Wheatstone Bridge Participant Guide

7/28/2019 Wheatstone Bridge Participant Guide

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Wheatstone Bridge LearningWheatstone Bridge Learning

ModuleModule

Wheatstone Bridge (WB) UnitWheatstone Bridge (WB) UnitPressure Sensor Model ActivityPressure Sensor Model Activity

WB Derivation ActivityWB Derivation Activity

Participant GuideParticipant Guide

www.scmewww.scme--nm.orgnm.org


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Southwest Center for Microsystems Education (SCME)

University of New Mexico

MEMS Introduction Topic

Wheatstone Bridge OverviewPrimary Knowledge (PK)

Shareable Content Object (SCO)

This SCO is part of the Learning Module

Wheatstone Bridge Overview

Target audiences: High School, Community College.

Support for this work was provided by the National Science Foundation's Advanced Technological Education(ATE) Program through Grants #0830384 and 092411.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors

and creators, and do not necessarily reflect the views of the National Science Foundation.

Copyright 2009 - 2011 by the Southwest Center for Microsystems Education

andThe Regents of the University of New Mexico

Southwest Center for Microsystems Education (SCME)800 Bradbury Drive SE, Ste. 235

Albuquerque, NM 87106-4346Phone: 505-272-7150

Website: www.scme-nm.org email contact: [email protected]
http://www.scme-nm.org/http://www.scme-nm.org/mailto:[email protected]:[email protected]:[email protected]://www.scme-nm.org/


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Southwest Center for Micr osystems Education (SCME) Page 2 of 14

Int_WheatB_PK01_PG_061411 Wheatstone Bridge PK


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Primary Knowledge

Participant Guide

Description and Estimated Time

This Wheatstone Bridge Overview provides information on the electronic circuitry of a WheatstoneBridge. This overview will help you to understand how a Wheatstone Bridge is used for sensing

changes in pressure when used in a MEMS pressure sensor.

Estimated Time to CompleteAllow approximately 1 hour to complete.

Introduction

A Wheatstone bridge is an electrical circuit design dating back to

the early 1800's. It is named for its most famous user, SirCharles Wheatstone. Sir Wheatstone never claimed to have

invented it; however, he did develop multiple uses for it. TheWheatstone bridge circuit was invented by Samuel Hunter

Christie (1784-1865) and first described in 18331. Sir

Wheatstone actually called the circuit a Differential Resistance

Measurer.

The Wheatstone bridge is one of the most sensitive and precisemethods of measuring small changes in resistance. This is

possible through its use of transducers (devices which changeone form of energy into another, such as mechanical to electrical

or electrical to mechanical). The Wheatstone bridge incorporatesone or more electrical transducers that change resistance as a result

of an environmental change or input (e.g., temperature, pressure,stress). This change is sensed by the circuitry of the Wheatstone bridge which provides a useable

electrical output (voltage) representative of the input. The Wheatstone bridge is widely used todayin both macro-sized and micro-sized sensors.

This unit will describe the basics of the Wheatstone bridge circuit.

Sir Charles WheatstoneNational Portrait Gallery, London


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Objectives

Define the variable components of the Wheatstone bridge.

Describe how the Wheatstone bridge works.

Key Terms (These terms are defined in the glossary at this end of this unit.)

Calibration Curve

Electric circuitKirchhoffs Voltage Law

Ohms LawResistance

ResistivityResistorSignal to Noise Ratio

TransducerVoltage

Wheatstone Bridge

The Wheatstone Bridge

A Wheatstone bridge is a simple circuit used to measure small changes in resistance of a transducer.

The classic Wheatstone bridge configuration consists of four resistors, three of which are of fixedvalue and a fourth which is variable, see R4 in the diagram below. The variable resistor is the

sensing element (transducer). Its design will allow its resistance to change due to a change in anenvironmental factor such as stress, pressure, or temperature.

Basic Wheatstone Bridge Configuration with one transducer or sensing element (R4)


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Some Wheatstone bridge designs include two variable resistors (sensing elements) to improve thesensitivity of the system, and to provide an enhanced voltage variation as a function of the changinginput. When applied to a microsystems pressure sensor system, the bridge circuit has two fixed

resistors (R2 and R3 below), and two variable resistors (R1 and R4) that are the transducers (seediagram below). A direct current (DC) voltage source such as a battery provides the input Voltage.

The Wheatstone bridge output is called the gap voltage (Vg) and is proportional to the difference inthe transducers resistance values relative to the reference resistance in the bridge configuration.

This design allows for the measurement of very small changes in the environmental factor thataffects the transducer resistance. The design of the circuit reduces the effects of noise on the output

voltage. For example, if the input voltage varies, it does not influence the output voltage since it isrelated to the ratio of the resistances. Also, a variation in temperature affects all the resistor

elements equally and therefore cancel each other out. Therefore, this circuit greatly suppresseselectrical noise and thereby improves the signal to noise ratio.

Basic Wheatstone Bridge Configuration with two transducers or sensing elements (R1 and R4)


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Background Circuits

The Wheatstone bridge is based on a simpler circuit element called the voltage divider. There are two

basic concepts needed to understand how these circuit elements operate:

Ohms Law (I=V/R)

Kirchoffs Circuit Laws

Resistor Voltage Dividers

The figure below is made up of two resistors placed in series labeled R1, R2, and a power supply Vin(battery).

The electron flow or currentIin is measured in Amperes (A), and travels from the negative terminal ofthe battery through the resistors to the positive terminal of the battery. As the electrons move through

the resistors, they loss some of their energy, and this is measured as voltage drop (reduction) acrossthe resistors.

