating

materials because magnetic and insulating materials can be deposited in the same process step). Electro-

plating, as a technique for deposition of laminated multilayer structures, in general, requires different

processes to deposit magnetic and insulating materials (layers).

The major processes involved in the electromagnetic microtransducer fabrication are etching and

electroplating magnetic vias and through-holes, and then fabricating the inductor-type microstructures

on top of the through-hole wafer using multilayer thick photoresist processes [5–7]. For example, let us

use the silicon substrate (100-oriented n-type double-sided polished silicon wafers) with a thin layer of

thermally grown silicon dioxide (SiO

). Through-holes are patterned on the topside of the Si–SiO

wafer

(photolithography process) and then etched in the KOH system (different etch rate can be attained based

upon the concentration and temperature). Then, the wafer is removed from the KOH solution with

20–30

m of silicon remaining to be etched. A seed layer of Ti–Cu or Cr–Cu (20–40 nm and 400–500 nm

thickness, respectively) are deposited on the backside of the wafer using electron beam evaporation. The

copper acts as the electroplating seed layer, while a titanium (or chromium) layer is used to increase

adhesion of the copper layer to the silicon wafer. On the copper seed layer, a protective NiFe thin film

layer is electroplated directly above the through-holes to attain protection and stability. The through-

holes are fully etched again (in the KOH system), and then the remaining SiO

is stripped (using the

BHF solution) to reveal the backside metal layers. Then, the titanium adhesion layer is etched in the HF

solution (chromium, if the Cr–Cu seed layer is used, can be removed using the K

Fe(CN)

–NaOH

solution). This allows the electroplating of through-holes from the exposed copper seed layer. The empty

through-holes are electroplated with NiFe thin film. This forms the magnetic vias. Because the KOH-

based etching process is crystallographically dependent, the sidewalls of the electroplating mold are the

111-oriented crystal planes (54.7° angular orientation to the surface). As a result of these 54.7°-angularly

1/(

µσ

Ξ EH×=

average

σδ

δπ

µσ

–

9258_C021_Sect002-005.fm Page 101 Wednesday, October 10, 2007 7:10 PM