Ohm's Law

Ohm's Law determines the voltage drop (or change) across a resistorR for a given currentI. Ohm'sLaw states: V = IR where Vis the voltage difference across a resistorR that has currentIflowing

through it. In the Resistive Voltage Divider circuit above, the voltage drop, V1 across resistorR1 iswritten as

V1 = IinR1

and the voltage drop, V2 across resistorR2 is

V2 = IinR2.

To measure the V2 acrossR2 with reference to ground, a voltmeter is placed across the resistor. One

lead is connected to the node located between R1 and R2, and the other lead is connected to ground(or the negative side of the voltage source). Ground reference voltage is 0 V. The voltmeter reads V2= IinR2 and this is the voltage difference which drives current through R2.

Resistive Voltage Divider


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Note that the current,I, is conserved, in other words, the amount of current flowing into the circuit

is the same as the amount flowing out of the circuit. This is analogous to saying that the amount ofwater flowing into a houses plumbing circuit is equal to the amount of water flowing out of the

same circuit. Water flow is analogous to electrical current flow. However, the water pressuremeasured coming into the house is higher than the pressure measured going out of the house. The

water pressure is analogous to the voltage on a circuit. A thin pipe in a plumbing circuit will allowless water flow (current) and it will also result in a greater pressure drop (voltage change). This

thinner pipe is analogous to a resistor having higher resistance.

Let's put some numbers to this Voltage divider circuit and check out our calculations.

Vin = 10V R1 = R2 = 500

The total circuit resistance Rt is equal to R1 + R2:

Rt= 500 + 500 = 1000 or 1 k

Using Ohm's Law, calculate Iin.

Now you know Iin and can determine V1.

The voltage drop, V1 across resistorR1 is

V1 = IinR1or 10mA*500 = 0.01A*500 =5V

The voltage drop, V2 across resistorR2 is

V2 = IinR2 or 10mA*500 = 0.01A*500 =5V

mAk

V

R

VI

t

in

in10

1

10


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Kirchoffs Laws

Two of Kirchoffs Laws can be applied to find out the voltages and currents in DC circuits.Kirchoffs current law, states that the sum of all currents entering a node in the circuit is zero.

Another way to look at this is that the current flowing into a node is equal to the current flowing outof it. Kirchhoffs voltage law, states that the sum of the voltage drops across a collection of resistors

arranged in series (in a line, one after the other) within a circuit is equal to the applied voltage acrossall the resistors (Vin). In this example, it can then be written as

2121

RRIRIRIVinininin

or

21VVV

in

Notice in that the previous problem shows this to be true: 10 v (Vin) = 5 v + 5v

The voltage drop across a specific resistor in series with other resistors is the fraction of that resistorto the sum of the series resistors, multiplied by the applied voltage. (The formula is derived below.)

21RR

VI

in

in

in

in

inV

RR

RR

RR

VRIV

21

2

2

21

22

Applying the values of the previous circuit, we get

The Wheatstone bridge has two such voltage dividers connected in parallel; therefore, the analysis

of the resistive voltage dividercircuit can be applied to the Wheatstone bridge circuit. Can youidentify the two voltage divider circuits in the circuit below?

Wheatstone Bridge with two variable resistors

VVV 510500500

5002


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Wheatstone Bridge and Difference Voltage

One Variable Resistor

Wheatstone Bridge with one variable resistor

The figure above shows the schematic circuit diagram of a Wheatstone bridge. The resistor pair R1and R2 is a resistive voltage dividerand resistors R3 and R4 form another voltage divider in parallel

with R1 and R2. The circuit is sensitive to the difference in voltage between node-a and node-b. Va

and Vbcan be found by

inaV

RR

RV

21

2

inbV

RR

RV

43

4

so that

inabbaV

RR

R

RR

RVVV

43

4

21

2

This can also be written as

= + +

When R2R3 = R1R4, the circuit output is zero, Vab =0. The bridge is said to be balanced when Vab =

0 volts. This occurs whenR1/R2 = R3/R4. In a typical sensing device, a variable resistorR4, is used.

The other three resistors are fixed. We will now refer toR4 asRS. The Wheatstone Bridge isinitially balanced with all ofthe Rs having the same resistance value by design, includingRS (theresistance of the sensing element when there is nothing to sense). The value ofRSchanges when the

external environment changes thus affecting Vab as

in

S

S

abV

RR

R

RR

RV

321

2


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Assuming the input voltage, Vin = 10V and the transducer resistanceRS is initially 100 Ohms (),

andR1 =R2 =R3 = 100 , as well, then Vab can be plotted as a function ofRS:

Notice that whenRS= 100 Vab=0 volts and the bridge is balanced. Changes in the environmenton the transducer affects its resistance, Rs, creating an unbalanced bridge which results in a voltage

related to the resistance change. Based on the graph, if the resistance of RS increases, Vab decreases.

A similar plot can be made plotting Vab versus the environmental variable associated with thechange in resistance.


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Two Variable Resistors

Looking carefully at the equations and the circuit diagrams, one can design a more sensitive circuit

where R1 and R4 are both variable resistors. Such a circuit is shown below:

If the R1 and R4 resistors are both variable and react in the same manner to an external

environmental change, then the effect on the output voltage, Vab is amplified!

Reconsider the case where all resistances are initially at 100 each and Vin is 10 V. How would Vabbe affected if both R1 and R4both increased to 110 ohms? Graphing Vab as a function of the

variable resistances of R1 and R4 (in this case changing by the same amount while the other two, R2and R3remain constant at 100) is shown in the following graph. Note: the variable resistors in the

case of a strain gauge pressure sensor will only increase from the nominal value (why would thisbe?). In the graph below, the blue line represents the case when there is only one variable resistor.The red line represents the transducer response when both R1 and R4 are variable.


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When the Wheatstone bridge is used in a pressure sensor, the resistors are oriented such that R1 andR4 are variable under the stress of a flexible membrane on which they are made.

Wheatstone Bridge layout used in a Pressure Sensor

Actual pressure sensor photo showing the Wheatstone bridge circuit (gold) pattern on top of thesilicon nitride membrane. This pattern is slightly different than the schematic.[Image of a pressure sensor built at the Manufacturing Technology Training Center (MTTC) at the University of New

Mexico (UNM)]

Membrane(Diaphragm)


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Calibration

To calibrate a Wheatstone bridge as a pressure transducer, a series of known pressure differences is

applied to the sensing element(s). The output voltage (Vab) is measured using a voltmeter, and Vabversus pressure is plotted. Such a plot is referred to as a calibration curve. When an unknown

pressure is subsequently applied and the output voltage read, the calibration curve ofVabvs.Pressure can be used to determine the actual pressure.

The graph below is an example of a calibration curve based on an actual MEMS pressure sensor

utilizing a Wheatstone bridge5. This graphic shows how to read the curve, for example, if an output

voltage of .22 V is read, the corresponding pressure is approximately 82psi.

Summary

A Wheatstone bridge is a simple circuit used to measure transducer responses by measuring changesin voltage. Basic circuit analysis is used to determine the resistance, voltage and current when the

bridge is balanced. Any change in transducer resistance causes the bridge output voltage to change

corresponding to the change in pressure. A voltmeter measures the output of the Wheatstone bridgeand the corresponding pressure is read off of the calibration curve. In a MEMS where theWheatstone bridge is part of the sensing circuit, its output can be amplified and processed to send

information or to initiate a mechanical or electrical response.


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References

http://en.wikipedia.org/wiki/Wheatstone_bridge2http://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstone3Dr. Chuck Hawkins, University of New Mexico , Wheatstone Bridge v3.doc

4Wheatstone Bridge www.geocities.com/CapeCanaveral/8341/bridge.htm

5Hsun-Heng Tsai*, Chi-Chang Hsieh, Cheng-Wen Fan, Young-Chang Chen and Wei-Te Wu

Design and Characterization of Temperature-Robust Piezoresistive Micro-Pressure Sensor with Double Wheatstone

Bridge Bridge Structure, DTIP of MEMS & MOEMS, 1 -3 April, Rome, Italy, 2009.

Glossary of Key Terms

Calibration CurveA plot of data acquired in the calibration of instrument or device. The curve isused to show how an instrument meets a standard or specification.

Electric circuitA path or group of interconnected paths capable of carrying electric current.

Kirchhoffs Voltage LawThe algebraic sum of all voltages in a closed loop of electric circuit must

equal zero.

Ohms Law - The law stating that the direct current flowing in a conductor is directly proportional tothe potential difference between its ends. It is usually formulated as V=IR, where Vis the potential

difference, or voltage,Iis the current, andR is the resistance of the conductor.

ResistanceA components opposition to current passing through it,resulting in a change ofelectrical energy into heat or another form of energy.

ResistivityThe measure of how strongly a material opposes the flow of current.

ResistorAn electronic device designed with a specific amount of resistance; used to limit currentflow or to provide a voltage drop.

Signal to Noise Ratio (SNR)The ratio of the amplitude of a desired signal at any point to theamplitude of noise signals at that same point. (i.e., The ratio of a desired signal to the level of

background noise.) A ratio less than 1:1 indicates that the background noise is greater than thedesired (or reference) noise.

TransducerA device that converts one form of energy to another form of energy. (e.g., A motor

converts electrical energy to mechanical energy.)

VoltageA representation of the electric potential energy per unit charge. A measurement of theenergy contained within an electric field, or an electric circuit, at a given point.

Wheatstone BridgeA four armed bridge circuit, each arm having a resistor (fixed or variable). It

is used to measure an unknown resistance by balancing two arms of the bridge, one of whichcontains the unknown resistance.

Support for this work was provided by the National Science Foundation's Advanced Technological Education

(ATE) Program.
http://en.wikipedia.org/wiki/Wheatstone_bridgehttp://en.wikipedia.org/wiki/Wheatstone_bridgehttp://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstonehttp://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstonehttp://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstonehttp://c/Documents%20and%20Settings/Dr.%20Pleil/My%20Documents/SCOS/www.geocities.com/CapeCanaveral/8341/bridge.htmhttp://c/Documents%20and%20Settings/Dr.%20Pleil/My%20Documents/SCOS/www.geocities.com/CapeCanaveral/8341/bridge.htmhttp://c/Documents%20and%20Settings/Dr.%20Pleil/My%20Documents/SCOS/www.geocities.com/CapeCanaveral/8341/bridge.htmhttp://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstonehttp://en.wikipedia.org/wiki/Wheatstone_bridge


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Pressure Sensor Model ActivityShareable Content Object (SCO)

This SCO is part of the Learning ModuleWheatstone Bridge Overview



(ATE) Program through Grants #0830384 and 0902411.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authorsand creators, and do not necessarily reflect the views of the National Science Foundation.


andThe Regents of the University of New Mexico


800 Bradbury Drive SE, Ste. 235Albuquerque, NM 87106-4346

Phone: 505-272-7150Website: www.scme-nm.org email contact: [email protected]


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Southwest Center for Microsystems Education (SCME) Page 2 of 18Int_WheatB_AC02_PG_061511 PS Model Activity

Pressure Sensor Model Activity

Wheatstone Bridge Overview Learning Module

Participant Guide

Description and Estimated Time to Complete

In this activity you will use basic materials to build

a macro pressure sensor with a Wheatstone bridgesensing circuit (circuit right) on a flexible

diaphragm. The results will simulate a MEMSpressure sensor(see Introduction). To test your

sensor, you will apply variable pressures to thediaphragm while monitoring the resistance change

and resulting voltage output of the bridge.

The unit Wheatstone Bridge Overview, explains the operation of a Wheatstone bridge. If you

havent already reviewed this unit, you should review it before you test your pressure sensormodel. Complete this activity through Making a conductive bridge pattern. As your pattern

dries, review the Wheatstone Bridge Overview. This will help you to better understand theworkings of this device and the results of your testing.

Estimated Time to Complete

Allow at least two hours to complete this activity.


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MEMS Pressure Sensor Applications

MEMS pressure sensors are designed to measure absolute or differential pressures. Theyconvert physical quantities such as air flow and liquid levels into pressure values that are

measured by an electronic system. MEMS pressure sensors can be used in conjunction withother sensors such as temperature sensors and accelerometers for multisensing applications or

other components.

In the automotive industry, MEMS pressure sensors monitor the absolute air pressure within theintake manifold of the engine. MEMS are also being designed to sense tire pressure, fuel

pressure, and air flow.

In the biomedical field, current and developing applications for MEMSpressure sensors include blood pressure sensors (see photo right), single

and multipoint catheters, intracranial pressure sensors, cerebrospinal fluidpressure sensors, intraocular pressure (IOP) monitors, and other implanted

coronary pressure measurements. The photo shows three blood pressure

sensors on the head of a pin. These sensors were developed by LucasNovaSensor to measure blood pressure and provide an electrical outputrepresentative of the pressure. RF elements are incorporated into the

MEMS device allowing the sensor to transmit its measurements to an

external receiver.

MEMS pressure sensors are also incorporated

into endoscopes for measuring pressure in thestomach and other organs, infusion pumps for monitoring blockage, and noninvasive blood

pressure monitors. Applications of MEMS pressure sensors within the biomedical field andother industries are numerous.

A MEMS Pressure Sensor

Many MEMS pressure sensors use a Wheatstone

bridge configuration as the sensing circuit. In MEMSthe Wheatstone bridge circuit is mounted on a

membrane or diaphragm. The resistors in theWheatstone bridge are made of a piezoresistive

material, a material which changes its resistance whenmechanical stress is applied.

MEMS Blood Pressure Sensors on the head

of a pin. [Photo courtesy of LucasNovaSensor, Fremont, CA]


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In the example below, a conductive material such as gold is used for the bridge circuit. The

pressure sensor diaphragm is a thin layer of material which is resistant to chemical change suchas, in this case, silicon nitride (see image below). One side of the diaphragm is sealed to provide

a reference pressure. The other side is open to the environment and subject to air pressurevariation. As the diaphragm moves due to pressure changes, the membrane expands and

stretches. The bridge resistors mounted on the membrane also expand and stretch. Thisexpansion of the bridge translates to a change of resistance in the conductive material of the

bridge. As the conductive material stretches, its resistance increases.

All materials have electrical resistance. The resistance to electrical current flow of an object(resistor) is related to a material property called resistivity (), and its geometry - length, width,

and thickness. It is the combination of the geometry (shape) and material property (resistivity)which determines the overall electrical characteristic (resistance). To calculate the resistance (R)

of a material, one can use the following formula:

=

where L, and A are the length and cross-sectional area of the resistor, respectively. In the case

of a rectangular cross section, the area can be written as

=

where t and w are the thickness and width of the structure, respectively.

In the Wheatstone bridge application presented in this activity, the resistivity,, is a physical

property of the material. Resistivity remains constant under constant temperature and stress(e.g., pressure). It should be pointed out that the resistivity of a material, , is inversely

proportional to its conductivity, :

=

1

As the conductive (resistive) material stretches, the length increases while the area decreases.

This increase in length and decrease in area results in an increase in overall resistance.

Pressure Sensor illustrating the

Wheatstone bridge and the SiliconNitride Membrane (Diaphragm)

[Image of a pressure sensor built at theManufacturing Technology Training

Center (MTTC) at the University of NewMexico (UNM)]


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You may ask, I understand why the resistor gets longer when the membrane it is adhered to

stretches, but why does the cross sectional area decrease? If you consider that the overall massof the resistor (the total amount of the material) does not change due to the conservation of mass

principal, and that the density of the material doesnt change either, you can therefore assumethat the total volume of the resistor has to stay constant. Since volume, V, can be written as a

product of length (L) and area (A),

=

then asL gets longer,A must get smaller in order for the volume to remain constant.

NOTE: We have assumed the density of the material does not change; however, it could, if the

temperature of the material changes. Therefore it is critical for the bridge circuit design toautomatically compensate for temperature fluctuations (which could occur in a wide variety of

applications).

To re-cap, one can now see from the resistance equation, =

, that as a conductor stretches,

the length increases as the cross-sectional area simultaneously decreases resulting in the L/Aratio in the equation to increase.

What is Graphene?

In this activity you will be using graphite to construct the electronic circuit. Graphite consists of

stacks of graphene sheets. So what is graphene? Graphene is a material formed when carbonatoms arrange in sheets. Graphene is a one-atom-thick planar sheet of carbon atoms densely

packed in a honeycomb crystal lattice (as shown in the graphic below). Graphene is also used asthe structural element for fullerenes such as carbon nanotubes and buckyballs. In this activity,

the mixture of graphite (pencil lead) and rubber cement used to construct the Wheatstone bridgecontains sheets of graphene. These sheets are thought to slide on top of each other as the

material stretches while still maintaining contact. You should see the effect of this when youapply pressure to your pressure sensor model diaphragm.

Graphene SheetGraphite is composed of several

stacked sheets of graphene


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Activity Objectives and Outcomes

Activity Objectives

Explain how a change in length and cross-sectional area affects a material's resistance. Using your pressure sensor model, demonstrate and explain how pressure affects the

resistance and output voltage of a Wheatstone bridge sensing circuit.

Activity Outcomes

In this activity you construct a macro-size pressure sensor with a Wheatstone bridge sensingcircuit on a flexible diaphragm. You also discuss microsystems applications. Upon completion

of this activity, you should be able to answer the following questions:

How does the length of a conductive material affect its resistance? What is meant when a Wheatstone bridge is balanced? What are some applications pressure sensors in microsystems technology? What are the advantages and disadvantages of using a Wheatstone bridge sensing circuit in

the micro and nano-scales?

Resources

SCME Wheatstone Bridge Learning Module

Teamwork

Working with one to two other participants will promote a better understanding of this activity.

Facilities / Workspace / Safety Precautions

You will need a flat table as a workspace.

For safety, it is recommended that you wear safety glasses and latex or nitrile gloves whenworking with the graphite and rubber cement.


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Supplies / Equipment

Supplies provided by Instructor

Safety glasses and gloves Wipes or paper towels Metric Ruler 1 bottle of Rubber cement Scissors Blue painters tape 1 (or electrical tape) 6 large paperclips Small brush (to brush out mortar) Multimeter with clip-on leads Marker (e.g., Sharpie) 1 small sheet of cardstock (thick paper) Two sheet of paper or cone shaped coffee

filters (No. 2 work great)

Ice pick or large nailSupplies included in SCME Kit*

2 quart paint cans (empty and unused) 6 Balloons (12 ) (shown) Pencil Lead (0.9 mm thick HB hardness)2 packs 15 leads each (shown) Mortar and pestle (shown) Copper foil tape wide conductive on both sides (3M) (shown) Four 3 cc (3 mL) Plastic Syringes with tip (shown) Two (2) leads with alligator clip at each end (Leads should be the same length) Two glass vials with cap size 20-25ml 3 volt source, AAA battery holder with leads and alligator clips 2 AAA batteries or 2 AA batteries One Wheatstone Bridge Overview Learning Module - Instructor Guide One Wheatstone Bridge Overview Learning Module - Participant GuideDocumentation

Write a report to include the following:

Hypothesis and predictions Your procedure Any problems that occurred and how these problems affected the outcome All of your measurements An analysis of the results (Did the outcome agree with your hypothesis and predictions?) Answers to the Post-Activity questions.


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Expectations

This activity allows you to build and explore the operation of a Wheatstone bridge strain-basedtransducer. Hypothesis: Write a statement that describes what you expect as an outcome.

Make predictions:

What factors will affect the outcome?

What effect will a change in applied pressure have on the circuit's resistance? Why? What effect will a change in applied pressure have on the circuit's voltage? Why?Preparation / Setup

Gather all of the supplies for this activity. Set up a workspace on a flat table top large enough

for all of the materials and for at least two students to work together to build this device.

Activity: Pressure Sensor Model

Description: Using an empty paint can, balloon and ground mechanical pencil lead (graphene)

mixed with rubber cement, you will build a macro-size pressure sensor using a Wheatstonebridge sensing circuit.

Safetya. From the Internet, download a Material Safety Data Sheet (MSDS) for rubber cement.

b. Answer the following questions relative to rubber cement.a. What are two hazards of rubber cement that you need to be constantly aware of?

b. What type of personal protective equipment should you wear when handling rubbercement?

c. What conditions should be avoided when working with rubber cement?


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Building the Pressure Sensor Model

Constructing the DiaphragmFigure 1.

Remove the lid from the paint can (if applicable).1. Using the stencil provided (see attached at the end of this

document), cut the bridge pattern from a piece of the cardboard orcardstock. (Figure 1)

2. Cut the neck off the balloon to about 4 cm from top opening or atleast 1 cm below the curvature of neck (Figure 2)

3. Stretch the balloon tightly over the open end of the paint can.(Figure 3). You want an even stretch.

4. Secure the edges of the balloon to the can with painters tape. (Figure 4)

Figure 2 Figure 3 Figure 4


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Creating the leads and bridge pattern

1. Center the template over the balloon diaphragm as shown in Figure 1.2. Outline the pattern with a marker onto the top of the diaphragm. Remove template from

diaphragm. (Figure 5)

3. Cut four810 cm strips of conductive copper tape.4.

Remove the backing off one strip of conductive tape. Place one end of the tape on themembrane (balloon) in line and on top of part of the circuit as shown in Figure 6.

5. Pinch the middle of the strip of tape to create a tab and attach the other end of theconductive tape to the side of can (as shown in Figure 6). The tab will be used to

connect the meter leads for measuring resistance and voltage.

6. Repeat steps 5 and 6 with the other three leads (strips of conductive tape). (See Figure 7for placement of all four pieces of conductive tape)

Making the conductive material (carbon paste)

1. Put on gloves and safety glasses.2. Carefully break one pack of the graphite leads (15 pieces) into small pieces and place in

the mortar.

3. Grind the graphite into as fine of a carbon powder as possible. Grind until you see nograin pieces and the graphite is a powder. The finer the better. You will be mixing

this powder with rubber cement and then forcing the mixture through a syringe tip. A

small graphite chunk could clog the syringe.

4. Pour the carbon powder onto sheet of paper or into the coffee filter. Use a small brush toget all of the carbon out of the mortar.

5. Fold the paper/filter and carefully pour all of the powder into a glass vial.6. Using the syringe with tip attached, extract approximately 3 ml of rubber cement.7. Transfer the rubber cement to the vial containing the graphite powder.

Figure 6

(Creating the connection)

Figure 5

(Template outline)

Figure 7

(Conductive tapeplacement)


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8. Unfold a large paperclip, but leave the smaller looped end intact. (This will be yourstirring mechanism.)

9. Using the paperclip, stir the powder and rubber cement mixture in the vial. The color ofthe mixture should be black, and the viscosity (thickness) should be close to the original

cement. If it is too thick, add a little more rubber cement. If too thin, add more carbon

powder. (A commentYou will be applying this graphite/rubber cement mixture onto

the diaphragm in the same manner as decorating a cake; therefore, the viscosity of themixture should similar to that of toothpaste.

Your conductive material is now made and ready for use.

Making a conductive bridge

1. Pull liquid from the vial with the syringe. Fill the syringe with the mixture.2. To eliminate the air from the syringe, insert the paperclip into the tip of the needle,

through the liquid and into the air gap at the top of the syringe.

3. Burp the air from the syringe, by gently compressing the liquid in the syringe until alittle comes out of the needle. *Note: It is important when filling the syringe that there are no airbubbles because when applying the conductive material it is essential that there are no gaps in the lines.

4. If the syringe does not have at least 2 ml of liquid, place the syringe tip back into the vialand continue to fill the syringe to the 2 ml mark.

5. Using a wipe or paper towel, wipe the tip clean.6. Using the syringe, carefully apply about a 1 to 2 mm line (width) of your conductive

material (rubber cement and graphite mixture) following the pattern transferred from the

template. Try to keep the width and height of the carbon/cement line consistent. Be sure

to flow ON TOP of and over the copper wire at the bridge corners. You need to make

good electrical contact. (Figure 8)7. Check for any opens in your circuit. Close them with

the graphene solution.

You have now created a pressure sensor with a Wheatstone br idge.

8. Before testing your bridge circuit, you should let it set for 15 to 30 minutes.9. Squeeze any unused graphite/cement mixture from the syringe, back into the vial.10.Cap the vial. The remaining mixture should stay fluid for several weeks.11.Clean or properly dispose of the syringe.

Figure 8

(Conductive material placed on pattern and ontop of conductive tape)


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Testing your Pressure Sensor (Measuring Resistance)

The above diagrams are of the pressure sensor Wheatstone bridge in a circular configuration.This is the circuit you constructed in the previous steps of this activity. When comparing the

actual circuit components to the Wheatstone bridge circuit, resistors R2 and R3 are configuredparallel to the edge of the can, and hence, will not stretch as much when the membrane expands.

Resistors R1 and R4 are configured over the open part of the membrane or can, parallel to theradius, and will be subject to the highest tension (stretching), experiencing the greatest

piezoresistive effect.

To help you better relate to the specific resistors in your circuit, label your circuit with specificresistor notation (R1, R2, R3, R4).

So lets see how your circuit works.


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1. Clip one of the leads from the multimeter to one of the connecting leads (copper tabs).2. Clip the other multimeter lead to the "opposite" connecting lead as shown below in

Figure 9. Do not hook the battery up yet, you will only be measuring resistance of the

circuit.

Figure 9

3. Gently press down a couple of times on the diaphragm to pre-stretch it.4. Set your multimeter to read resistance.5. Record your reference circuit's total resistance. RR= _________________

(NOTE: The multimeter may indicate a continual drop in pressure as the diaphragm

comes to rest at its reference position.)

6. Gently push down on middle of the balloon. You should see the resistance change.NOTE: Be creative. Develop a systematic approach to applying pressure. For example,youcould use coins, small weights, marbles, or any of the same object that is heavy enough to flex

the diaphragm. Of course if the object is conductive (e.g., coins), a balloon should be used asan insulator between the weights and the circuit.

7. Record the resistance for three different applied pressures, increasing the pressure beforeeach recording.

a. R1 = __________________b. R2 = __________________c. R3 = __________________

(NOTE: Because of the elasticity characteristics of the balloon, your resistance reading

may not return to the original reference resistance once the applied pressure is removed.

The balloon may lose some of its original rigidity as different pressures are applied.)

8. How did the applied pressure affect the resistance of the bridge?__________________________________________________________________


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9. Explain how the following formula relates to your Wheatstone bridge circuit. =

10.Draw the equivalent circuit with the resistance meter hookup in the space below.

Now let's apply some voltage to your circuit.


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Testing your Pressure Sensor (Measuring Voltage)

11.Using the other two leads with alligator clips, attached a voltage source (2AAA batteries)across the bridge circuit. Follow the setup shown in the photograph below (Figure 10.)

(NOTE: When hooking up a voltage source, always connect the ground lead (- lead)

first.)

Figure 10 (Hookup for Voltage Measurements)

12.Switch meter to measure voltage.13.Record initial voltage. VR= _______________________NOTE: A balanced bridge should have a zero voltage as VR. Why does your bridge not

measure zero?

14.Press down on the middle of the diaphragm.15.Record the voltage for three different pressures, increasing the pressure before eachrecording.

a. V1 = __________________b. V2 = __________________c. V3 = __________________

16.How did the applied pressure affect the voltage across the bridge?


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_________________________________________________________________

The following steps allows you to further explore this device and the effects that pressure has on

the resistance and voltage of a Wheatstone bridge sensing circuit.

17.Using the ice pick or nail, punch a hole in the side of the paint can. The hole should bebig enough to insert the TT tip of a syringe.

18.Pull an empty syringe to about 1.5 ml of air.19.Place the tip of the syringe in the hole. Make it snug and as airtight as possible.20.You can now simulate increases in pressure (pushing on the syringe) and decreases in

pressure (pulling on the syringe).

21.Test your pressure sensor model using various changes in pressure.22.This model could also be used to show how a MEMS pressure sensor is affected by

temperature. Find ways to increase or decrease the ambient temperature or the

temperature of the air trapped inside the can. Study the effects on the circuits output.


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Post-Activity Questions

1. In the above procedure, what factors could have an effect on the outcome (the resistivityof the bridge circuit)?

2. What is meant by the reference voltage or reference resistance of the Wheatstonebridge? Does this stay consistent? Why or why not?

3. What determines the reference voltage / resistance?

4. What causes a change in resistance or voltage?

5. Describe three (3) MEMS that use a diaphragm pressure sensor.

6. How could this pressure sensor model be improved upon?

Summary

A common MEMS pressure sensor uses a Wheatstone bridge sensing circuit on a flexible

diaphragm. A change in pressure creates a deflection of the diaphragm. This deflection causes

the variable resistors of the bridge to expand, increasing circuit resistance indicating a change inpressure. The amount of change in resistance is proportional to the change in pressure fromreference pressure to applied pressure.


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Related SCME Units

Wheatstone Bridge Overview unit Wheatstone Bridge Derivation Activity MTTC Pressure Sensor Learning Module

If using a one-quart paint can, this template should

print out to approximately 3 3/8" (8.57 cm) in diameterand can be used as a template to trace out the

piezoresistive Wheatstone bridge structure.

Disclaimer

The information contained herein is considered to be true and accurate; however the Southwest

Center for Microsystems Education (SCME) makes no guarantees concerning the authenticity ofany statement. SCME accepts no liability for the content of this unit, or for the consequences ofany actions taken on the basis of the information provided.

Support for this work was provided by the National Science Foundation's Advanced

Technological Education (ATE) Program through Grants #0830384 and 0902411.


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Wheatstone Bridge Derivation ActivityShareable Content Object (SCO)

This SCO is part of the Learning Module




(ATE) Program through Grants #0830384 and 0902411.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authorsand creators, and do not necessarily reflect the views of the National Science Foundation.


and

The Regents of the University of New Mexico


800 Bradbury Drive SE, Ste. 235Albuquerque, NM 87106-4346

Phone: 505-272-7150Website: www.scme-nm.org email contact: [email protected]


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Southwest Center for Microsystems Education (SCME) Page 2 of 6

Int_WheatB_AC01_PG_061411 WB Derivation Activity

Wheatstone Bridge Derivation Activity

Participant Guide

Description and Estimated Time to Complete

This activity will involve using your knowledge of the Wheatstone bridge to derive the relationshipbetween Vin (Input Voltage) and Vg (Gauge Voltage) for a given circuit. You will also design a

Wheatstone bridge layout to get the maximum effect on the gauge voltage, Vg .It is recommended that you review the unit Wheatstone Bridge Overview if you haven't already. Itwill enhance your understanding of the Wheatstone bridge circuitry as you complete this activity.

Estimated Time to Complete

Allow approximately two hours to complete this activity.

Introduction

The Wheatstone bridge is one of the most sensitive and precise methods of measuring smallchanges in resistance. This is possible through its use of transducers (devices which change one

form of energy into another, such as mechanical to electrical or electrical to mechanical). TheWheatstone bridge incorporates one or more electrical transducers that change resistance as a resultof an environmental change or input (e.g. temperature, pressure, stress). This change is sensed by

the circuitry of the Wheatstone bridge which provides a useable electrical output (voltage)representative of the input. The Wheatstone bridge is widely used today in macro-sized and micro-

sized sensors.

Basic Wheatstone Bridge Configuration


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Activity Objectives

Objectives

Derive the mathematical relationship between output voltage (Vg, also referred to as gaugevoltage) and resistance in a Wheatstone bridge circuit.

Design the orientation of the resistors on a pressure sensor membrane to maximize theeffect on the gauge voltage.

Procedure I: Derivation Activity

1. Using basic laws of electronics (e.g. Ohm's and Kirchhoff's), derive the mathematicalrelationship between input voltage, Vin, vs. gauge voltage, Vg in terms of input voltage, Vinand resistance for the circuit given below.

Vg=Vin {f(R1,R2,R3,R4)}Hint: Starting point would be Vg = VDVB.

2. Using your results from 1), above, show that the Wheatstone bridge is balanced whenR3/R4 = R1/R2.

a. What values of R1, R2, R3, and R4 would yield a balanced bridge circuit?b. Verify your mathematical derivation using these values of resistors.c. Did your derivation yield a Vg = 0 V? If not, then find and correct the problem and

repeat 2b.

3. Given a Wheatstone bridge with the following Vin and R values, what is Vg? ________ Vin = 10 volts R1 = 75 R2 = 100 R3 = 100 R4= 75

4. If R2 and R3 are both variable resistors (transducer elements) and continue to increase above100 , what effect would it have on Vg?


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Procedure II: Design a Wheatstone Bridge for a Pressure Sensor

In the case of a pressure sensor, all resistances are designed with the same geometries, therefore, allthe resistors have the same resistance values and the circuit is initially balanced and Vg (gauge

voltage) is zero.

Variable resisters in the bridge change due to stress on the resistor's material. This is due to thefact that resistance is a function of the resistor's material (resistivity or), length (L) and cross

sectional area (A):

R= (L/A)When metal is stressed, it stretches (for instance, a gold resistor on a pressure sensor membrane).

The length,L, increases, which results in an increase in resistance,R. The cross-sectional area,A,decreases; however, does not change as it is a property of the material.

In a pressure sensor, the Wheatstone bridge can be fabricated so that two of the four resistors are

effectively stressed when the membrane is stretched. The stress on the other two resistors is

ineffective or negligible. Such fabrication will result in a response from the Wheatstone bridgethat is sensitive to small changes in pressure. All four resistors on fabricated on the membrane.Why? Because there is also a temperature dependence of resistance and you want all of theresistors exposed to the exact same temperature environment. All four resistors should be of the

same length, width and thickness so they are balanced under no stress. Most pressure sensorsystems have an offset circuit to make up for slight variations in the fabrication process.

Questions

1. For maximum effect on the gauge voltage, Vg, which two resistors in the schematic (left)could be variable and which two resistors could be fixed?

2.

Using the image to on the right, how would you orient the resistors (narrow gray lines) on amembrane (green in the right image)?a. On the schematic, indicate the variable resistors with an arrow.b. On the pressure sensor diagram, label the four resistors on the diaphgragm and the

electrical nodes (A, B, C, and D), indicating Vin and Vg connections.


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Post-Activity Questions

Here is an example of a pressure sensor Wheatstone bridge in a circular configuration. This is thecircuit you will build if you complete the "Pressure Sensor Model Activity. This bridge is created

by stretching a balloon membrane across an open can and applying a graphite circuit to themembrane. Note, resistors R2 and R3 are configured parallel to the edge of the can, and hence, will

not stretch as the membrane expands. R1 and R4 resistors are configured over the open part of themembrane or can, parallel to the radius, and will be subject to the highest tension (stretching) and

experiencing the greatest piezoresistive effect.

1. Based on the schematic given above, write the equation for Vab in terms of resistance and Vin.

2. Sketch a graph that shows the relationship between Vab and Variable Resistance (Rv).

3. How would the graph change if R2 and R3 were variable and R1 and R4 were fixed? (Justifyyour answer with formulas and/or a graph.)


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Disclaimer

The information contained herein is considered to be true and accurate; however the Southwest

Center for Microsystems Education (SCME) makes no guarantees concerning the authenticity ofany statement. SCME accepts no liability for the content of this unit, or for the consequences ofany actions taken on the basis of the information provided.

Support for this work was provided by the National Science Foundation's Advanced Technological

Education (ATE) Program.


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Learning Modules available for download @ scme-nm.org

MEMS Introductory Topics

MEMS History

MEMS: Making Micro Machines DVD and LM (Kit

available)

Units of Weights and Measures

A Comparison of Scale: Macro, Micro, and Nano

Introduction to Transducers, Sensors and Actuators

Wheatstone Bridge (Pressure Sensor Model Kitavailable)

MEMS Applications

MEMS Applications Overview

Microcantilevers (Dynamic Cantilever Kit available)

Micropumps Overview

BioMEMS

BioMEMS Overview

BioMEMS Applications Overview

DNA Overview

DNA to Protein Overview

CellsThe Building Blocks of Life

Biomolecular Applications for bioMEMS

BioMEMS Therapeutics OverviewBioMEMS Diagnostics Overview

Clinical Laboratory Techniques and MEMS

MEMS for Environmental and BioterrorismApplications

Regulations of bioMEMS

DNA Microarrays (GeneChip

Model Kit available)

MEMS Fabrication

Crystallography for Microsystems (Breaking Wafers

and Origami Crystal Kits available)

Oxidation Overview for Microsystems (RainbowWafer Kit available)

Deposition Overview Microsystems

Photolithography Overview for Microsystems

Etch Overview for Microsystems (Rainbow Waferand Anisotropic Etch Kits available)

MEMS Micromachining Overview

LIGA Micromachining Simulation Activities (LIGASimulation Kit available)

Manufacturing Technology Training Center PressureSensor Process (Three Activity Kits available)

MEMS Innovators Activity (Activity Kit available)

Safety

Hazardous Materials

Material Safety Data Sheets

Interpreting Chemical Labels / NFPA

Chemical Lab Safety

Personal Protective Equipment (PPE)

Check our website regularl y for the most recent

versions of our Learning Modules.

For more information about SCMEand its Learning Modules and kits,

visit our website

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Wheatstone Bridge Participant Guide

Documents

Transcript of Wheatstone Bridge Participant Guide